🔭Data Science: Procedures (Just the Quotes)

"Science is simply setting out on a fishing expedition to see whether it cannot find some procedure which it can call measurement of space and some procedure which it can call the measurement of time, and something which it can call a system of forces, and something which it can call masses." (Alfred N Whitehead, "The Concept of Nature", 1920)

"The futile elaboration of innumerable measures of correlation, and the evasion of the real difficulties of sampling problems under cover of a contempt for small samples, were obviously beginning to make its pretensions ridiculous. These procedures were not only ill-aimed, but for all their elaboration, not sufficiently accurate." (Sir Ronald A Fisher,"Statistical Methods for Research Workers", 1925)

"Statistics is a scientific discipline concerned with collection, analysis, and interpretation of data obtained from observation or experiment. The subject has a coherent structure based on the theory of Probability and includes many different procedures which contribute to research and development throughout the whole of Science and Technology." (Egon Pearson, 1936)

"Precision is expressed by an international standard, viz., the standard error. It measures the average of the difference between a complete coverage and a long series of estimates formed from samples drawn from this complete coverage by a particular procedure or drawing, and processed by a particular estimating formula." (W Edwards Deming, "On the Presentation of the Results of Sample Surveys as Legal Evidence", Journal of the American Statistical Association Vol 49" (268), 1954)

"The first step in data analysis is often an omnibus step. We dare not expect otherwise, but we equally dare not forget that this step, and that step, and other step, are all omnibus steps and that we owe the users of such techniques a deep and important obligation to develop ways, often varied and competitive, of replacing omnibus procedures by ones that are more sharply focused." (John W Tukey, "The Future of Processes of Data Analysis", 1965)

"[...] the test of significance has been carrying too much of the burden of scientific inference. It may well be the case that wise and ingenious investigators can find their way to reasonable conclusions from data because and in spite of their procedures. Too often, however, even wise and ingenious investigators [...] tend to credit the test of significance with properties it does not have." (David Bakan ,"The test of significance in psychological research", Psychological Bulletin 66, 1966) 

"Design problems - generating or discovering alternatives - are complex largely because they involve two spaces, an action space and a state space, that generally have completely different structures. To find a design requires mapping the former of these on the latter. For many, if not most, design problems in the real world systematic algorithms are not known that guarantee solutions with reasonable amounts of computing effort. Design uses a wide range of heuristic devices - like means-end analysis, satisficing, and the other procedures that have been outlined - that have been found by experience to enhance the efficiency of search. Much remains to be learned about the nature and effectiveness of these devices." (Herbert A Simon, "The Logic of Heuristic Decision Making", [inThe Logic of Decision and Action"], 1966)

"Quantitative techniques will be more likely to illuminate if the data analyst is guided in methodological choices by a substantive understanding of the problem he or she is trying to learn about. Good procedures in data analysis involve techniques that help to" (a) answer the substantive questions at hand," (b) squeeze all the relevant information out of the data, and" (c) learn something new about the world." (Edward R Tufte, "Data Analysis for Politics and Policy", 1974)

"The matching procedure often helps inform the reader what is going on in the data […] Matching has some defects, chiefly that it is difficult to do a very good job of matching in complex situations without a large number of cases. […] One limitation of matching, then, is that quite often the match is not very accurate. A second limitation is that if we want to control for more than one variable using matching procedures, the tables begin to have combinations of categories without any cases at all in them, and they become somewhat more difficult for the reader to understand." (Edward R Tufte ,"Data Analysis for Politics and Policy", 1974)

"The use of statistical methods to analyze data does not make a study any more 'scientific', 'rigorous', or 'objective'. The purpose of quantitative analysis is not to sanctify a set of findings. Unfortunately, some studies, in the words of one critic, 'use statistics as a drunk uses a street lamp, for support rather than illumination'. Quantitative techniques will be more likely to illuminate if the data analyst is guided in methodological choices by a substantive understanding of the problem he or she is trying to learn about. Good procedures in data analysis involve techniques that help to" (a) answer the substantive questions at hand," (b) squeeze all the relevant information out of the data, and" (c) learn something new about the world." (Edward R Tufte, "Data Analysis for Politics and Policy", 1974)

"When the statistician looks at the outside world, he cannot, for example, rely on finding errors that are independently and identically distributed in approximately normal distributions. In particular, most economic and business data are collected serially and can be expected, therefore, to be heavily serially dependent. So is much of the data collected from the automatic instruments which are becoming so common in laboratories these days. Analysis of such data, using procedures such as standard regression analysis which assume independence, can lead to gross error. Furthermore, the possibility of contamination of the error distribution by outliers is always present and has recently received much attention. More generally, real data sets, especially if they are long, usually show inhomogeneity in the mean, the variance, or both, and it is not always possible to randomize." (George E P Box, "Some Problems of Statistics and Everyday Life", Journal of the American Statistical Association, Vol. 74" (365), 1979)

"Symmetry is also important because it can simplify our thinking about the distribution of a set of data. If we can establish that the data are (approximately) symmetric, then we no longer need to describe the  shapes of both the right and left halves. (We might even combine the information from the two sides and have effectively twice as much data for viewing the distributional shape.) Finally, symmetry is important because many statistical procedures are designed for, and work best on, symmetric data." (John M Chambers et al, "Graphical Methods for Data Analysis", 1983)

"Theoretical scientists, inching away from the safe and known, skirting the point of no return, confront nature with a free invention of the intellect. They strip the discovery down and wire it into place in the form of mathematical models or other abstractions that define the perceived relation exactly. The now-naked idea is scrutinized with as much coldness and outward lack of pity as the naturally warm human heart can muster. They try to put it to use, devising experiments or field observations to test its claims. By the rules of scientific procedure it is then either discarded or temporarily sustained. Either way, the central theory encompassing it grows. If the abstractions survive they generate new knowledge from which further exploratory trips of the mind can be planned. Through the repeated alternation between flights of the imagination and the accretion of hard data, a mutual agreement on the workings of the world is written, in the form of natural law." (Edward O Wilson, “Biophilia”, 1984)

"Scientific laws give algorithms, or procedures, for determining how systems behave. The computer program is a medium in which the algorithms can be expressed and applied. Physical objects and mathematical structures can be represented as numbers and symbols in a computer, and a program can be written to manipulate them according to the algorithms. When the computer program is executed, it causes the numbers and symbols to be modified in the way specified by the scientific laws. It thereby allows the consequences of the laws to be deduced." (Stephen Wolfram, "Computer Software in Science and Mathematics", 1984)

"Models are often used to decide issues in situations marked by uncertainty. However statistical differences from data depend on assumptions about the process which generated these data. If the assumptions do not hold, the inferences may not be reliable either. This limitation is often ignored by applied workers who fail to identify crucial assumptions or subject them to any kind of empirical testing. In such circumstances, using statistical procedures may only compound the uncertainty." (David A Greedman & William C Navidi," Regression Models for Adjusting the 1980 Census", Statistical Science Vol. 1" (1), 1986)

"Axiomatic theories of choice introduce preference as a primitive relation, which is interpreted through specific empirical procedures such as choice or pricing. Models of rational choice assume a principle of procedure invariance, which requires strategically equivalent methods of elicitation to yield the same preference order." (Amos Tversky et al, "The Causes of Preference Reversal", The American Economic Review Vol. 80" (1), 1990)

"Management is not founded on observation and experiment, but on a drive towards a set of outcomes. These aims are not altogether explicit; at one extreme they may amount to no more than an intention to preserve the status quo, at the other extreme they may embody an obsessional demand for power, profit or prestige. But the scientist's quest for insight, for understanding, for wanting to know what makes the system tick, rarely figures in the manager's motivation. Secondly, and therefore, management is not, even in intention, separable from its own intentions and desires: its policies express them. Thirdly, management is not normally aware of the conventional nature of its intellectual processes and control procedures. It is accustomed to confuse its conventions for recording information with truths-about-the-business, its subjective institutional languages for discussing the business with an objective language of fact and its models of reality with reality itself." (Stanford Beer, "Decision and Control", 1994)

"Theories of choice are at best approximate and incomplete. One reason for this pessimistic assessment is that choice is a constructive and contingent process. When faced with a complex problem, people employ a variety of heuristic procedures in order to simplify the representation and the evaluation of prospects. These procedures include computational shortcuts and editing operations, such as eliminating common components and discarding nonessential differences. The heuristics of choice do not readily lend themselves to formal analysis because their application depends on the formulation of the problem, the method of elicitation, and the context of choice." (Amos Tversky & Daniel Kahneman,Advances in Prospect Theory: Cumulative Representation of Uncertainty" [inChoices, Values, and Frames"], 2000)

"The important thing is to understand that frequentist and Bayesian methods are answering different questions. To combine prior beliefs with data in a principled way, use Bayesian inference. To construct procedures with guaranteed long run performance, such as confidence intervals, use frequentist methods. Generally, Bayesian methods run into problems when the parameter space is high dimensional." (Larry A Wasserman, "All of Statistics: A concise course in statistical inference", 2004)

"Two things explain the importance of the normal distribution:" (1) The central limit effect that produces a tendency for real error distributions to be 'normal like'." (2) The robustness to nonnormality of some common statistical procedures, where 'robustness' means insensitivity to deviations from theoretical normality." (George E P Box et al, "Statistics for Experimenters: Design, discovery, and innovation" 2nd Ed., 2005)

"Put simply, statistics is a range of procedures for gathering, organizing, analyzing and presenting quantitative data. […] Essentially […], statistics is a scientific approach to analyzing numerical data in order to enable us to maximize our interpretation, understanding and use. This means that statistics helps us turn data into information; that is, data that have been interpreted, understood and are useful to the recipient. Put formally, for your project, statistics is the systematic collection and analysis of numerical data, in order to investigate or discover relationships among phenomena so as to explain, predict and control their occurrence." (Reva B Brown & Mark Saunders, "Dealing with Statistics: What You Need to Know", 2008)

