🔭Data Science: Domains (Just the Quotes)

"Methods perform well if the conditions of their derivation are met, with no method capable of covering all possible conditions. More strongly put, each good method has a domain on which it may be best, and different methods have different domains so the task is to characterize those domains and then figure out which domain a given problem’s solution is likely to be in. This of course, is extraordinarily difficult in its own right." (Bertrand Clarke et al, "Principles and Theory for Data Mining and Machine Learning", 2009)

"Much of machine learning is concerned with devising different models, and different algorithms to fit them. We can use methods such as cross validation to empirically choose the best method for our particular problem. However, there is no universally best model - this is sometimes called the no free lunch theorem. The reason for this is that a set of assumptions that works well in one domain may work poorly in another." (Kevin P Murphy, "Machine Learning: A Probabilistic Perspective", 2012)

"An attempt to use the wrong model for a given data set is likely to provide poor results. Therefore, the core principle of discovering outliers is based on assumptions about the structure of the normal patterns in a given data set. Clearly, the choice of the 'normal' model depends highly upon the analyst’s understanding of the natural data patterns in that particular domain." (Charu C Aggarwal, "Outlier Analysis", 2013)

"Bayesian networks provide a more flexible representation for encoding the conditional independence assumptions between the features in a domain. Ideally, the topology of a network should reflect the causal relationships between the entities in a domain. Properly constructed Bayesian networks are relatively powerful models that can capture the interactions between descriptive features in determining a prediction." (John D Kelleher et al, "Fundamentals of Machine Learning for Predictive Data Analytics: Algorithms, worked examples, and case studies", 2015)

"Bayesian networks use a graph-based representation to encode the structural relationships - such as direct influence and conditional independence - between subsets of features in a domain. Consequently, a Bayesian network representation is generally more compact than a full joint distribution (because it can encode conditional independence relationships), yet it is not forced to assert a global conditional independence between all descriptive features. As such, Bayesian network models are an intermediary between full joint distributions and naive Bayes models and offer a useful compromise between model compactness and predictive accuracy." (John D Kelleher et al, "Fundamentals of Machine Learning for Predictive Data Analytics: Algorithms, worked examples, and case studies", 2015)

"Big data is based on the feedback economy where the Internet of Things places sensors on more and more equipment. More and more data is being generated as medical records are digitized, more stores have loyalty cards to track consumer purchases, and people are wearing health-tracking devices. Generally, big data is more about looking at behavior, rather than monitoring transactions, which is the domain of traditional relational databases. As the cost of storage is dropping, companies track more and more data to look for patterns and build predictive models." (Neil Dunlop, "Big Data", 2015)

"The main advantage of decision tree models is that they are interpretable. It is relatively easy to understand the sequences of tests a decision tree carried out in order to make a prediction. This interpretability is very important in some domains. [...] Decision tree models can be used for datasets that contain both categorical and continuous descriptive features. A real advantage of the decision tree approach is that it has the ability to model the interactions between descriptive features. This arises from the fact that the tests carried out at each node in the tree are performed in the context of the results of the tests on the other descriptive features that were tested at the preceding nodes on the path from the root. Consequently, if there is an interaction effect between two or more descriptive features, a decision tree can model this."  (John D Kelleher et al, "Fundamentals of Machine Learning for Predictive Data Analytics: Algorithms, Worked Examples, and Case Studies", 2015)

"Feature extraction is also the most creative part of data science and the one most closely tied to domain expertise. Typically, a really good feature will correspond to some real‐world phenomenon. Data scientists should work closely with domain experts and understand what these phenomena mean and how to distill them into numbers." (Field Cady, "The Data Science Handbook", 2017)

"Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. The data sets themselves are explicitly linked as a form of representation to an observational or otherwise empirical domain of interest. 'Structure' has long been understood as symmetry which can take many forms with respect to any transformation, including point, translational, rotational, and many others. Symmetries directly point to invariants, which pinpoint intrinsic properties of the data and of the background empirical domain of interest. As our data models change, so too do our perspectives on analysing data." (Fionn Murtagh, "Data Science Foundations: Geometry and Topology of Complex Hierarchic Systems and Big Data Analytics", 2018)

"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)

"Using data science, we can uncover the important patterns in a data set, and these patterns can reveal the important attributes in the domain. The reason why data science is used in so many domains is that it doesn’t matter what the problem domain is: if the right data are available and the problem can be clearly defined, then data science can help."  (John D Kelleher & Brendan Tierney, "Data Science", 2018)

"The ability to go beyond human domain knowledge is usually achieved by inductive learning methods that are unfettered from the imperfections in the domain knowledge of deductive methods." (Charu C Aggarwal, "Artificial Intelligence: A Textbook", 2021)

🔭Data Science: Success (Just the Quotes)

 "[…] the statistical prediction of the future from the past cannot be generally valid, because whatever is future to any given past, is in tum past for some future. That is, whoever continually revises his judgment of the probability of a statistical generalization by its successively observed verifications and failures, cannot fail to make more successful predictions than if he should disregard the past in his anticipation of the future. This might be called the ‘Principle of statistical accumulation’." (Clarence I Lewis, "Mind and the World-Order: Outline of a Theory of Knowledge", 1929)

"The most important application of the theory of probability is to what we may call 'chance-like' or 'random' events, or occurrences. These seem to be characterized by a peculiar kind of incalculability which makes one disposed to believe - after many unsuccessful attempts - that all known rational methods of prediction must fail in their case. We have, as it were, the feeling that not a scientist but only a prophet could predict them. And yet, it is just this incalculability that makes us conclude that the calculus of probability can be applied to these events." (Karl R Popper, "The Logic of Scientific Discovery", 1934)

"[Statistics] is both a science and an art. It is a science in that its methods are basically systematic and have general application; and an art in that their successful application depends to a considerable degree on the skill and special experience of the statistician, and on his knowledge of the field of application, e.g. economics." (Leonard H C Tippett, "Statistics", 1943)

"Statistics provides a quantitative example of the scientific process usually described qualitatively by saying that scientists observe nature, study the measurements, postulate models to predict new measurements, and validate the model by the success of prediction." (Marshall J Walker, "The Nature of Scientific Thought", 1963)

"Changes of variables can be helpful for iterative and parametric solutions even if they do not linearize the problem. For example, a change of variables may change the 'shape' of J(x) into a more suitable form. Unfortunately there seems to be no general way to choose the 'right' change of variables. Success depends on the particular problem and the engineer's insight. However, the possibility of a change of variables should always be considered."(Fred C Scweppe, "Uncertain dynamic systems", 1973)