"A priori, it is clear that no method will always be the best [...]. However, it is reasonable to argue that each method will have a set of functions, a type of data, and a range of sample sizes for which it is optimal – a sort of catchment region for each procedure. Ideally, one could partition a space of regression problems into catchment regions, depending on which methods were under consideration, and determine which catchment region seemed most appropriate for each method. This ideal solution would amount to a selection principle for nonparametric methods. Unfortunately, it is unclear how to do this, not least because the catchment regions are unknown." (Bertrand Clarke et al, "Principles and Theory for Data Mining and Machine Learning", 2009)

"An algorithm refers to a successive and finite procedure by which it is possible to solve a certain problem. Algorithms are the operational base for most computer programs. They consist of a series of instructions that, thanks to programmers’ prior knowledge about the essential characteristics of a problem that must be solved, allow a step-by-step path to the solution." (Diego Rasskin-Gutman,"Chess Metaphors: Artificial Intelligence and the Human Mind", 2009)

"Cybernetics is the art of creating equilibrium in a world of possibilities and constraints. This is not just a romantic description, it portrays the new way of thinking quite accurately. Cybernetics differs from the traditional scientific procedure, because it does not try to explain phenomena by searching for their causes, but rather by specifying the constraints that determine the direction of their development." (Ernst von Glasersfeld, "Partial Memories: Sketches from an Improbable Life", 2010)

"Scientists pursue ideas in an ill-defined but effective way that is often called the scientific method. There is no strict rule of procedure that will lead you from a good idea to a Nobel prize or even to a publishable discovery. Some scientists are meticulously careful; others are highly creative. The best scientists are probably both careful and creative. Although there are various scientific methods in use, a typical approach consists of a series of steps." (Peter Atkins et al,"Chemical Principles: The Quest for Insight" 6th ed., 2013)

"A wide variety of statistical procedures" (regression, t-tests, ANOVA) require three assumptions:" (i) Normal observations or errors." (ii) Independent observations" (or independent errors, which is equivalent, in normal linear models to independent observations)." (iii) Equal variance - when that is appropriate" (for the one-sample t-test, for example, there is nothing being compared, so equal variances do not apply)." (DeWayne R Derryberry, "Basic data analysis for time series with R", 2014)

"When data is not normal, the reason the formulas are working is usually the central limit theorem. For large sample sizes, the formulas are producing parameter estimates that are approximately normal even when the data is not itself normal. The central limit theorem does make some assumptions and one is that the mean and variance of the population exist. Outliers in the data are evidence that these assumptions may not be true. Persistent outliers in the data, ones that are not errors and cannot be otherwise explained, suggest that the usual procedures based on the central limit theorem are not applicable." (DeWayne R Derryberry, "Basic data analysis for time series with R", 2014)

"Overlapping confidence intervals do not mean two values are not significantly different. Checking confidence intervals or standard errors will mislead. It’s always best to use the appropriate hypothesis test instead. Your eyeball is not a well-defined statistical procedure." (Alex Reinhart, "Statistics Done Wrong: The Woefully Complete Guide", 2015)

"The closer that sample-selection procedures approach the gold standard of random selection - for which the definition is that every individual in the population has an equal chance of appearing in the sample - the more we should trust them. If we don’t know whether a sample is random, any statistical measure we conduct may be biased in some unknown way." (Richard E Nisbett, "Mindware: Tools for Smart Thinking", 2015)

"There is exactly one situation when visually checking confidence intervals works, and it is when comparing the confidence interval against a fixed value, rather than another confidence interval. If you want to know whether a number is plausibly zero, you may check to see whether its confidence interval overlaps with zero. There are, of course, formal statistical procedures that generate confidence intervals that can be compared by eye and that even correct for multiple comparisons automatically. Unfortunately, these procedures work only in certain circumstances;" (Alex Reinhart, "Statistics Done Wrong: The Woefully Complete Guide", 2015)

"Many researchers have fallen into the trap of assuming percentiles are interval data and using them in Statistical procedures that require interval data. The results are somewhat distorted under these conditions since the scores are actually only ordinal data." (Martin L Abbott, "Using Statistics in the Social and Health Sciences with SPSS and Excel", 2016)

"Often when people relate essentially the same variable in two different groups, or at two different times, they see this same phenomenon - the tendency of the response variable to be closer to the mean than the predicted value. Unfortunately, people try to interpret this by thinking that the performance of those far from the mean is deteriorating, but it’s just a mathematical fact about the correlation. So, today we try to be less judgmental about this phenomenon and we call it regression to the mean. We managed to get rid of the term 'mediocrity', but the name regression stuck as a name for the whole least squares fitting procedure - and that’s where we get the term regression line." (Richard D De Veaux et al,"Stats: Data and Models", 2016)

"When memorization happens, you may have the illusion that everything is working well because your machine learning algorithm seems to have fitted the in sample data so well. Instead, problems can quickly become evident when you start having it work with out-of-sample data and you notice that it produces errors in its predictions as well as errors that actually change a lot when you relearn from the same data with a slightly different approach. Overfitting occurs when your algorithm has learned too much from your data, up to the point of mapping curve shapes and rules that do not exist [...]. Any slight change in the procedure or in the training data produces erratic predictions." (John P Mueller & Luca Massaron, "Machine Learning for Dummies", 2016)

"Good estimators are those that usually yield estimates close to the truth, with minimal variation. Therefore, we typically summarize a sampling distribution using its standard deviation, which we refer to as the standard error. In quoting the standard error of an estimator’s sampling distribution, you are saying: 'If I were to take repeated samples from the population and use this estimator for every sample, my estimate is typically off from the truth by about this much. 'Notice again that this is a claim about a procedure, not a particular estimate. The bigger the standard error, the less stable the estimator across different samples, and the less you can trust the estimate for any particular sample." (James G Scott, "Statistical Modeling: A Gentle Introduction", 2017)

"Measurements must be standardized. There must be clear, replicable, and precise procedures for collecting data so that each person who collects it does it in the same way." (Daniel J Levitin, "Weaponized Lies", 2017)

"Samples give us estimates of something, and they will almost always deviate from the true number by some amount, large or small, and that is the margin of error. […] The margin of error does not address underlying flaws in the research, only the degree of error in the sampling procedure. But ignoring those deeper possible flaws for the moment, there is another measurement or statistic that accompanies any rigorously defined sample: the confidence interval." (Daniel J Levitin, "Weaponized Lies", 2017)

"A neural-network algorithm is simply a statistical procedure for classifying inputs" (such as numbers, words, pixels, or sound waves) so that these data can mapped into outputs. The process of training a neural-network model is advertised as machine learning, suggesting that neural networks function like the human mind, but neural networks estimate coefficients like other data-mining algorithms, by finding the values for which the model’s predictions are closest to the observed values, with no consideration of what is being modeled or whether the coefficients are sensible." (Gary Smith & Jay Cordes, "The 9 Pitfalls of Data Science", 2019)

"Many statistical procedures perform more effectively on data that are normally distributed, or at least are symmetric and not excessively kurtotic" (fat-tailed), and where the mean and variance are approximately constant. Observed time series frequently require some form of transformation before they exhibit these distributional properties, for in their 'raw' form they are often asymmetric." (Terence C Mills, "Applied Time Series Analysis: A practical guide to modeling and forecasting", 2019)

"There are many ways for error to creep into facts and figures that seem entirely straightforward. Quantities can be miscounted. Small samples can fail to accurately reflect the properties of the whole population. Procedures used to infer quantities from other information can be faulty. And then, of course, numbers can be total bullshit, fabricated out of whole cloth in an effort to confer credibility on an otherwise flimsy argument. We need to keep all of these things in mind when we look at quantitative claims. They say the data never lie - but we need to remember that the data often mislead." (Carl T Bergstrom & Jevin D West, "Calling Bullshit: The Art of Skepticism in a Data-Driven World", 2020)

"In statistical inference and machine learning, we often talk about estimates and estimators. Estimates are basically our best guesses regarding some quantities of interest given" (finite) data. Estimators are computational devices or procedures that allow us to map between a given" (finite) data sample and an estimate of interest." (Aleksander Molak, "Causal Inference and Discovery in Python", 2023)

"Multiple regression provides scientists and analysts with a tool to perform statistical control - a procedure to remove unwanted influence from certain variables in the model." (Aleksander Molak, "Causal Inference and Discovery in Python", 2023)

🔭Data Science: Expertize (Just the Quotes)

"An old jest runs to the effect that there are three degrees of comparison among liars. There are liars, there are outrageous liars, and there are scientific experts. This has lately been adapted to throw dirt upon statistics. There are three degrees of comparison, it is said, in lying. There are lies, there are outrageous lies, and there are statistics." (Robert Giffen, "Economic Journal 2 (6), 1892)

"Prediction about the future assumes that the statistical model will continue to fit future data. There are several reasons this is often implausible, but it also seems clear that the model will often degenerate slowly in quality, so that the model will fit data only a few periods in the future almost as well as the data used to fit the model. To some degree, the reliability of extrapolation into the future involves subject-matter expertise." (DeWayne R Derryberry, "Basic data analysis for time series with R", 2014

"In the field of design, experts speak of objects having 'affordances'. These are aspects inherent to the design that make it obvious how the product is to be used. For example, a knob affords turning, a button affords pushing, and a cord affords pulling. These characteristics suggest how the object is to be interacted with or operated. When sufficient affordances are present, good design fades into the background and you don’t even notice it." (Cole N Knaflic, "Storytelling with Data: A Data Visualization Guide for Business Professionals", 2015)

"Will you be encountering each other for the first time through this communication, or do you have an established relationship? Do they already trust you as an expert, or do you need to work to establish credibility? These are important considerations when it comes to determining how to structure your communication and whether and when to use data, and may impact the order and flow of the overall story you aim to tell." (Cole N Knaflic, "Storytelling with Data: A Data Visualization Guide for Business Professionals", 2015)

"We are a storytelling species, and a social species, easily swayed by the opinions of others. We have three ways to acquire information: We can discover it ourselves, we can absorb it implicitly, or we can be told it explicitly. Much of what we know about the world falls in this last category - somewhere along the line, someone told us a fact or we read about it, and so we know it only second-hand. We rely on people with expertise to tell us." (Daniel J Levitin, "Weaponized Lies", 2017)

"Data scientists should have some domain expertise. Most data science projects begin with a real-world, domain-specific problem and the need to design a data-driven solution to this problem. As a result, it is important for a data scientist to have enough domain expertise that they understand the problem, why it is important, an dhow a data science solution to the problem might fit into an organization’s processes. This domain expertise guides the data scientist as she works toward identifying an optimized solution." (John D Kelleher & Brendan Tierney, "Data Science", 2018)

"Every dataset has subtleties; it can be far too easy to slip down rabbit holes of complications. Being systematic about the operationalization can help focus our conversations with experts, only introducing complications when needed." (Danyel Fisher & Miriah Meyer, "Making Data Visual", 2018)

"One of the biggest myths is the belief that data science is an autonomous process that we can let loose on our data to find the answers to our problems. In reality, data science requires skilled human oversight throughout the different stages of the process. [...] The second big myth of data science is that every data science project needs big data and needs to use deep learning. In general, having more data helps, but having the right data is the more important requirement. [...] A third data science myth is that modern data science software is easy to use, and so data science is easy to do. [...] The last myth about data science [...] is the belief that data science pays for itself quickly. The truth of this belief depends on the context of the organization. Adopting data science can require significant investment in terms of developing data infrastructure and hiring staff with data science expertise. Furthermore, data science will not give positive results on every project." (John D Kelleher & Brendan Tierney, "Data Science", 2018)

"You no longer need to have the words 'data' or 'analyst' in your job title to be immersed in numbers and be expected to use them on a regular basis. Data is now everyone’s responsibility. In fact, the Achilles’ heel of any analyst is a lack of context - something most business users have in spades. A sharp analyst can miss something in the data that is easily spotted by the seasoned eyes of a business user, who can draw on years of domain expertise. Data doesn’t care who you are or what your analytical skill level is - it’s willing to yield up insights to whoever is diligent and curious enough to find them. Greater data access means valuable insights can be discovered by people of all backgrounds - not just technical ones." (Brent Dykes, "Effective Data Storytelling: How to Drive Change with Data, Narrative and Visuals", 2019)

"I believe that the backlash against statistics is due to four primary reasons. The first, and easiest for most people to relate to, is that even the most basic concepts of descriptive and inferential statistics can be difficult to grasp and even harder to explain. […] The second cause for vitriol is that even well-intentioned experts misapply the tools and techniques of statistics far too often, myself included. Statistical pitfalls are numerous and tough to avoid. When we can't trust the experts to get it right, there's a temptation to throw the baby out with the bathwater. The third reason behind all the hate is that those with an agenda can easily craft statistics to lie when they communicate with us  […] And finally, the fourth cause is that often statistics can be perceived as cold and detached, and they can fail to communicate the human element of an issue." (Ben Jones, "Avoiding Data Pitfalls: How to Steer Clear of Common Blunders When Working with Data and Presenting Analysis and Visualizations", 2020) 

"The myth of replacing domain experts comes from people putting too much faith in the power of ML to find patterns in the data. [...] ML looks for patterns that are generally pretty crude - the power comes from the sheer scale at which they can operate. If the important patterns in the data are not sufficiently crude then ML will not be able to ferret them out. The most powerful classes of models, like deep learning, can sometimes learn good-enough proxies for the real patterns, but that requires more training data than is usually available and yields complicated models that are hard to understand and impossible to debug. It’s much easier to just ask somebody who knows the domain!" (Field Cady, "Data Science: The Executive Summary: A Technical Book for Non-Technical Professionals", 2021)

🔭Data Science: Bootstrapping (Just the Quotes)

"If there was ever an idea in statistics which evokes the reaction, 'Why the hell didn’t I think of that', it has to be the bootstrap." (James R Thompson, [Interface Proceedings] 1997)

"This computationally intensive operation [bootstrapping] is not one calculated to endear a user to a database administrator." (Leland Wilkinson, "The Grammar of Graphics", 1999)

"The estimate of the standard error (SE) is more sensitive to the Normality assumption than the estimate of the coefficients. There are two options available which do not require this assumption; these are the bootstrap and the robust standard error." (Michael J Campbell, "Statistics at Square Two: Understanding modern statistical applications in medicine" 2nd Ed., 2006)

"Not all data sets lend themselves to data splitting. The data set may be too small to split and/or the fitted model may be a local smoother. In the first case, there is too little data upon which to build a model if the data is split; and in the second case, it is not expected the model for any part of the data to directly interpolate/extrapolate to any other part of the model. For these cases, a different approach to cross-validation is possible, something similar to bootstrapping." (DeWayne R Derryberry, "Basic Data Analysis for Time Series with R" 1st Ed, 2014)

"An obvious question is: do bootstrapped confidence intervals satisfy the frequentist coverage property? If your sample is fairly representative of the population, then the answer is a qualified yes. That is, the bootstrapping procedure yields nominal X% intervals that cover the true value 'approximately' X% of the time. Moreover, as the size of the original sample gets bigger, the quality of the approximation gets better. Alas, it is necessary to appeal to some very advanced probability theory to put both of these claims on firm footing." (James G Scott, "Statistical Modeling: A Gentle Introduction", 2017)

"At the core of the resampling approach to statistical inference lies a simple idea. Most of the time, we can’t feasibly take repeated samples of size n from the population, to see how our estimate changes from one sample to the next. But we can repeatedly take samples of size n from the sample itself, and apply our estimator afresh to each notional sample. The idea is that the variability of the estimates across all these samples can be used to approximate our estimator’s true sampling distribution. This process—pretending that our sample is the whole population, and taking repeated samples of size n with replacement from our original sample of size n - is called bootstrap resampling, or just bootstrapping" (James G Scott, "Statistical Modeling: A Gentle Introduction", 2017)

"Resampling won’t yield the true sampling distribution of an estimator, but it is often good enough for approximating the standard error (which you’ll remember is just the standard deviation of the sampling distribution). We use the term bootstrapped standard error for the standard deviation of the bootstrapped sampling distribution. The bootstrapped standard error is an estimate of the true standard error." (James G Scott, "Statistical Modeling: A Gentle Introduction", 2017)

"Bootstrapping provides an intuitive, computer-intensive way of assessing the uncertainty in our estimates, without making strong assumptions and without using probability theory. But the technique is not feasible when it comes to, say, working out the margins of error on unemployment surveys of 100,000 people. Although bootstrapping is a simple, brilliant and extraordinarily effective idea, it is just too clumsy to bootstrap such large quantities of data, especially when a convenient theory exists that can generate formulae for the width of uncertainty intervals." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)

"But [bootstrap-based] simulations are clumsy and time-consuming, especially with large data sets, and in more complex circumstances it is not straightforward to work out what should be simulated. In contrast, formulae derived from probability theory provide both insight and convenience, and always lead to the same answer since they don’t depend on a particular simulation. But the flip side is that this theory relies on assumptions, and we should be careful not to be deluded by the impressive algebra into accepting unjustified conclusions." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)

"What recourse do we have if our groups do not have homogeneous variances? If we stick to parametric statistics, when we use a t-test, there is a correction that is performed for groups whose variances are not the same. If we use an ANOVA there is no such correction, but we could choose not to compare groups that have non-homogeneous variances or combine certain groups to achieve a better effect. Again, the main effect of not having homogeneous variances is that, although group differences may actually exist, we might not be able to find them. Thus, if you perform a statistical test and find that the group differences you thought would be there are not found, you might consider that this result is due to non-homogeneous variances.Another possibility to avoid problems with non-homogeneous groups is to use robust statistical procedures, such as bootstrapping and means trimming. These robust methods deal with problems due to both violations of normal distributions and homogeneity of variances in a manner that is objective and more robust to violations than parametric statistics." (Jenifer Larson-Hall, "A Guide to Doing Statistics in Second Language Research Using SPSS and R" 2nd Ed., 2016)

🖍️Hayden Van Der Post - Collected Quotes

"A critical aspect of neural networks is their ability to learn from data. This learning occurs during the training phase, where the network is exposed to vast datasets, allowing it to adjust its internal parameters - the weights and biases associated with each neuron. The goal of this adjustment is to minimize the difference between the network's predictions and the actual outcomes, a process known as optimization. Through techniques such as gradient descent and backpropagation, neural networks iteratively refine their parameters, enhancing their ability to make accurate predictions or decisions based on new input."(Hayden Van Der Post, "Neural Network: Mastering the Art of Algorithmic Trading", 2024)

"Beyond the choice of model, the accuracy of neural network predictions in trading significantly depends on the quality and relevance of the data fed into them. This underscores the importance of meticulous data preparation, encompassing cleaning, normalization, and feature engineering. By ensuring that the input data is reflective of the market's complexities, traders can fine-tune their neural networks to produce more accurate and actionable predictions." (Hayden Van Der Post, "Neural Network: Mastering the Art of Algorithmic Trading", 2024)

"Deep learning algorithms are exceptionally adept at identifying anomalies within large datasets, making them an indispensable tool for detecting fraudulent transactions and financial irregularities. By learning from historical transaction data, these models can pinpoint patterns and behaviors indicative of fraudulent activities with remarkable accuracy. This ability not only aids in safeguarding assets but also ensures compliance with increasingly stringent regulatory standards aimed at preventing financial fraud and misconduct." (Hayden Van Der Post, "Neural Network: Mastering the Art of Algorithmic Trading", 2024)