"There is a universality about mathematics; what was created to explain one phenomenon is very often later found to be useful in explaining other, apparently unrelated, phenomena. Theories that were developed to explain some poorly measured effects are often found to fit later, much more accurate measurements. Furthermore, from measurements over a limited range the theory is often found to fit a far wider range. Finally, and perhaps most unreasonably, quite regularly from the mathematics alone new phenomena, previously unknown and unsuspected, are successfully predicted. This universality of mathematics could, of course, be a reflection of the way the human mind works and not of the external world, but most people believe it reflects reality." (Richard W Hamming, "Methods of Mathematics Applied to Calculus, Probability, and Statistics", 1985)

"One of the critical success factors for any method and its application is its ability to facilitate communication, avoiding information overload. So for larger models, the question is how to guide the reader into different parts of the model." (Peter Coad & Edward Yourdon, "Object-Oriented Analysis" 2nd Ed., 1991)

"The ability of neural networks to operate successfully on inputs that did not form part of the training set is one of their most important characteristics. Networks are capable of finding common elements in all the training examples belonging to the same class, and will then respond appropriately when these elements are encountered again. Optimising this capability is an important consideration when designing a network." (Paul Cilliers, "Complexity and Postmodernism: Understanding Complex Systems", 1998)

"Most dashboards fail to communicate efficiently and effectively, not because of inadequate technology (at least not primarily), but because of poorly designed implementations. No matter how great the technology, a dashboard's success as a medium of communication is a product of design, a result of a display that speaks clearly and immediately. Dashboards can tap into the tremendous power of visual perception to communicate, but only if those who implement them understand visual perception and apply that understanding through design principles and practices that are aligned with the way people see and think." (Stephen Few, "Information Dashboard Design", 2006)

"Information design, when successful - whether in print, on the web, or in the environment - represents the functional balance of the meaning of the information, the skills and inclinations of the designer, and the perceptions, education, experience, and needs of the audience." (Joel Katz, "Designing Information: Human factors and common sense in information design", 2012)

"Successful information design in movement systems gives the user the information he needs - and only the information he needs - at every decision point." (Joel Katz, "Designing Information: Human factors and common sense in information design", 2012) 

"You can give your data product a better chance of success by carefully setting the users’ expectations. [...] One under-appreciated facet of designing data products is how the user feels after using the product. Does he feel good? Empowered? Or disempowered and dejected?" (Dhanurjay Patil, "Data Jujitsu: The Art of Turning Data into Product", 2012)

"Data mining is a craft. As with many crafts, there is a well-defined process that can help to increase the likelihood of a successful result. This process is a crucial conceptual tool for thinking about data science projects. [...] data mining is an exploratory undertaking closer to research and development than it is to engineering." (Foster Provost, "Data Science for Business", 2013)

"Decision trees are an important tool for decision making and risk analysis, and are usually represented in the form of a graph or list of rules. One of the most important features of decision trees is the ease of their application. Being visual in nature, they are readily comprehensible and applicable. Even if users are not familiar with the way that a decision tree is constructed, they can still successfully implement it. Most often decision trees are used to predict future scenarios, based on previous experience, and to support rational decision making." (Jelena Djuris et al, "Neural computing in pharmaceutical products and process development", Computer-Aided Applications in Pharmaceutical Technology, 2013)

"We are seduced by patterns and we want explanations for these patterns. When we see a string of successes, we think that a hot hand has made success more likely. If we see a string of failures, we think a cold hand has made failure more likely. It is easy to dismiss such theories when they involve coin flips, but it is not so easy with humans. We surely have emotions and ailments that can cause our abilities to go up and down. The question is whether these fluctuations are important or trivial." (Gary Smith, "Standard Deviations", 2014)

"We emphasize that while there are some common techniques for feature learning one may want to try, the No-Free-Lunch theorem implies that there is no ultimate feature learner. Any feature learning algorithm might fail on some problem. In other words, the success of each feature learner relies (sometimes implicitly) on some form of prior assumption on the data distribution. Furthermore, the relative quality of features highly depends on the learning algorithm we are later going to apply using these features." (Shai Shalev-Shwartz & Shai Ben-David, "Understanding Machine Learning: From Theory to Algorithms", 2014)

"Whether or not a model works is also a matter of opinion. After all, a key component of every model, whether formal or informal, is its definition of success." (Cathy O'Neil, "Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy", 2016)

"All human storytellers bring their subjectivity to their narratives. All have bias, and possibly error. Acknowledging and defusing that bias is a vital part of successfully using data stories. By debating a data story collaboratively and subjecting it to critical thinking, organizations can get much higher levels of engagement with data and analytics and impact their decision making much more than with reports and dashboards alone." (James Richardson, 2017)

"Extracting good features is the most important thing for getting your analysis to work. It is much more important than good machine learning classifiers, fancy statistical techniques, or elegant code. Especially if your data doesn’t come with readily available features (as is the case with web pages, images, etc.), how you reduce it to numbers will make the difference between success and failure." (Field Cady, "The Data Science Handbook", 2017)

"The field of big-data analytics is still littered with a few myths and evidence-free lore. The reasons for these myths are simple: the emerging nature of technologies, the lack of common definitions, and the non-availability of validated best practices. Whatever the reasons, these myths must be debunked, as allowing them to persist usually has a negative impact on success factors and Return on Investment (RoI). On a positive note, debunking the myths allows us to set the right expectations, allocate appropriate resources, redefine business processes, and achieve individual/organizational buy-in." (Prashant Natarajan et al, "Demystifying Big Data and Machine Learning for Healthcare", 2017)

"Uncertainty is an adversary of coldly logical algorithms, and being aware of how those algorithms might break down in unusual circumstances expedites the process of fixing problems when they occur - and they will occur. A data scientist’s main responsibility is to try to imagine all of the possibilities, address the ones that matter, and reevaluate them all as successes and failures happen." (Brian Godsey, "Think Like a Data Scientist", 2017)

"The no free lunch theorems set limits on the range of optimality of any method. That is, each methodology has a ‘catchment area’ where it is optimal or nearly so. Often, intuitively, if the optimality is particularly strong then the effectiveness of the methodology falls off more quickly outside its catchment area than if its optimality were not so strong. Boosting is a case in point: it seems so well suited to binary classification that efforts to date to extend it to give effective classification (or regression) more generally have not been very successful. Overall, it remains to characterize the catchment areas where each class of predictors performs optimally, performs generally well, or breaks down." (Bertrand S Clarke & Jennifer L. Clarke, "Predictive Statistics: Analysis and Inference beyond Models", 2018)

"[...] the focus on Big Data AI seems to be an excuse to put forth a number of vague and hand-waving theories, where the actual details and the ultimate success of neuroscience is handed over to quasi- mythological claims about the powers of large datasets and inductive computation. Where humans fail to illuminate a complicated domain with testable theory, machine learning and big data supposedly can step in and render traditional concerns about finding robust theories. This seems to be the logic of Data Brain efforts today. (Erik J Larson, "The Myth of Artificial Intelligence: Why Computers Can’t Think the Way We Do", 2021)

"The idea that we can predict the arrival of AI typically sneaks in a premise, to varying degrees acknowledged, that successes on narrow AI systems like playing games will scale up to general intelligence, and so the predictive line from artificial intelligence to artificial general intelligence can be drawn with some confidence. This is a bad assumption, both for encouraging progress in the field toward artificial general intelligence, and for the logic of the argument for prediction." (Erik J Larson, "The Myth of Artificial Intelligence: Why Computers Can’t Think the Way We Do", 2021)

🔭Data Science: Central Tendency (Just the Quotes)

"An average value is a single value within the range of the data that is used to represent all of the values in the series. Since an average is somewhere within the range of the data, it is sometimes called a measure of central value." (Frederick E Croxton & Dudley J Cowden, "Practical Business Statistics", 1937

"A good estimator will be unbiased and will converge more and more closely (in the long run) on the true value as the sample size increases. Such estimators are known as consistent. But consistency is not all we can ask of an estimator. In estimating the central tendency of a distribution, we are not confined to using the arithmetic mean; we might just as well use the median. Given a choice of possible estimators, all consistent in the sense just defined, we can see whether there is anything which recommends the choice of one rather than another. The thing which at once suggests itself is the sampling variance of the different estimators, since an estimator with a small sampling variance will be less likely to differ from the true value by a large amount than an estimator whose sampling variance is large." (Michael J Moroney, "Facts from Figures", 1951)

"The mode would form a very poor basis for any further calculations of an arithmetical nature, for it has deliberately excluded arithmetical precision in the interests of presenting a typical result. The arithmetic average, on the other hand, excellent as it is for numerical purposes, has sacrificed its desire to be typical in favour of numerical accuracy. In such a case it is often desirable to quote both measures of central tendency.(Michael J Moroney,Facts from Figures", 1951)

"An average is sometimes called a 'measure of central tendency' because individual values of the variable usually cluster around it. Averages are useful, however, for certain types of data in which there is little or no central tendency." (William A Spirr & Charles P Bonini,Statistical Analysis for Business Decisions" 3rd Ed., 1967)

"Central tendency is the formal expression for the notion of where data is centered, best understood by most readers as 'average'. There is no one way of measuring where data are centered, and different measures provide different insights." (Charles Livingston & Paul Voakes,Working with Numbers and Statistics: A handbook for journalists", 2005)

"Distributional shape is an important attribute of data, regardless of whether scores are analyzed descriptively or inferentially. Because the degree of skewness can be summarized by means of a single number, and because computers have no difficul ty providing such measures (or estimates) of skewness, those who prepare research reports should include a numerical index of skewness every time they provide measures of central tendency and variability." (Schuyler W Huck, "Statistical Misconceptions", 2008)

"It is best to think of the various kinds of central tendency indices as falling into three categories based on the computational procedures one uses to summarize the data. One category deals with means, with techniques put into this category if scores are added together and then divided by the number of scores that are summed. The second category involves different kinds of medians, with various techniques grouped here if the goal is to find some sort of midpoint. The third category contains different kinds of modes, with these techniques focused on the frequency with which scores appear in the data." (Schuyler W Huck, "Statistical Misconceptions", 2008)

"Various measures of central tendency have been invented because the proper notion of the 'average' score can vary from study to study. Depending on the kind of data collected, the degree of skewness in the data, and the possible existence of outliers, it may be that the most appropriate measure of central tendency is found by doing something other than (1) dividing the sum of the scores by the number of scores (to get the mean), (2) calculating the midpoint in the distribution (to get the median), or (3) determining the most frequently observed score (to get the mode)." (Schuyler W Huck, "Statistical Misconceptions", 2008)

"Measures of central tendency and variability work together to give you a concise summary of your data. When you don’t have any outliers, the mean is the most common indicator of central tendency. But on its own, the mean doesn’t tell you much. It isn’t until you also take the standard deviation into account that you really have a sense of your data."  (Shonna D Watters et al, "The Practical Guide for HR Analytics: Using data to inform, transform, and empower HR decisions", 2019)

"Statistical analysis seeks to develop concise summary figures which describe a large body of quantitative data. One of the most widely used set of summary figures is known as measures of location, which are often referred to as averages, measures of central tendency or central location. The purpose for computing an average value for a set of observations is to obtain a single value which is representative of all the items and which the mind can grasp simply and quickly. The single value is the point or location around which the individual items cluster." (Lawrence J Kaplan)

🔭Data Science: Fitting (Just the Quotes)

"It may often happen that an inefficient statistic is accurate enough to answer the particular questions at issue. There is however, one limitation to the legitimate use of inefficient statistics which should be noted in advance. If we are to make accurate tests of goodness of fit, the methods of fitting employed must not introduce errors of fitting comparable to the errors of random sampling; when this requirement is investigated, it appears that when tests of goodness of fit are required, the statistics employed in fitting must be not only consistent, but must be of 100 percent efficiency. This is a very serious limitation to the use of inefficient statistics, since in the examination of any body of data it is desirable to be able at any time to test the validity of one or more of the provisional assumptions which have been made." (Sir Ronald A Fisher, "Statistical Methods for Research Workers", 1925)

"The empirical data are usually available in the form of a table exhibiting pairs of corresponding values of the variables. Since the given values do not lie exactly along a straight hne, a parabola, an exponential curve or a power curve, it is necessar}' to find a curve that fits the given data approximately. This process is called curve fitting, and the equation of the curve which fits the data approximately is called an empirical equation. When fitting a curve to a set of given points, we must assume a general form for the equation which we are going to use to represent the curve." (William L Schaaf, "Analytic Geometry; a college course guide", 1962)

"[…] fitting lines to relationships between variables is often a useful and powerful method of summarizing a set of data. Regression analysis fits naturally with the development of causal explanations, simply because the research worker must, at a minimum, know what he or she is seeking to explain." (Edward R Tufte, "Data Analysis for Politics and Policy", 1974)

"Fitting lines to relationships between variables is the major tool of data analysis. Fitted lines often effectively summarize the data and, by doing so, help communicate the analytic results to others. Estimating a fitted line is also the first step in squeezing further information from the data." (Edward R Tufte, "Data Analysis for Politics and Policy", 1974)

"Exploratory data analysis, EDA, calls for a relatively free hand in exploring the data, together with dual obligations: (•) to look for all plausible alternatives and oddities - and a few implausible ones, (graphic techniques can be most helpful here) and (•) to remove each appearance that seems large enough to be meaningful - ordinarily by some form of fitting, adjustment, or standardization [...] so that what remains, the residuals, can be examined for further appearances." (John W Tukey, "Introduction to Styles of Data Analysis Techniques", 1982)