"Deep learning is an advanced subset of machine learning, distinguished by its ability to process data through layers of neural networks, each layer abstracting information from the one preceding it. This hierarchical approach enables the model to handle complex, high-dimensional data, learning features and patterns at multiple levels of abstraction. [...] Traditional neural networks, with their shallower architectures, often struggle with the nuances of financial data, limited by their capacity to extrapolate and interpret intricate patterns. Deep learning, however, with its deeper, more sophisticated networks, can navigate these complexities, offering nuanced insights into market dynamics." (Hayden Van Der Post, "Neural Network: Mastering the Art of Algorithmic Trading", 2024)

"Feature selection is the first critical step in model optimization. It's the art of identifying which features in your dataset contribute most significantly to the outcome you're trying to predict. This not only helps in enhancing the model's accuracy but also in reducing computational complexity, leading to more efficient models. [...] While feature selection is about cherry-picking the most useful features, feature engineering is about creating new features that increase the predictive strength of the model. This is where creativity and domain knowledge come into play, especially in financial data, where market sentiment, economic indicators, and other external factors can influence market movements." (Hayden Van Der Post, "Neural Network: Mastering the Art of Algorithmic Trading", 2024)

"Genetic programming represents a frontier in feature engineering, allowing for the automated creation of new features through the application of evolutionary algorithms. By combining existing features in non-linear and complex ways, genetic programming can uncover hidden relationships in the data that were not apparent through manual exploration. This technique, while computationally intensive, holds the promise of discovering novel predictors that can enhance the performance of trading algorithms." (Hayden Van Der Post, "Neural Network: Mastering the Art of Algorithmic Trading", 2024)

"Neural networks are structured into layers, each comprising a collection of neurons. The arrangement begins with an input layer, which receives the raw data. This is followed by one or more hidden layers, where the actual processing happens through a complex web of interconnected neurons. The journey through the layers culminates in an output layer, where the network delivers its final decision or prediction. The hidden layers are the cradle of the network’s learning capability, enabling it to detect patterns, make associations, and refine its predictions through repeated exposure to data." (Hayden Van Der Post, "Neural Network: Mastering the Art of Algorithmic Trading", 2024)

"Predictive analytics, involves the use of data, statistical algorithms, and machine learning techniques to identify the likelihood of future outcomes based on historical data. Neural networks, with their remarkable ability to learn and model complex patterns, have become the backbone of modern forecasting methods. Their application ranges from predicting consumer behavior in retail to forecasting the stock market trends, from anticipating weather patterns to foreseeing potential healthcare outbreaks." (Hayden Van Der Post, "Neural Network: Mastering the Art of Algorithmic Trading", 2024)

"The beauty of neural networks lies in their ability to learn and improve. Through a process known as 'training', a neural network is fed large amounts of data along with feedback on its performance. This feedback guides the network in adjusting its internal parameters, known as weights, to minimize errors in its predictions. This iterative process of learning from mistakes closely mirrors the cognitive and learning processes of the human brain, making neural networks particularly adept at tasks that involve pattern recognition, such as image and speech recognition [...]" (Hayden Van Der Post, "Neural Network: Mastering the Art of Algorithmic Trading", 2024)

"The essence of backpropagation is captured in the gradient descent algorithm, which seeks to minimize the error by iteratively adjusting the weights in the direction that most steeply decreases the error function. This rigorous process requires a meticulous balance; too large a weight adjustment can lead to erratic learning, while too small an adjustment can trap the network in local minima. In algorithmic trading, the capacity to learn from past predictions and refine strategies accordingly is invaluable, allowing for the continual optimization of trading algorithms in alignment with market dynamics." (Hayden Van Der Post, "Neural Network: Mastering the Art of Algorithmic Trading", 2024)

"The power of neural networks lies in their flexibility and adaptability. They are not confined to a single type of problem or dataset but can be tailored to a wide range of applications, from voice recognition and image classification to forecasting financial market movements. This versatility stems from the network's ability to capture and model complex, non-linear relationships within the data it is trained on, making it a potent tool in the arsenal of data scientists and algorithmic traders alike." (Hayden Van Der Post, "Neural Network: Mastering the Art of Algorithmic Trading", 2024)

"Weights and biases are pivotal in shaping the neural network's decision-making process. Weights determine the strength of the connection between two neurons, influencing how much of the input signal is passed forward. Biases, added to the weighted sum before the activation function, allow neurons to adjust their output independently of their input, providing an additional degree of freedom. The process of learning in a neural network involves adjusting these weights and biases based on the error between the network's predictions and the actual data, typically using an algorithm like gradient descent." (Hayden Van Der Post, "Neural Network: Mastering the Art of Algorithmic Trading", 2024)

"While forward propagation provides the prediction, backpropagation is the mechanism through which a neural network learns from its errors and enhances its accuracy. Backpropagation, a form of reverse engineering of the forward propagation process, involves calculating the error between the predicted output and the actual output, and then distributing this error back through the network. This distribution occurs layer by layer, in reverse order from output to input, adjusting the weights of the connections based on the magnitude of the error." (Hayden Van Der Post, "Neural Network: Mastering the Art of Algorithmic Trading", 2024)

🤖Prompt Engineering: Challenges (Just the Quotes)

"Another problem that can be confusing is that LLMs seldom put out the same thing twice. [...] Traditional databases are straightforward - you ask for something specific, and you get back exactly what was stored. Search engines work similarly, finding existing information. LLMs work differently. They analyze massive amounts of text data to understand statistical patterns in language. The model processes information through multiple layers, each capturing different aspects - from simple word patterns to complex relationships between ideas." (Jeremy C Morgan, "Coding with AI: Examples in Python", 2025)

"Chain-of-thought prompting is a method that forces LLMs to reason through a series of steps, resulting in more structured, transparent, and precise outputs. The goal is to break down complex tasks into smaller, interconnected subtasks, allowing the LLM to address each subtask in a stepby-step manner. This not only helps the model to 'focus' on specific aspects of the problem, but also encourages it to generate intermediate outputs, making it easier to identify and debug potential issues along the way. Another significant advantage of chain-of-thought prompting is the improved interpretability and transparency of the LLM-generated response. By offering insights into the model’s reasoning process, we, as users, can better understand and qualify how the final output was derived, which promotes trust in the model’s decision-making abilities." (Sinan Ozdemir, "Quick Start Guide to Large Language Models: Strategies and Best Practices for Using ChatGPT and Other LLMs", 2024) 

"AI isn’t just going to be about our digital world. It’s also about our physical world; and applied properly, imagine what AI can do for the pace of discovery and innovation. It’s not just makeup; imagine what it can do for new materials discovery for medicine, energy, climate, and all the other pressing challenges we face as a species - these are the same challenges of makeup, just described with a different 'language'. And quantum computing evolves, we’re bound to see a synergy of these innovations that we can use to tackle these problem domains and more." (Rob Thomas et al, "AI Value Creators: Beyond the Generative AI User Mindset", 2025)

"LLMs can inadvertently produce toxic content or biased language, leak private information, or be vulnerable to jailbreak prompts. These risks carry serious legal and reputational consequences. To mitigate them, evaluation tools must integrate automated filters and classifiers that flag problematic outputs in real time, as we discussed earlier in the chapter. Metrics such as safety scores, toxicity indices, and bias measurements should be collected alongside model metadata for auditing purposes." (Abi Aryan, "LLMOps: Managing Large Language Models in Production", 2025)

"LLM developers can train the model simply to perform well on the benchmarks, like a student memorizing the answers to an upcoming exam. This is a very serious problem in practice. It’s not uncommon to see an LLM perform well in general benchmarks, only to perform below the level of GPT-3.5 (a now-obsolete but inexpensive model) in a practical application, like describing a scene. When this happens, there’s usually little reason to use the model that has the higher general scores - your users should have the final word. Another problem is that LLMs are highly sensitive to the compatibility of the data used in training and prompts used in evaluation. A seemingly minor change in the prompt can lead to drastically different outputs. This makes it difficult to design prompts that consistently elicit the desired response and assess the LLM’s true capabilities." (Abi Aryan, "LLMOps: Managing Large Language Models in Production", 2025)

"The art of mega-prompts spanning multiple written pages and looking like essays has become commonplace for complex tasks when building applications to get things `just right'. Unfortunately, they bring with them lots of issues: errors, portability, complexity, and more. The GenAI world didn’t plan for mega-prompts. They have simply evolved into what they’ve become today because practitioners kept wanting to do more and more complex things, and their only way to express those intents was with a prompt. But step back and look at some of these prompts [...] Lurking just below the surface are a bunch of classical computing concepts like data, programming instructions, control flows, memory, and stora - all the components typically associated with classical computing elements." (Rob Thomas et al, "AI Value Creators: Beyond the Generative AI User Mindset", 2025)

"The same difficulties that characterize training deep feedforward networks also apply to RNNs; gradients tend to die out over long distances using traditional activation functions (or explode if the gradients become greater than 1). However, unlike feedforward networks, RNNs aren’t trained with traditional backpropagation, but rather a variant known as Backpropagation through Time (BPTT): the network is unrolled, as before, and backpropagation is used, averaging over errors at each time point (since an 'output', the hidden state, occurs at each step). Also, in the case of RNNs, we run into the problem that the network has a very short memory; it only incorporates information from the most recent unit before the current one and has trouble maintaining long-range context. For applications such as translation, this is clearly a problem, as the interpretation of a word at the end of a sentence may depend on terms near the beginning, not just those directly preceding it." (Joseph Babcock & Raghav Bali, "Generative AI with Python and PyTorch" 2nd. Ed., 2025)

"When there are hidden layers between the input and output, the problem becomes more complex: when do we change the internal weights to compute the activations that feed into the final output? How do we modify them in relation to the input weights? The insight of the backpropagation technique is that we can use the chain rule from calculus to efficiently compute the derivatives of each parameter of a network with respect to a loss function and, combined with a learning rule, this provides a scalable way to train multilayer networks." (Joseph Babcock & Raghav Bali, "Generative AI with Python and PyTorch" 2nd. Ed., 2025)

"There is no law of physics tdictates AI must remain expensive. The cost of training and inference isn’t fixed - it is an engineering challenge to solved. Businesses, both incumbents and upstarts, have the ingenuity to push these costs down and make AI more practical and widespread." (Rob Thomas et al, "AI Value Creators: Beyond the Generative AI User Mindset", 2025)

"While the backpropagation procedure provides a way to update interior weights within the network in a principled way, it has several shortcomings that make deep networks difficult to use in practice. One is the problem of vanishing gradients. [...] As the value of the sigmoid function increases or decreases toward the extremes (0 or 1, representing either 'off' or 'on' ), the values of the gradient vanish to near zero. This means that the updates to and , which are products of these gradients from hidden activation functions , shrink toward zero, making the weights change little between iterations and making the parameters of the hidden layer neurons change very slowly during backpropagation. Clearly, one problem here is that the sigmoid function saturates; thus, choosing another nonlinearity might circumvent this problem." (Joseph Babcock & Raghav Bali, "Generative AI with Python and PyTorch" 2nd. Ed., 2025)

🖍️Andreas C Müller - Collected Quotes

"A major challenge in unsupervised learning is evaluating whether the algorithm learned something useful. Unsupervised learning algorithms are usually applied to data that does not contain any label information, so we don’t know what the right output should be. Therefore, it is very hard to say whether a model 'did well'. [...] As a consequence, unsupervised algorithms are used often in an exploratory setting, when a data scientist wants to understand the data better, rather than as part of a larger automatic system. Another common application for unsupervised algorithms is as a preprocessing step for supervised algorithms. Learning a new representation of the data can sometimes improve the accuracy of supervised algorithms, or can lead to reduced memory and time consumption." (Andreas C Müller & Sarah Guido, "Introduction to Machine Learning with Python: A Guide for Data Scientists", 2017)

"An important property of neural networks is that their weights are set randomly before learning is started, and this random initialization affects the model that is learned. That means that even when using exactly the same parameters, we can obtain very different models when using different random seeds. If the networks are large, and their complexity is chosen properly, this should not affect accuracy too much, but it is worth keeping in mind (particularly for smaller networks)." (Andreas C Müller & Sarah Guido, "Introduction to Machine Learning with Python: A Guide for Data Scientists", 2017)

"[...]  adding nonlinear features to the representation of our data can make linear models much more powerful. However, often we don’t know which features to add, and adding many features (like all possible interactions in a 100-dimensional feature space) might make computation very expensive. Luckily, there is a clever mathematical trick that allows us to learn a classifier in a higher-dimensional space without actually computing the new, possibly very large representation. This is known as the kernel trick, and it works by directly computing the distance (more precisely, the scalar products) of the data points for the expanded feature representation, without ever actually computing the expansion." (Andreas C Müller & Sarah Guido, "Introduction to Machine Learning with Python: A Guide for Data Scientists", 2017)

"Agglomerative clustering produces what is known as a hierarchical clustering. The clustering proceeds iteratively, and every point makes a journey from being a single point cluster to belonging to some final cluster. Each intermediate step provides a clustering of the data (with a different number of clusters). It is sometimes helpful to look at all possible clusterings jointly. [...] While this visualization provides a very detailed view of the hierarchical clustering, it relies on the two-dimensional nature of the data and therefore cannot be used on datasets that have more than two features. There is, however, another tool to visualize hierarchical clustering, called a dendrogram, that can handle multidimensional datasets." (Andreas C Müller & Sarah Guido, "Introduction to Machine Learning with Python: A Guide for Data Scientists", 2017)

"Before building a machine learning model it is often a good idea to inspect the data, to see if the task is easily solvable without machine learning, or if the desired information might not be contained in the data. Additionally, inspecting your data is a good way to find abnormalities and peculiarities. Maybe some of your irises were measured using inches and not centimeters, for example. In the real world, inconsistencies in the data and unexpected measurements are very common." (Andreas C Müller & Sarah Guido, "Introduction to Machine Learning with Python: A Guide for Data Scientists", 2017)

"Decision trees have two advantages over many of the algorithms [...]: the resulting model can easily be visualized and understood by nonexperts (at least for smaller trees), and the algorithms are completely invariant to scaling of the data. As each feature is processed separately, and the possible splits of the data don’t depend on scaling, no preprocessing like normalization or standardization of features is needed for decision tree algorithms. In particular, decision trees work well when you have features that are on completely different scales, or a mix of binary and continuous features. The main downside of decision trees is that even with the use of pre-pruning, they tend to overfit and provide poor generalization performance. Therefore, in most applications, the ensemble methods we discuss next are usually used in place of a single decision tree." (Andreas C Müller & Sarah Guido, "Introduction to Machine Learning with Python: A Guide for Data Scientists", 2017)

"Essentially, random forests share all of the benefits of decision trees, while making up for some of their deficiencies. One reason to still use decision trees is if you need a compact representation of the decision-making process. It is basically impossible to interpret tens or hundreds of trees in detail, and trees in random forests tend to be deeper than decision trees (because of the use of feature subsets). Therefore, if you need to summarize the prediction making in a visual way to nonexperts, a single decision tree might be a better choice. While building random forests on large datasets might be somewhat time consuming, it can be parallelized across multiple CPU cores within a computer easily." (Andreas C Müller & Sarah Guido, "Introduction to Machine Learning with Python: A Guide for Data Scientists", 2017)

"For regression tasks, the goal is to predict a continuous number, or a floating-point number in programming terms (or real number in mathematical terms). Predicting a person’s annual income from their education, their age, and where they live is an example of a regression task. When predicting income, the predicted value is an amount, and can be any number in a given range. [...] An easy way to distinguish between classification and regression tasks is to ask whether there is some kind of continuity in the output. If there is continuity between possible outcomes, then the problem is a regression problem." (Andreas C Müller & Sarah Guido, "Introduction to Machine Learning with Python: A Guide for Data Scientists", 2017)

"Gradient boosted decision trees are among the most powerful and widely used models for supervised learning. Their main drawback is that they require careful tuning of the parameters and may take a long time to train. Similarly to other tree-based models, the algorithm works well without scaling and on a mixture of binary and continuous features. As with other tree-based models, it also often does not work well on high-dimensional sparse data." (Andreas C Müller & Sarah Guido, "Introduction to Machine Learning with Python: A Guide for Data Scientists", 2017)

"How well the uncertainty actually reflects uncertainty in the data depends on the model and the parameters. A model that is more overfitted tends to make more certain predictions, even if they might be wrong. A model with less complexity usually has more uncertainty in its predictions. A model is called calibrated if the reported uncertainty actually matches how correct it is - in a calibrated model, a prediction made with 70% certainty would be correct 70% of the time." (Andreas C Müller & Sarah Guido, "Introduction to Machine Learning with Python: A Guide for Data Scientists", 2017)

"In binary classification we often speak of one class being the positive class and the other class being the negative class. Here, positive doesn’t represent having benefit or value, but rather what the object of the study is. So, when looking for spam, “positive” could mean the spam class. Which of the two classes is called positive is often a subjective matter, and specific to the domain." (Andreas C Müller & Sarah Guido, "Introduction to Machine Learning with Python: A Guide for Data Scientists", 2017)

"It’s important to note that model complexity is intimately tied to the variation of inputs contained in your training dataset: the larger variety of data points your data‐ set contains, the more complex a model you can use without overfitting. Usually, collecting more data points will yield more variety, so larger datasets allow building more complex models. However, simply duplicating the same data points or collecting very similar data will not help." (Andreas C Müller & Sarah Guido, "Introduction to Machine Learning with Python: A Guide for Data Scientists", 2017)

"Kernelized support vector machines are powerful models and perform well on a variety of datasets. SVMs allow for complex decision boundaries, even if the data has only a few features. They work well on low-dimensional and high-dimensional data (i.e., few and many features), but don’t scale very well with the number of samples. Running an SVM on data with up to 10,000 samples might work well, but working with datasets of size 100,000 or more can become challenging in terms of runtime and memory usage. Another downside of SVMs is that they require careful preprocessing of the data and tuning of the parameters. This is why, these days, most people instead use tree-based models such as random forests or gradient boosting (which require little or no pre‐ processing) in many applications. Furthermore, SVM models are hard to inspect; it can be difficult to understand why a particular prediction was made, and it might be tricky to explain the model to a nonexpert." (Andreas C Müller & Sarah Guido, "Introduction to Machine Learning with Python: A Guide for Data Scientists", 2017) 

"Learning a decision tree means learning the sequence of if/else questions that gets us to the true answer most quickly. In the machine learning setting, these questions are called tests (not to be confused with the test set, which is the data we use to test to see how generalizable our model is). Usually data does not come in the form of binary yes/no features as in the animal example, but is instead represented as continuous features [...]. The tests that are used on continuous data are of the form 'Is feature i larger than value a?'" (Andreas C Müller & Sarah Guido, "Introduction to Machine Learning with Python: A Guide for Data Scientists", 2017)

"Linear regression, or ordinary least squares (OLS), is the simplest and most classic linear method for regression. Linear regression finds the parameters w and b that minimize the mean squared error between predictions and the true regression targets, y, on the training set. The mean squared error is the sum of the squared differences between the predictions and the true values. Linear regression has no parameters, which is a benefit, but it also has no way to control model complexity." (Andreas C Müller & Sarah Guido, "Introduction to Machine Learning with Python: A Guide for Data Scientists", 2017)

"Manifold learning algorithms are mainly aimed at visualization, and so are rarely used to generate more than two new features. Some of them, including t-SNE, com‐ pute a new representation of the training data, but don’t allow transformations of new data. This means these algorithms cannot be applied to a test set: rather, they can only transform the data they were trained for. Manifold learning can be useful for exploratory data analysis, but is rarely used if the final goal is supervised learning. The idea behind t-SNE is to find a two-dimensional representation of the data that preserves the distances between points as best as possible. t-SNE starts with a random twodimensional representation for each data point, and then tries to make points that are close in the original feature space closer, and points that are far apart in the original feature space farther apart. t-SNE puts more emphasis on points that are close by, rather than preserving distances between far-apart points. In other words, it tries to preserve the information indicating which points are neighbors to each other." (Andreas C Müller & Sarah Guido, "Introduction to Machine Learning with Python: A Guide for Data Scientists", 2017)