"Fitting data means finding mathematical descriptions of structure in the data. An additive shift is a structural property of univariate data in which distributions differ only in location and not in spread or shape. […] The process of identifying a structure in data and then fitting the structure to produce residuals that have the same distribution lies at the heart of statistical analysis. Such homogeneous residuals can be pooled, which increases the power of the description of the variation in the data." (William S Cleveland, "Visualizing Data", 1993)

"Many good things happen when data distributions are well approximated by the normal. First, the question of whether the shifts among the distributions are additive becomes the question of whether the distributions have the same standard deviation; if so, the shifts are additive. […] A second good happening is that methods of fitting and methods of probabilistic inference, to be taken up shortly, are typically simple and on well understood ground. […] A third good thing is that the description of the data distribution is more parsimonious." (William S Cleveland, "Visualizing Data", 1993)

"Many of the applications of visualization in this book give the impression that data analysis consists of an orderly progression of exploratory graphs, fitting, and visualization of fits and residuals. Coherence of discussion and limited space necessitate a presentation that appears to imply this. Real life is usually quite different. There are blind alleys. There are mistaken actions. There are effects missed until the very end when some visualization saves the day. And worse, there is the possibility of the nearly unmentionable: missed effects." (William S Cleveland, "Visualizing Data", 1993)

"Time-series forecasting is essentially a form of extrapolation in that it involves fitting a model to a set of data and then using that model outside the range of data to which it has been fitted. Extrapolation is rightly regarded with disfavour in other statistical areas, such as regression analysis. However, when forecasting the future of a time series, extrapolation is unavoidable." (Chris Chatfield, "Time-Series Forecasting" 2nd Ed, 2000)

"It is not always convenient to remember that the right model for a population can fit a sample of data worse than a wrong model - even a wrong model with fewer parameters. We cannot rely on statistical diagnostics to save us, especially with small samples. We must think about what our models mean, regardless of fit, or we will promulgate nonsense." (Leland Wilkinson, "The Grammar of Graphics" 2nd Ed., 2005)

"You might say that there’s no reason to bother with model checking since all models are false anyway. I do believe that all models are false, but for me the purpose of model checking is not to accept or reject a model, but to reveal aspects of the data that are not captured by the fitted model." (Andrew Gelman, "Some thoughts on the sociology of statistics", 2007)

"A complete data analysis will involve the following steps: (i) Finding a good model to fit the signal based on the data. (ii) Finding a good model to fit the noise, based on the residuals from the model. (iii) Adjusting variances, test statistics, confidence intervals, and predictions, based on the model for the noise." (DeWayne R Derryberry, "Basic data analysis for time series with R", 2014)

"Either a logarithmic or a square-root transformation of the data would produce a new series more amenable to fit a simple trigonometric model. It is often the case that periodic time series have rounded minima and sharp-peaked maxima. In these cases, the square root or logarithmic transformation seems to work well most of the time." (DeWayne R Derryberry, "Basic data analysis for time series with R", 2014)

"Once a model has been fitted to the data, the deviations from the model are the residuals. If the model is appropriate, then the residuals mimic the true errors. Examination of the residuals often provides clues about departures from the modeling assumptions. Lack of fit - if there is curvature in the residuals, plotted versus the fitted values, this suggests there may be whole regions where the model overestimates the data and other whole regions where the model underestimates the data. This would suggest that the current model is too simple relative to some better model." (DeWayne R Derryberry, "Basic data analysis for time series with R", 2014)

"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

"An oft-repeated rule of thumb in any sort of statistical model fitting is 'you can't fit a model with more parameters than data points'. This idea appears to be as wide-spread as it is incorrect. On the contrary, if you construct your models carefully, you can fit models with more parameters than datapoints [...]. A model with more parameters than datapoints is known as an under-determined system, and it's a common misperception that such a model cannot be solved in any circumstance. [...] this misconception, which I like to call the 'model complexity myth' [...] is not true in general, it is true in the specific case of simple linear models, which perhaps explains why the myth is so pervasive." (Jake Vanderplas, "The Model Complexity Myth", 2015)

"Supervised learning, or function approximation, is simply fitting data to a function of any variety.  […] Unsupervised learning involves figuring out what makes the data special. […] Reinforcement learning involves figuring out how to play a multistage game with rewards and payoffs. Think of it as the algorithms that optimize the life of something." (Matthew Kirk, "Thoughtful Machine Learning", 2015)

"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)

"Just as they did thirty years ago, machine learning programs (including those with deep neural networks) operate almost entirely in an associational mode. They are driven by a stream of observations to which they attempt to fit a function, in much the same way that a statistician tries to fit a line to a collection of points. Deep neural networks have added many more layers to the complexity of the fitted function, but raw data still drives the fitting process. They continue to improve in accuracy as more data are fitted, but they do not benefit from the 'super-evolutionary speedup'."  (Judea Pearl & Dana Mackenzie, "The Book of Why: The new science of cause and effect", 2018)

"Random forests are essentially an ensemble of trees. They use many short trees, fitted to multiple samples of the data, and the predictions are averaged for each observation. This helps to get around a problem that trees, and many other machine learning techniques, are not guaranteed to find optimal models, in the way that linear regression is. They do a very challenging job of fitting non-linear predictions over many variables, even sometimes when there are more variables than there are observations. To do that, they have to employ 'greedy algorithms', which find a reasonably good model but not necessarily the very best model possible." (Robert Grant, "Data Visualization: Charts, Maps and Interactive Graphics", 2019)

"Fitting models to data is a bit like designing shirts to fit people. If you fit a shirt too closely to one particular person, it will fit other people poorly. Likewise, a model that fits a particular data set too well might not fit other data sets well." (Rahul Parsa, [Speaking to the Iowa SAS User’s Group])

🔭Data Science: Transformations (Just the Quotes)

"Logging size transforms the original skewed distribution into a more symmetrical one by pulling in the long right tail of the distribution toward the mean. The short left tail is, in addition, stretched. The shift toward symmetrical distribution produced by the log transform is not, of course, merely for convenience. Symmetrical distributions, especially those that resemble the normal distribution, fulfill statistical assumptions that form the basis of statistical significance testing in the regression model." (Edward R Tufte, "Data Analysis for Politics and Policy", 1974)

"Logging skewed variables also helps to reveal the patterns in the data. […] the rescaling of the variables by taking logarithms reduces the nonlinearity in the relationship and removes much of the clutter resulting from the skewed distributions on both variables; in short, the transformation helps clarify the relationship between the two variables. It also […] leads to a theoretically meaningful regression coefficient." (Edward R Tufte, "Data Analysis for Politics and Policy", 1974)

"The logarithmic transformation serves several purposes: (1) The resulting regression coefficients sometimes have a more useful theoretical interpretation compared to a regression based on unlogged variables. (2) Badly skewed distributions - in which many of the observations are clustered together combined with a few outlying values on the scale of measurement - are transformed by taking the logarithm of the measurements so that the clustered values are spread out and the large values pulled in more toward the middle of the distribution. (3) Some of the assumptions underlying the regression model and the associated significance tests are better met when the logarithm of the measured variables is taken." (Edward R Tufte, "Data Analysis for Politics and Policy", 1974)