"Neural networks - particularly the large and powerful ones - often take a long time to train. They also require careful preprocessing of the data, as we saw here. Similarly to SVMs, they work best with 'homogeneous' data, where all the features have similar meanings. For data that has very different kinds of features, tree-based models might work better. Tuning neural network parameters is also an art unto itself. In our experiments, we barely scratched the surface of possible ways to adjust neural network models and how to train them."  (Andreas C Müller & Sarah Guido, "Introduction to Machine Learning with Python: A Guide for Data Scientists", 2017)

"Ridge regression is also a linear model for regression, so the formula it uses to make predictions is the same one used for ordinary least squares. In ridge regression, though, the coefficients (w) are chosen not only so that they predict well on the training data, but also to fit an additional constraint. We also want the magnitude of coef‐ficients to be as small as possible; in other words, all entries of w should be close to zero. Intuitively, this means each feature should have as little effect on the outcome as possible (which translates to having a small slope), while still predicting well. This constraint is an example of what is called regularization. Regularization means explicitly restricting a model to avoid overfitting." (Andreas C Müller & Sarah Guido, "Introduction to Machine Learning with Python: A Guide for Data Scientists", 2017)

"The gradient boosted regression tree is another ensemble method that combines multiple decision trees to create a more powerful model. Despite the 'regression' in the name, these models can be used for regression and classification. In contrast to the random forest approach, gradient boosting works by building trees in a serial manner, where each tree tries to correct the mistakes of the previous one. By default, there is no randomization in gradient boosted regression trees; instead, strong pre-pruning is used. Gradient boosted trees often use very shallow trees, of depth one to five, which makes the model smaller in terms of memory and makes predictions faster. The main idea behind gradient boosting is to combine many simple models (in this context known as weak learners), like shallow trees. Each tree can only provide good predictions on part of the data, and so more and more trees are added to iteratively improve performance." (Andreas C Müller & Sarah Guido, "Introduction to Machine Learning with Python: A Guide for Data Scientists", 2017)

"Typically only a subset of the training points matter for defining the decision boundary: the ones that lie on the border between the classes. These are called support vectors and give the support vec‐ tor machine its name. To make a prediction for a new point, the distance to each of the support vectors is measured. A classification decision is made based on the distances to the support vector, and the importance of the support vectors that was learned during training.". (Andreas C Müller & Sarah Guido, "Introduction to Machine Learning with Python: A Guide for Data Scientists", 2017)

"Unsupervised transformations of a dataset are algorithms that create a new representation of the data which might be easier for humans or other machine learning algorithms to understand compared to the original representation of the data. A common application of unsupervised transformations is dimensionality reduction, which takes a high-dimensional representation of the data, consisting of many features, and finds a new way to represent this data that summarizes the essential characteristics with fewer features. A common application for dimensionality reduction is reduction to two dimensions for visualization purposes." (Andreas C Müller & Sarah Guido, "Introduction to Machine Learning with Python: A Guide for Data Scientists", 2017)

🤖Prompt Engineering: Training (Just the Quotes)

"[...] building an effective LLM-based application can require more than just plugging in a pre-trained model and retrieving results - what if we want to parse them for a better user experience? We might also want to lean on the learnings of massively large language models to help complete the loop and create a useful end-to-end LLM-based application. This is where prompt engineering comes into the picture." (Sinan Ozdemir, "Quick Start Guide to Large Language Models: Strategies and Best Practices for Using ChatGPT and Other LLMs", 2024)

"Fine-tuning involves training the LLM on a smaller, task-specific dataset to adjust its parameters for the specific task at hand. This allows the LLM to leverage its pre-trained knowledge of the language to improve its accuracy for the specific task. Fine-tuning has been shown to drastically improve performance on domain-specific and task-specific tasks and lets LLMs adapt quickly to a wide variety of NLP applications." (Sinan Ozdemir, "Quick Start Guide to Large Language Models: Strategies and Best Practices for Using ChatGPT and Other LLMs", 2024)

"[...] LLMs are pre-trained on large corpora and sometimes fine-tuned on smaller datasets for specific tasks. Recall that one of the factors behind the Transformer’s effectiveness as a language model is that it is highly parallelizable, allowing for faster training and efficient processing of text. What really sets the Transformer apart from other deep learning architectures is its ability to capture long-range dependencies and relationships between tokens using attention. In other words, attention is a crucial component of Transformer-based LLMs, and it enables them to effectively retain information between training loops and tasks (i.e., transfer learning), while being able to process lengthy swatches of text with ease." (Sinan Ozdemir, "Quick Start Guide to Large Language Models: Strategies and Best Practices for Using ChatGPT and Other LLMs", 2024) 

"The idea behind transfer learning is that the pre-trained model has already learned a lot of information about the language and relationships between words, and this information can be used as a starting point to improve performance on a new task. Transfer learning allows LLMs to be fine-tuned for specific tasks with much smaller amounts of task-specific data than would be required if the model were trained from scratch. This greatly reduces the amount of time and resources needed to train LLMs." (Sinan Ozdemir, "Quick Start Guide to Large Language Models: Strategies and Best Practices for Using ChatGPT and Other LLMs", 2024)

"Transfer learning is a technique used in machine learning to leverage the knowledge gained from one task to improve performance on another related task. Transfer learning for LLMs involves taking an LLM that has been pre-trained on one corpus of text data and then fine-tuning it for a specific 'downstream' task, such as text classification or text generation, by updating themodel’s parameters with task-specific data." (Sinan Ozdemir, "Quick Start Guide to Large Language Models: Strategies and Best Practices for Using ChatGPT and Other LLMs", 2024)

"Data drift manifests in several distinct ways. Input drift typically shows up as an increase in adversarial or malformed queries that deviate from the original training or design expectations. This can stress the system’s robustness and degrade output quality. Retriever drift occurs when the relevance of the documents returned by retrieval components declines, even if the retrieval algorithms and configurations remain unchanged. Similarly, embedding drift arises when the vector representations used to compare semantic similarity become less effective, causing retrieval systems to fail despite stable system parameters." (Abi Aryan, "LLMOps: Managing Large Language Models in Production", 2025)

"Despite their impressive capabilities, LLMs are not without limitations. One of the most significant challenges is the problem of hallucination, where an LLM generates factually incorrect or misleading information that appears plausible. This is particularly problematic in domains requiring high factual accuracy, such as healthcare, finance, and legal applications. To mitigate hallucinations and enhance the reliability of LLM outputs,  Retrieval-Augmented Generation (RAG) has emerged as a powerful technique. RAG works by dynamically retrieving relevant information from an external knowledge source (such as a knowledge graph) at inference time, rather than just relying on pre-trained knowledge. This approach ensures that the model has access to up-to-date and accurate data, grounding answers in verified information rather than generating content purely from its internal representations." (Aldo Marzullo et al, "Graph Machine Learning" 2nd Ed., 2025)

"Generative AI for coding and language tools is based on the LLM concept. A large language model is a type of neural network that processes and generates text in a humanlike way. It does this by being trained on a massive dataset of text, which allows it to learn human language patterns, as described previously. It lets LLMs translate, write, and answer questions with text. LLMs can contain natural language, source code, and  more." (Jeremy C Morgan, "Coding with AI: Examples in Python", 2025)

"In a nutshell, training LLMs involves optimizing a large number of parameters on very large datasets. This process, known as pretraining, typically employs unsupervised learning objectives, such as predicting missing words in a sentence (masked language modeling) or forecasting subsequent words (causal language modeling). As a side effect, the pre-training phase lets the model learn and 'understand' a language, resulting in a remarkable ability to generalize across various tasks, often achieving state-of-the-art performance. LLMs have demonstrated proficiency in a diverse array of applications, reflecting their versatility and depth of language understanding. Key areas include text generation, language translation, question answering, and summarization, among many others." (Aldo Marzullo et al, "Graph Machine Learning" 2nd Ed., 2025)

"LLMs are trained on large volumes of data, which inherently provides them with an immense knowledge base and understanding of different languages. Yet, LLMs at their core are complex text completion engines. Since this knowledge and understanding of language is compressed in a very high-dimensional latent space. LLMs end up using these in a very fluid and intelligible way (which often leads to hallucinations). In order to guide LLMs to focus on specific topics or pieces of information to solve certain tasks, (for instance, question-answering from a given piece of text), it is important to provide contextual information explicitly. While most current generations of LLMs have extremely wide context windows, it is recommended to preprocess context into overlapping smaller chunks for better results, reduced latency, and so on. For similar reasons, it is also recommended to preprocess contextual information in clear and task-specific formats. This aspect of context preprocessing is extremely useful in Retrieval-Gugmented Generation (RAG) scenarios." (Joseph Babcock & Raghav Bali, "Generative AI with Python and PyTorch" 2nd. Ed., 2025)

"The pre-training step is by far the biggest in terms of data and compute requirements for the whole of the LLM’s lifecycle. Yet fine-tuning is quite resource-intensive when we compare it to traditional machine learning and deep learning workflows. Fine-tuning is also a very important step in improving the quality of the models; hence, it makes sense to understand how we can optimize this step without impacting the performance. Efficiencies in this step also enable us to iterate faster, thereby improving adaptability in many fast-moving domains. In this section, we will focus on some interesting efficient method." (Joseph Babcock & Raghav Bali, "Generative AI with Python and PyTorch" 2nd. Ed., 2025)