"The logarithm is one of many transformations that we can apply to univariate measurements. The square root is another. Transformation is a critical tool for visualization or for any other mode of data analysis because it can substantially simplify the structure of a set of data. For example, transformation can remove skewness toward large values, and it can remove monotone increasing spread. And often, it is the logarithm that achieves this removal." (William S Cleveland, "Visualizing Data", 1993)

"Compound errors can begin with any of the standard sorts of bad statistics - a guess, a poor sample, an inadvertent transformation, perhaps confusion over the meaning of a complex statistic. People inevitably want to put statistics to use, to explore a number's implications. [...] The strengths and weaknesses of those original numbers should affect our confidence in the second-generation statistics." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)

"All forms of complex causation, and especially nonlinear transformations, admittedly stack the deck against prediction. Linear describes an outcome produced by one or more variables where the effect is additive. Any other interaction is nonlinear. This would include outcomes that involve step functions or phase transitions. The hard sciences routinely describe nonlinear phenomena. Making predictions about them becomes increasingly problematic when multiple variables are involved that have complex interactions. Some simple nonlinear systems can quickly become unpredictable when small variations in their inputs are introduced." (Richard N Lebow, "Forbidden Fruit: Counterfactuals and International Relations", 2010)

"Either a logarithmic or a square-root transformation of the data would produce a new series more amenable to fit a simple trigonometric model. It is often the case that periodic time series have rounded minima and sharp-peaked maxima. In these cases, the square root or logarithmic transformation seems to work well most of the time." (DeWayne R Derryberry, "Basic data analysis for time series with R", 2014)

"Transformations of data alter statistics. For example, the mean of a data set can be found, but it is not easy to relate the mean of a data set to the mean of the logarithm of that data set. The median is far friendlier to transformations. If the median of a data set is found, then the logarithm of the data set is analyzed; the median of the log transformed data will be the log of the original median." (DeWayne R Derryberry, "Basic data analysis for time series with R", 2014) 

"Transforming data to measurements of a different kind can clarify and simplify hypotheses that have already been generated and can reveal patterns that would otherwise be hidden." (Forrest W Young et al, "Visual Statistics: Seeing data with dynamic interactive graphics", 2016)

"Feature generation (or engineering, as it is often called) is where the bulk of the time is spent in the machine learning process. As social science researchers or practitioners, you have spent a lot of time constructing features, using transformations, dummy variables, and interaction terms. All of that is still required and critical in the machine learning framework. One difference you will need to get comfortable with is that instead of carefully selecting a few predictors, machine learning systems tend to encourage the creation of lots of features and then empirically use holdout data to perform regularization and model selection. It is common to have models that are trained on thousands of features." (Rayid Ghani & Malte Schierholz, "Machine Learning", 2017)

"Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. The data sets themselves are explicitly linked as a form of representation to an observational or otherwise empirical domain of interest. 'Structure' has long been understood as symmetry which can take many forms with respect to any transformation, including point, translational, rotational, and many others. Symmetries directly point to invariants, which pinpoint intrinsic properties of the data and of the background empirical domain of interest. As our data models change, so too do our perspectives on analysing data." (Fionn Murtagh, "Data Science Foundations: Geometry and Topology of Complex Hierarchic Systems and Big Data Analytics", 2018)

"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)

🔭Data Science: Gradients (Just the Quotes)

"There are many control parameters to a learning system. The question is to identify, at a sufficiently high level, the ones that can play a key role in sequencing effects. Because learning can be seen as the search for an optimal hypothesis in a given space under an inductive criteria defined over the training set, three means to control learning readily appear. The first one corresponds to a change of the hypothesis space. The second consists in modifying the optimization landscape. This can be done by changing either the training set (for instance, by a forgetting mechanism) or the inductive criteria. Finally, one can also fiddle with the exploration process. For instance, in the case of a gradient search, slowing down the search process can prevent the system from having time to find the local optimum, which, in turn, can introduce sequencing effects." (Antoine Cornuéjol, "The Necessity of Order in Machine Learning: Is Order in Order?", 2007)

"Deep learning is about using a stacked hierarchy of feature detectors. [...] we use pattern detectors and we build them into networks that are arranged in hundreds of layers and then we adjust the links between these layers, usually using some kind of gradient descent." (Joscha Bach,Joscha: Computational Meta-Psychology", 2015)

"Boosting is a non-linear flexible regression technique that helps increase the accuracy of trees by assigning more weights to wrong predictions. The reason for inducing more weight is so the model can emphasize more on these wrongly predicted samples and tune itself to increase accuracy. The gradient boosting method solves the inherent problem in boosting trees" (i.e., low speed and human interpretability). The algorithm supports parallelism by specifying the number of threads." (Danish Haroon,Python Machine Learning Case Studies", 2017)

"In Boosting, the selection of samples is done by giving more and more weight to hard-to-classify observations. Gradient boosting classification produces a prediction model in the form of an ensemble of weak predictive models, usually decision trees. It generalizes the model by optimizing for the arbitrary differentiable loss function. At each stage, regression trees fit on the negative gradient of binomial or multinomial deviance loss function." (Danish Haroon,Python Machine Learning Case Studies", 2017)

"The beauty of quantum machine learning is that we do not need to depend on an algorithm like gradient descent or convex objective function. The objective function can be nonconvex or something else." (Amit Ray,Quantum Computing Algorithms for Artificial Intelligence", 2018)

"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)

"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 process of defining a custom loss function calls for a clear understanding of the objective of your task and the nature of your data. This requires understanding how your model learns and how its predictions can be compared to the actual targets in a meaningful and helpful way. Additionally, it’s crucial to consider the balance between complexity and interpretability of your loss function. While complex functions might capture the task’s intricacies better, they might also make training more challenging and results harder to interpret. At a lower level, we also have to make sure that a custom loss function is differentiable - that is, it must have a derivative everywhere. This requirement arises because learning in these models is accomplished through gradient descent, which requires computing the derivative of the loss function." (Sinan Ozdemir, "Quick Start Guide to Large Language Models: Strategies and Best Practices for Using ChatGPT and Other LLMs", 2024) 

"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)

"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)

🔭Data Science: Optimization (Just the Quotes)

"[...] any hope that we are smart enough to find even transiently optimum solutions to our data analysis problems is doomed to failure, and, indeed, if taken seriously, will mislead us in the allocation of effort, thus wasting both intellectual and computational effort." (John W Tukey, "Choosing Techniques for the Analysis of Data", 1981)