"Transformers are complex models built like LEGO blocks using multiple smart and specialized components. [...] Briefly, a vanilla transformer model consists of separate stacks of encoders and decoders. Each encoder block includes multi-head self-attention, enabling the model to capture relationships between tokens regardless of their positions. Residual connections help maintain gradient flow, preventing the vanishing gradient problem. Layer normalization ensures training stability, and feed-forward layers introduce non-linearity and learn complex token interactions. Decoder blocks contain the same components but also include an encoder-decoder attention mechanism to incorporate context from the encoder. The model uses embedding layers to convert tokens into a continuous latent space for contextual learning and positional encoding to preserve the order of tokens in the sequence." (Joseph Babcock & Raghav Bali, "Generative AI with Python and PyTorch" 2nd. Ed., 2025)

🖍️Joseph Babcock - Collected Quotes

"An important capability for our LLM app to become smarter is to maintain a working memory of its interactions with us - otherwise, it will approach each prompt with no knowledge of our previous interactions. For example, it won’t remember details like where we live or what our interests are, which would make it more challenging to develop useful LLM assistants that can use personal information about us to provide more engaging, relevant responses. It also makes it practically more challenging to code a personalized application if we have to explicitly pass context for this personalized information with each interaction, rather than maintaining it 'for free' through LangChain’s memory functionality. It can also allow us to make the LLM specialized for different users by maintaining different memories on different 'threads' that we can visualize and retrieve from LangSmith."(Joseph Babcock & Raghav Bali, "Generative AI with Python and PyTorch" 2nd. Ed., 2025)

"At the simplest level, a model, be it machine learning or a more classical method such as linear regression, is a mathematical description of how a target variable changes in response to variation in a predictive variable; that relationship could be a linear slope or any of a number of more complex mathematical transformations." (Joseph Babcock & Raghav Bali, "Generative AI with Python and PyTorch" 2nd. Ed., 2025)

"Data efficiency in LLMs is about maximizing the quality of learning from the available data while minimizing the required dataset size and computational resources. Large datasets are costly to process, and redundant or noisy data can negatively impact model performance. Therefore, data efficiency techniques aim to achieve high model accuracy and generalization with a reduced or optimized dataset. This process includes filtering data for quality, reducing redundancy, and applying sampling techniques to emphasize high-value samples." (Joseph Babcock & Raghav Bali, "Generative AI with Python and PyTorch" 2nd. Ed., 2025)

"Interpretability is an important requirement when it comes to NLP tasks. For computer vision use cases, visual cues are good enough indicators for understanding how a model perceives or generates outputs (quantification is also a problem there, but we can skip it for now). For NLP tasks, since the textual data is first required to be transformed into a vector, it is important to understand what those vectors capture and how they are used by the models." (Joseph Babcock & Raghav Bali, "Generative AI with Python and PyTorch" 2nd. Ed., 2025)

"LLMs are great at generating responses while following instructions but a general empirical observation is a marked improvement in performance when prompts are coupled with a few examples (as opposed to zero-shot scenarios). This is not to say that zero-shot performance is bad but the fact that, in real-life settings, our tasks/requirements are generally a bit more nuanced. For instance, LLMs have an inherent capability to infer sentiment for an input sentence but giving a few examples of how to use that inferred sentiment in responding to customer feedback helps." (Joseph Babcock & Raghav Bali, "Generative AI with Python and PyTorch" 2nd. Ed., 2025)

"LLMs are trained on large volumes of data, which inherently provides them with an immense knowledge base and understanding of different languages. Yet, LLMs at their core are complex text completion engines. Since this knowledge and understanding of language is compressed in a very high-dimensional latent space. LLMs end up using these in a very fluid and intelligible way (which often leads to hallucinations). In order to guide LLMs to focus on specific topics or pieces of information to solve certain tasks, (for instance, question-answering from a given piece of text), it is important to provide contextual information explicitly. While most current generations of LLMs have extremely wide context windows, it is recommended to preprocess context into overlapping smaller chunks for better results, reduced latency, and so on. For similar reasons, it is also recommended to preprocess contextual information in clear and task-specific formats. This aspect of context preprocessing is extremely useful in Retrieval-Gugmented Generation (RAG) scenarios." (Joseph Babcock & Raghav Bali, "Generative AI with Python and PyTorch" 2nd. Ed., 2025)

"[...] simply put, prompt engineering is the practice of designing and refining prompts to guide generative models, particularly LLMs, to produce desired outputs. A prompt is the input to these models, often in plain language, consisting of task instructions (implicit or explicit) with or without examples, enabling users to tap into the model’s vast capabilities." (Joseph Babcock & Raghav Bali, "Generative AI with Python and PyTorch" 2nd. Ed., 2025)

"The pre-training step is by far the biggest in terms of data and compute requirements for the whole of the LLM’s lifecycle. Yet fine-tuning is quite resource-intensive when we compare it to traditional machine learning and deep learning workflows. Fine-tuning is also a very important step in improving the quality of the models; hence, it makes sense to understand how we can optimize this step without impacting the performance. Efficiencies in this step also enable us to iterate faster, thereby improving adaptability in many fast-moving domains. In this section, we will focus on some interesting efficient method." (Joseph Babcock & Raghav Bali, "Generative AI with Python and PyTorch" 2nd. Ed., 2025)

"Transformers are complex models built like LEGO blocks using multiple smart and specialized components. [...] Briefly, a vanilla transformer model consists of separate stacks of encoders and decoders. Each encoder block includes multi-head self-attention, enabling the model to capture relationships between tokens regardless of their positions. Residual connections help maintain gradient flow, preventing the vanishing gradient problem. Layer normalization ensures training stability, and feed-forward layers introduce non-linearity and learn complex token interactions. Decoder blocks contain the same components but also include an encoder-decoder attention mechanism to incorporate context from the encoder. The model uses embedding layers to convert tokens into a continuous latent space for contextual learning and positional encoding to preserve the order of tokens in the sequence." (Joseph Babcock & Raghav Bali, "Generative AI with Python and PyTorch" 2nd. Ed., 2025)

"When there are hidden layers between the input and output, the problem becomes more complex: when do we change the internal weights to compute the activations that feed into the final output? How do we modify them in relation to the input weights? The insight of the backpropagation technique is that we can use the chain rule from calculus to efficiently compute the derivatives of each parameter of a network with respect to a loss function and, combined with a learning rule, this provides a scalable way to train multilayer networks." (Joseph Babcock & Raghav Bali, "Generative AI with Python and PyTorch" 2nd. Ed., 2025)

"While the backpropagation procedure provides a way to update interior weights within the network in a principled way, it has several shortcomings that make deep networks difficult to use in practice. One is the problem of vanishing gradients. [...] As the value of the sigmoid function increases or decreases toward the extremes (0 or 1, representing either 'off' or 'on' ), the values of the gradient vanish to near zero. This means that the updates to and , which are products of these gradients from hidden activation functions , shrink toward zero, making the weights change little between iterations and making the parameters of the hidden layer neurons change very slowly during backpropagation. Clearly, one problem here is that the sigmoid function saturates; thus, choosing another nonlinearity might circumvent this problem." (Joseph Babcock & Raghav Bali, "Generative AI with Python and PyTorch" 2nd. Ed., 2025)

"The same difficulties that characterize training deep feedforward networks also apply to RNNs; gradients tend to die out over long distances using traditional activation functions (or explode if the gradients become greater than 1). However, unlike feedforward networks, RNNs aren’t trained with traditional backpropagation, but rather a variant known as Backpropagation through Time (BPTT): the network is unrolled, as before, and backpropagation is used, averaging over errors at each time point (since an 'output', the hidden state, occurs at each step). Also, in the case of RNNs, we run into the problem that the network has a very short memory; it only incorporates information from the most recent unit before the current one and has trouble maintaining long-range context. For applications such as translation, this is clearly a problem, as the interpretation of a word at the end of a sentence may depend on terms near the beginning, not just those directly preceding it." (Joseph Babcock & Raghav Bali, "Generative AI with Python and PyTorch" 2nd. Ed., 2025)

🤖Prompt Engineering: Performance (Just the Quotes)

"The no free lunch theorem for machine learning states that, averaged over all possible data generating distributions, every classification algorithm has the same error rate when classifying previously unobserved points. In other words, in some sense, no machine learning algorithm is universally any better than any other. The most sophisticated algorithm we can conceive of has the same average performance (over all possible tasks) as merely predicting that every point belongs to the same class. [...] the goal of machine learning research is not to seek a universal learning algorithm or the absolute best learning algorithm. Instead, our goal is to understand what kinds of distributions are relevant to the 'real world' that an AI agent experiences, and what kinds of machine learning algorithms perform well on data drawn from the kinds of data generating distributions we care about." (Ian Goodfellow et al, "Deep Learning", 2015)

"Attention is a mechanism used in deep learning models (not just Transformers) that assigns different weights to different parts of the input, allowing the model to prioritize and emphasize the most important information while performing tasks like translation or summarization. Essentially, attention allows a model to 'focus' on different parts of the input dynamically, leading to improved performance and more accurate results. Before the popularization of attention, most neural networks processed all inputs equally and the models relied on a fixed representation of the input to make predictions. Modern LLMs that rely on attention can dynamically focus on different parts of input sequences, allowing them to weigh the importance of each part in making predictions." (Sinan Ozdemir, "Quick Start Guide to Large Language Models: Strategies and Best Practices for Using ChatGPT and Other LLMs", 2024)

"Different algorithms may perform better on different types of text data and will have different vector sizes. The choice of algorithm can have a significant impact on the quality of the resulting embeddings. Additionally, open-source alternatives may require more customization and finetuning than closed-source products, but they also provide greater flexibility and control over the embedding process." (Sinan Ozdemir, "Quick Start Guide to Large Language Models: Strategies and Best Practices for Using ChatGPT and Other LLMs", 2024)