"In constructing a model, we always attempt to maximize its usefulness. This aim is closely connected with the relationship among three key characteristics of every systems model: complexity, credibility, and uncertainty. This relationship is not as yet fully understood. We only know that uncertainty (predictive, prescriptive, etc.) has a pivotal role in any efforts to maximize the usefulness of systems models. Although usually (but not always) undesirable when considered alone, uncertainty becomes very valuable when considered in connection to the other characteristics of systems models: in general, allowing more uncertainty tends to reduce complexity and increase credibility of the resulting model. Our challenge in systems modelling is to develop methods by which an optimal level of allowable uncertainty can be estimated for each modelling problem." (George J Klir & Bo Yuan, "Fuzzy Sets and Fuzzy Logic: Theory and Applications", 1995)

"A strategy is usually expressed by a set of heuristic rules. The heuristic rules ease the process of searching for an optimal solution. The process is usually iterative and at one step either the global optimum for the whole problem (state) space is found and the process stops, or a local optimum for a subspace of the state space of the problem is found and the problem continues, if it is possible to improve." (Nikola K Kasabov, "Foundations of Neural Networks, Fuzzy Systems, and Knowledge Engineering", 1996)

"Heuristic methods may aim at local optimization rather than at global optimization, that is, the algorithm optimizes the solution stepwise, finding the best solution at each small step of the solution process and 'hoping' that the global solution, which comprises the local ones, would be satisfactory." (Nikola K Kasabov, "Foundations of Neural Networks, Fuzzy Systems, and Knowledge Engineering", 1996)

"[...] an algorithm’s average performance is determined by how 'aligned' it is with the underlying probability distribution over optimization problems on which it is run." (David H Wolpert & William G Macready, "No free lunch theorems for optimization", IEEE Transactions on Evolutionary Computation 1 (1), 1997)

"[...] despite the NFL theorems, algorithms can have a priori distinctions that hold even if nothing is specified concerning the optimization problems. In particular, we show that there can be 'head-to-head' minimax distinctions between a pair of algorithms, i.e., that when considering one function at a time ,a pair of algorithms may be distinguishable, even if they are not when one looks over all functions." (David H Wolpert & William G Macready, "No free lunch theorems for optimization", IEEE Transactions on Evolutionary Computation 1 (1), 1997)

"[...] if you have a general optimization involving uncertainty and very little prior knowledge, the situation is rather hopeless. Due to the NFL theorem, you cannot do any better than a blind search. Each blind search evaluation will be very expensive, with no hope of future improvement, theoretical or otherwise. And the number of performance searches required to get anywhere is simply too large. Neither time nor theoretical or technological progress are on your side. No grand optimization algorithm to end all algorithms is possible." (Yu-Chi Ho, "The no free lunch theorem and the human-machine interface", IEEE Control Systems Magazine, 1999)

"The No Free Lunch (NFL) theorem […] tells us that without any structural assumptions on an optimization problem, no algorithm can perform better on average than blind search." (Yu-Chi Ho, "The no free lunch theorem and the human-machine interface", IEEE Control Systems Magazine, 1999)

"A model is an imitation of reality and a mathematical model is a particular form of representation. We should never forget this and get so distracted by the model that we forget the real application which is driving the modelling. In the process of model building we are translating our real world problem into an equivalent mathematical problem which we solve and then attempt to interpret. We do this to gain insight into the original real world situation or to use the model for control, optimization or possibly safety studies." (Ian T Cameron & Katalin Hangos, "Process Modelling and Model Analysis", 2001)

"Because No Free Lunch theorems dictate that no optimization algorithm can be considered more efficient than any other when considering all possible functions, the desired function class plays a prominent role in the model. In particular, this provides a tractable way to answer the traditionally difficult question of what algorithm is best matched to a particular class of functions. Among the benefits of the model are the ability to specify the function class in a straightforward manner, a natural way to specify noisy or dynamic functions, and a new source of insight into No Free Lunch theorems for optimization." (Christopher K Monson, "No Free Lunch, Bayesian Inference, and Utility: A Decision-Theoretic Approach to Optimization", [thesis] 2006)

"In effect, machine learning research has already brought us several interesting concepts. Most prominently, it has stressed the benefit of distinguishing between the properties of the hypothesis space - its richness and the valuation scheme associated with it - and the characteristics of the actual search procedure in this space, guided by the training data. This in turn suggests two important factors related to sequencing effects, namely forgetting and the nonoptimality of the search procedure. Both are key parameters than need to be thoroughly understood if one is to master sequencing effects." (Antoine Cornuéjol, "The Necessity of Order in Machine Learning: Is Order in Order?", 2007)

"There are many control parameters to a learning system. The question is to identify, at a sufficiently high level, the ones that can play a key role in sequencing effects. Because learning can be seen as the search for an optimal hypothesis in a given space under an inductive criteria defined over the training set, three means to control learning readily appear. The first one corresponds to a change of the hypothesis space. The second consists in modifying the optimization landscape. This can be done by changing either the training set (for instance, by a forgetting mechanism) or the inductive criteria. Finally, one can also fiddle with the exploration process. For instance, in the case of a gradient search, slowing down the search process can prevent the system from having time to find the local optimum, which, in turn, can introduce sequencing effects." (Antoine Cornuéjol, "The Necessity of Order in Machine Learning: Is Order in Order?", 2007)

"There may be no significant difference between the point of view of inferring the true structure and that of making a prediction if an infinitely large quantity of data is available or if the data are noiseless. However, in modeling based on a finite quantity of real data, there is a significant gap between these two points of view, because an optimal model for prediction purposes may be different from one obtained by estimating the 'true model'." (Genshiro Kitagawa & Sadanori Konis, "Information Criteria and Statistical Modeling", 2007)

"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)

"When generating trees, it is usually optimal to grow a larger tree than is justifiable and then prune it back. The main reason this works well is that stop splitting rules do not look far enough forward. That is, stop splitting rules tend to underfit, meaning that even if a rule stops at a split for which the next candidate splits give little improvement, it may be that splitting them one layer further will give a large improvement in accuracy." (Bertrand Clarke et al, "Principles and Theory for Data Mining and Machine Learning", 2009)

"The problem of comparing classifiers is not at all an easy task. There is no single classifier that works best on all given problems, phenomenon related to the 'No-free-lunch' metaphor, i.e., each classifier (’restaurant’) provides a specific technique associated with the corresponding costs (’menu’ and ’price’ for it). It is hence up to us, using the information and knowledge at hand, to find the optimal trade-off." (Florin Gorunescu, "Data Mining Concepts, Models and Techniques", 2011)

"In an emergency, a data product that just produces more data is of little use. Data scientists now have the predictive tools to build products that increase the common good, but they need to be aware that building the models is not enough if they do not also produce optimized, implementable outcomes." (Jeremy Howard et al, "Designing Great Data Products", 2012)

"Briefly speaking, to solve a Machine Learning problem means you optimize a model to fit all the data from your training set, and then you use the model to predict the results you want. Therefore, evaluating a model need to see how well it can be used to predict the data out of the training set. Usually there are three types of the models: underfitting, fair and overfitting model [...]. If we want to predict a value, both (a) and (c) in this figure cannot work well. The underfitting model does not capture the structure of the problem at all, and we say it has high bias. The overfitting model tries to fit every sample in the training set and it did it, but we say it is of high variance. In other words, it fails to generalize new data." (Shudong Hao, "A Beginner’s Tutorial for Machine Learning Beginners", 2014)

"Deep learning is an area of machine learning that emerged from the intersection of neural networks, artificial intelligence, graphical modeling, optimization, pattern recognition and signal processing." (N D Lewis, "Deep Learning Made Easy with R: A Gentle Introduction for Data Science", 2016)

"Machine learning tends to be more focused on developing efficient algorithms that scale to large data in order to optimize the predictive model. Statistics generally pays more attention to the probabilistic theory and underlying structure of the model." (Peter C Bruce & Andrew G Bruce, "Statistics for Data Scientists: 50 Essential Concepts", 2016)

"Many classification and regression algorithms optimize a certain criteria or loss function. For example, logistic regression attempts to minimize the deviance. In the literature, some propose to modify the loss function in order to avoid the problems caused by a rare class. In practice, this is hard to do: classification algorithms can be complex and difficult to modify. Weighting is an easy way to change the loss function, discounting errors for records with low weights in favor of records of higher weights." (Peter C Bruce & Andrew G Bruce, "Statistics for Data Scientists: 50 Essential Concepts", 2016)

"Optimization is more than finding the best simulation results. It is itself a complex and evolving field that, subject to certain information constraints, allows data scientists, statisticians, engineers, and traders alike to perform reality checks on modeling results." (Chris Conlan, "Automated Trading with R: Quantitative Research and Platform Development", 2016)

"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, and how 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)

"Optimization is the process of finding the maximum or minimum of a given function (also known as a fitness function), by calculating the best values for its variables (also known as a 'solution'). Despite the simplicity of this definition, it is not an easy process; often involves restrictions, as well as complex relationships among the various variables. Even though some functions can be optimized using some mathematical process, most functions we encounter in data science are not as simple, requiring a more advanced technique." (Yunus E Bulut & Zacharias Voulgaris, "AI for Data Science: Artificial Intelligence Frameworks and Functionality for Deep Learning, Optimization, and Beyond", 2018)

"Optimization systems (or optimizers, as they are often referred to) aim to optimize in a systematic way, oftentimes using a heuristics-based approach. Such an approach enables the AI system to use a macro level concept as part of its low-level calculations, accelerating the whole process and making it more light-weight. After all, most of these systems are designed with scalability in mind, so the heuristic approach is most practical." (Yunus E Bulut & Zacharias Voulgaris, "AI for Data Science: Artificial Intelligence Frameworks and Functionality for Deep Learning, Optimization, and Beyond", 2018)

"Quantum machine learning promises to discover the optimal network topologies and hyperparameters automatically without human intervention. (Amit Ray, "Quantum Computing Algorithms for Artificial Intelligence", 2018)

"Unfortunately, because the search space is large, automatic techniques for optimization are not sufficient. Instead, the process of selecting an optimal model is complex and iterative, involving repeated cycling through feature engineering, model selection, and hyperparameter tuning. Results are evaluated after each iteration in order to arrive at the best combination of features, model, and parameters that will solve the problem at hand." (Benjamin Bengfort et al, "Applied Text Analysis with Python: Enabling Language-Aware Data Products with Machine Learning", 2018)

"The no free lunch theorems set limits on the range of optimality of any method. That is, each methodology has a ‘catchment area’ where it is optimal or nearly so. Often, intuitively, if the optimality is particularly strong then the effectiveness of the methodology falls off more quickly outside its catchment area than if its optimality were not so strong. Boosting is a case in point: it seems so well suited to binary classification that efforts to date to extend it to give effective classification (or regression) more generally have not been very successful. Overall, it remains to characterize the catchment areas where each class of predictors performs optimally, performs generally well, or breaks down." (Bertrand S Clarke & Jennifer L. Clarke, "Predictive Statistics: Analysis and Inference beyond Models", 2018)

"Cross-validation is a useful tool for finding optimal predictive models, and it also works well in visualization. The concept is simple: split the data at random into a 'training' and a 'test' set, fit the model to the training data, then see how well it predicts the test data. As the model gets more complex, it will always fit the training data better and better. It will also start off getting better results on the test data, but there comes a point where the test data predictions start going wrong." (Robert Grant, "Data Visualization: Charts, Maps and Interactive Graphics", 2019)

"Random forests are essentially an ensemble of trees. They use many short trees, fitted to multiple samples of the data, and the predictions are averaged for each observation. This helps to get around a problem that trees, and many other machine learning techniques, are not guaranteed to find optimal models, in the way that linear regression is. They do a very challenging job of fitting non-linear predictions over many variables, even sometimes when there are more variables than there are observations. To do that, they have to employ 'greedy algorithms', which find a reasonably good model but not necessarily the very best model possible." (Robert Grant, "Data Visualization: Charts, Maps and Interactive Graphics", 2019)

"A key point is that an increased number of attributes relative to training points provides additional degrees of freedom to the optimization problem, as a result of which irrelevant solutions become more likely. Therefore, a natural solution is to add a penalty for using additional features." (Charu C Aggarwal, "Artificial Intelligence: A Textbook", 2021)

"Generally speaking, all the unsupervised embedding algorithms based on matrix factorization use the same principle. They all factorize an input graph expressed as a matrix in different components. The main difference between each method lies in the loss function used during the optimization process and the constraints/formulations posed for the V and H matrices. Indeed, different loss functions allow the creation of an embedding space that emphasizes specific properties of the input graph." (Aldo Marzullo et al, "Graph Machine Learning" 2nd Ed., 2025)

🔭Data Science: Reinforcement Learning (Just the Quotes)

"A neural network training method based on presenting input vector x and looking at the output vector calculated by the network. If it is considered 'good', then a 'reward' is given to the network in the sense that the existing connection weights get increased, otherwise the network is "punished"; the connection weights, being considered as 'not appropriately set,' decrease." (Nikola K Kasabov, "Foundations of Neural Networks, Fuzzy Systems, and Knowledge Engineering", 1996)

"A training paradigm where the neural network is presented with a sequence of input data, followed by a reinforcement signal." (Joseph P Bigus, "Data Mining with Neural Networks: Solving Business Problems from Application Development to Decision Support", 1996)

"learning mode in which adaptive changes of the parameters due to reward or punishment depend on the final outcome of a whole sequence of behavior. The results of learning are evaluated by some performance index." (Teuvo Kohonen, "Self-Organizing Maps" 3rd Ed., 2001)