"Fine-tuning involves training the LLM on a smaller, task-specific dataset to adjust its parameters for the specific task at hand. This allows the LLM to leverage its pre-trained knowledge of the language to improve its accuracy for the specific task. Fine-tuning has been shown to drastically improve performance on domain-specific and task-specific tasks and lets LLMs adapt quickly to a wide variety of NLP applications." (Sinan Ozdemir, "Quick Start Guide to Large Language Models: Strategies and Best Practices for Using ChatGPT and Other LLMs", 2024)

"The idea behind transfer learning is that the pre-trained model has already learned a lot of information about the language and relationships between words, and this information can be used as a starting point to improve performance on a new task. Transfer learning allows LLMs to be fine-tuned for specific tasks with much smaller amounts of task-specific data than would be required if the model were trained from scratch. This greatly reduces the amount of time and resources needed to train LLMs." (Sinan Ozdemir, "Quick Start Guide to Large Language Models: Strategies and Best Practices for Using ChatGPT and Other LLMs", 2024)

"Transfer learning is a technique used in machine learning to leverage the knowledge gained from one task to improve performance on another related task. Transfer learning for LLMs involves taking an LLM that has been pre-trained on one corpus of text data and then fine-tuning it for a specific 'downstream' task, such as text classification or text generation, by updating themodel’s parameters with task-specific data." (Sinan Ozdemir, "Quick Start Guide to Large Language Models: Strategies and Best Practices for Using ChatGPT and Other LLMs", 2024)

"Agentic intelligence feels incredibly powerful in demos but breaks in production. Indeed, it is very fragile without solid infrastructure. Every day, I personally see tons of clever orchestrations around dumb prompt chains tied up in a brittle, underused LLMOps infrastructure. But building this infrastructure means acknowledging the costs: performance overhead, strict interface contracts, and state complexity, as well as a need for more LLMOps engineers to create the best practices, tooling, and frameworks to run these systems reliably, safely, and robustly." (Abi Aryan, "LLMOps: Managing Large Language Models in Production", 2025)

"As the tech industry moves from non-generative models to generative models, it is shifting away from feature engineering, or creating features to model the data and experimenting with different hyperparameters to optimize performance. Generative models, and specifically LLMs, do not require feature engineering. Today, the core requirements are usually prompt engineering or building a RAG pipeline - skills that lie within the domain of AI engineers." (Abi Aryan, "LLMOps: Managing Large Language Models in Production", 2025)

"In prompt engineering, we customize the prompts or questions we give the model to get more accurate or insightful responses. The way a prompt is structured has a massive impact on how well a model understands the task at hand and, ultimately, how well it performs. Given LLMs’ versatility, prompt engineering has become an important skill for getting the most out of these models across different domains and tasks. The key is to understand how different prompt structures lead to different model behaviors. There are various strategies - ranging from simple one-shot prompting to more complex techniques like chain-of-thought prompting - that can significantly improve the effectiveness of LLMs." (Abi Aryan, "LLMOps: Managing Large Language Models in Production", 2025)

"LLM-centric workloads change everything. Now the raw material is heterogeneous text, code, images, audio, and chat logs whose value depends on semantic richness - that is, the informational value of the content - rather than a rigid structure. Pipelines must tokenize, chunk, embed, and version this content; store it in vector indexes for similarity search; and apply filters for personally identifiable information, toxicity, and licensing constraints. Instead of ETL jobs, teams run continuous ingestion and reembedding loops so that RAG systems stay fresh, and they log every prompt–response pair so that the inputs and outputs can be evaluated and improve the future performance of this system. Data quality in this context is judged by grounding, factuality, and bias metrics - attributes that require automated red-teaming and humanin-the-loop (HITL) review rather than the data structure violation checks of the past." (Abi Aryan, "LLMOps: Managing Large Language Models in Production", 2025)

🖍️Mark Needham - Collected Quotes

"A random walk, in general, is sometimes described as being similar to how a drunk person traverses a city. They know what direction or end point they want to reach but may take a very circuitous route to get there. The algorithm starts at one node and somewhat randomly follows one of the relationships forward or backward to a neighbor node. It then does the same from that node and so on, until it reaches the set path length. ('We say somewhat randomly because the number of relationships a node has, and its neighbors have, influences the probability a node will be walked through.)'" (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

"Adding graph features and context improves predictions, especially in situations where connections matter. [...] Unfortunately, many machine learning approaches today miss a lot of rich contextual information. This stems from ML’s reliance on input data built from tuples, leaving out a lot of predictive relationships and network data. Furthermore, contextual information is not always readily available or is too difficult to access and process. Even finding connections that are four or more hops away can be a challenge at scale for traditional methods. Using graphs, we can more easily reach and incorporate connected data." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

"At the most abstract level, graph analytics is applied to forecast behavior and prescribe action for dynamic groups. Doing this requires understanding the relationships and structure within the group. Graph algorithms accomplish this by examining the overall nature of networks through their connections. With this approach, you can understand the topology of connected systems and model their processes." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

"Betweenness Centrality makes the assumption that all communication between nodes happens along the shortest path and with the same frequency, which isn’t always the case in real life. Therefore, it doesn’t give us a perfect view of the most influential nodes in a graph, but rather a good representation." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

"Centrality algorithms are used to understand the roles of particular nodes in a graph and their impact on that network. They’re useful because they identify the most important nodes and help us understand group dynamics such as credibility, accessibility, the speed at which things spread, and bridges between groups." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

"Community formation is common in all types of networks, and identifying them is essential for evaluating group behavior and emergent phenomena. The general prin‐ ciple in finding communities is that its members will have more relationships within the group than with nodes outside their group. Identifying these related sets reveals clusters of nodes, isolated groups, and network structure. This information helps infer similar behavior or preferences of peer groups, estimate resiliency, find nested relationships, and prepare data for other analyses. Community detection algorithms are also commonly used to produce network visualization for general inspection." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

"Feature extraction is a way to distill large volumes of data and attributes down to a set of representative descriptive attributes. The process derives numerical values (fea‐ tures) for distinctive characteristics or patterns in input data so that we can differenti‐ ate categories in other data. It’s used when data is difficult for a model to analyze directly - perhaps because of size, format, or the need for incidental comparisons. Feature selection is the process of determining the subset of extracted features that are most important or influential to a target goal. It’s used to surface predictive importance as well as for efficiency." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

"Graph algorithms provide one of the most potent approaches to analyzing connected data because their mathematical calculations are specifically built to operate on relationships. They describe steps to be taken to process a graph to discover its general qualities or specific quantities. Based on the mathematics of graph theory, graph algo‐ rithms use the relationships between nodes to infer the organization and dynamics of complex systems. Network scientists use these algorithms to uncover hidden infomation, test hypotheses, and make predictions about behavior." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

"Graph embedding is the representation of the nodes and relationships in a graph asfeature vectors. [...] Graph embedding uses graph data slightly differently than in connected feature extraction. It enables us to represent entire graphs, or subsets of graph data, in a numerical format ready for machine learning tasks. This is especially useful for unsu‐pervised learning, where the data is not categorized because it pulls in more contextual information through relationships. Graph embedding is also useful for data exploration, computing similarity between entities, and reducing dimensionality to aid in statistical analysis." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

"In classic graph theory, an acyclic graph that is undirected is called a tree. In computer science, trees can also be directed. A more inclusive definition would be a graph where any two nodes are connected by only one path. Trees are significant for understanding graph structures and many algorithms. They play a key role in designing networks, data structures, and search optimizations to improve categorization or organizational hierarchies." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

"Keep in mind that centrality measures represent the importance of a node in comparison to other nodes. Centrality is a ranking of the potential impact of nodes, not a measure of actual impact. For example, you might identify the two people with the highest cen‐ trality in a network, but perhaps policies or cultural norms are in play that actually shift influence to others. Quantifying actual impact is an active research area to develop additional influence metrics." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

"Machine learning is not artificial intelligence (AI), but a method for achieving AI. ML uses algorithms to train software through specific examples and progressive improvements based on expected outcome - without explicit programming of how to accomplish these better results. Training involves providing a lot of data to a model and enabling it to learn how to process and incorporate that information." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

"Make it a habit to run Connected Components to test whether a graph is connected as a preparatory step for general graph analysis. Performing this quick test can avoid accidentally running algorithms on only one disconnected component of a graph and getting incorrect results." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

"Sometimes the most important cog in the system is not the one with the most overt power or the highest status. Sometimes it’s the middlemen that connect groups or the brokers who the most control over resources or the flow of information. Betweenness Centrality is a way of detecting the amount of influence a node has over the flow of information or resources in a graph. It is typically used to find nodes that serve as a bridge from one part of a graph to another." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

"Putting together the right mix of features can increase accuracy because it fundamentally influences how our models learn. Because even modest improvements can make a significant difference, our focus in this chapter is on connected features. Connected features are features extracted from the structure of the data. These features can be derived from graph-local queries based on parts of the graph surrounding a node, or graph-global queries that use graph algorithms to identify predictive elements within data based on relationships for connected feature extraction." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

"Use Degree Centrality if you’re attempting to analyze influence by looking at the number of incoming and outgoing relationships, or find the “popularity” of individual nodes. It works well when you’re concerned with immediate connectedness or near-term probabilities. However, Degree Centrality is also applied to global analysis when you want to evaluate the minimum degree, maximum degree, mean degree, and standard deviation across the entire graph." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

"When using community detection algorithms, be conscious of the density of the relationships. If the graph is very dense, you may end up with all nodes congregating in one or just a few clusters. You can counteract this by filtering by degree, relationship weights, or similarity metrics. On the other hand, if the graph is too sparse with few connected nodes, you may end up with each node in its own cluster. In this case, try to incorporate additional relationship types that carry more relevant information." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)

"Without peripheral and related information, solutions that attempt to predict behav‐ ior or make recommendations for varying circumstances require more exhaustive training and prescriptive rules. This is partly why AI is good at specific, well-defined tasks, but struggles with ambiguity. Graph-enhanced ML can help fill in that missing contextual information that is so important for better decisions." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)