"A learning method which interprets feedback from an environment to learn optimal sets of condition/response relationships for problem solving within that environment" (Pi-Sheng Deng, "Genetic Algorithm Applications to Optimization Modeling", Encyclopedia of Artificial Intelligence, 2009)

"A sub-area of machine learning concerned with how an agent ought to take actions in an environment so as to maximize some notion of long-term reward. Reinforcement learning algorithms attempt to find a policy that maps states of the world to the actions the agent ought to take in those states. Differently from supervised learning, in this case there is no target value for each input pattern, only a reward based of how good or bad was the action taken by the agent in the existent environment." (Marley Vellasco et al, "Hierarchical Neuro-Fuzzy Systems" Part II, Encyclopedia of Artificial Intelligence, 2009)

"a type of machine learning in which an agent learns, through its own experience, to navigate through an environment, choosing actions in order to maximize the sum of rewards." (Lisa Torrey & Jude Shavlik, "Transfer Learning",  2010)

"a machine learning technique whereby actions are associated with credits or penalties, sometimes with delay, and whereby, after a series of learning episodes, the learning agent has developed a model of which action to choose in a particular environment, based on the expectation of accumulated rewards." (Apostolos Georgas, "Scientific Workflows for Game Analytics", Encyclopedia of Business Analytics and Optimization", 2014)

"A type of machine learning in which the machine learns what to do by discovering through trial and error the way to maximize a reward." (Gloria Phillips-Wren, "Intelligent Systems to Support Human Decision Making", 2014)

"it stands, in the context of computational learning, for a family of algorithms aimed at approximating the best policy to play in a certain environment (without building an explicit model of it) by increasing the probability of playing actions that improve the rewards received by the agent." (Fernando S Oliveira, "Reinforcement Learning for Business Modeling", 2014)

"a special case of supervised learning in which the cognitive computing system receives feedback on its performance to guide it to a goal or good outcome." (Judith S Hurwitz, "Cognitive Computing and Big Data Analytics", 2015)

"The knowledge is obtained using rewards and punishments which there is an agent (learner) that acts autonomously and receives a scalar reward signal that is used to evaluate the consequences of its actions." (Nuno Pombo et al, "Machine Learning Approaches to Automated Medical Decision Support Systems", 2015)

"It is also known as learning with a critic. The agent takes a sequence of actions and receives a reward/penalty only at the very end, with no feedback during the intermediate actions. Using this limited information, the agent should learn to generate the actions to maximize the reward in later trials. For example, in chess, we do a set of moves, and at the very end, we win or lose the game; so we need to figure out what the actions that led us to this result were and correspondingly credit them." (Ethem Alpaydın, "Machine learning : the new AI", 2016)

"A learning algorithm for a robot or a software agent to take actions in an environment so as to maximize the sum of rewards through trial and error." (Tomohiro Yamaguchi et al, "Analyzing the Goal-Finding Process of Human Learning With the Reflection Subtask", 2018)

"Training/learning method aiming to automatically determine the ideal behavior within a specific context based on rewarding desired behaviors and/or punishing undesired one." (Ioan-Sorin Comşa et al, "Guaranteeing User Rates With Reinforcement Learning in 5G Radio Access Networks", 2019)

"Brach of the Artificial Intelligence field devoted to obtaining optimal control sequences for agents only by interacting with a concrete dynamical system." (Juan Parras & Santiago Zazo, "The Threat of Intelligent Attackers Using Deep Learning: The Backoff Attack Case", 2020)

"Machine learning approaches often used in robotics. A reward is used to teach a system a desired behavior." (Jörg Frochte et al, "Concerning the Integration of Machine Learning Content in Mechatronics Curricula", 2020)

"This area of deep learning includes methods which iterates over various steps in a process to get the desired results. Steps that yield desirable outcomes are content and steps that yield undesired outcomes are reprimanded until the algorithm is able to learn the given optimal process. In unassuming terms, learning is finished on its own or effort on feedback or content-based learning." (Amit K Tyagi & Poonam Chahal, "Artificial Intelligence and Machine Learning Algorithms", 2020)

"A machine learning paradigm that utilizes evaluative feedback to cultivate desired behavior." (Marten H L Kaas, "Raising Ethical Machines: Bottom-Up Methods to Implementing Machine Ethics", 2021)

"Is an area of machine learning that learn for the experience in order to maximize the rewards." (Walaa Alnasser et al, "An Overview on Protecting User Private-Attribute Information on Social Networks", 2021)

"Of all the possible paths to superintelligence, AI seems to be the most promising one. Recent successes in the field based on reinforcement learning and neural networks have led to another AI spring, after a number of AI winters. Many even now believe that a superintelligence might not be as far away as we thought even a few years ago. The field currently is characterized by much faster advancements than originally predicted by experts only a short while ago." (Yves Hilpisch, "Artificial Intelligence in Finance A Python-Based Guide", 2021)

"Reinforcement learning is also a subset of AI algorithms which creates independent, self-learning systems through trial and error. Any positive action is assigned a reward and any negative action would result in a punishment. Reinforcement learning can be used in training autonomous vehicles where the goal would be obtaining the maximum rewards." (Vijayaraghavan Varadharajan & Akanksha Rajendra Singh, "Building Intelligent Cities: Concepts, Principles, and Technologies", 2021)

"The value of reinforcement learning lies in its ability to solve highly complex problems by mimicking human learning processes. The model undergoes continuous learning and improvement through interaction with its environment, making it highly accurate over time. Reinforcement learning is especially valuable when applied to tasks like robotics, autonomous driving, and game playing, where the agent constantly learns from new experiences. It also integrates well with neural networks, creating the foundation for deep reinforcement learning, which allows models to handle even more intricate tasks." (Bennie Haelen, "ML and Generative AI in the Data Lakehouse Building and Deploying AI Applications at Scale", 2026)

"Reinforcement Learning uses a kind of algorithm that works by trial and error, where the learning is enabled using a feedback loop of 'rewards' and 'punishments'. When the algorithm is fed a dataset, it treats the environment like a game, and is told whether it has won or lost each time it performs an action. In this way, reinforcement learning algorithms build up a picture of the 'moves' that result in success, and those that don't." (Accenture)

🔭Data Science: There's No Free Lunch (Just the Quotes)

"There is nothing in any object, consider'd in itself, which can afford us a reason for drawing a conclusion beyond it; […] even after the observation of the frequent or constant conjunction of objects, we have no reason to draw any inference concerning any object beyond those of which we have had experience." (David Hume, "A Treatise of Human Nature", 1739) [considered as the first attempt to underline the limits of inductive inference] 

"Consider any of the heuristics that people have come up with for supervised learning: avoid overfitting, prefer simpler to more complex models, boost your algorithm, bag it, etc. The no free lunch theorems say that all such heuristics fail as often (appropriately weighted) as they succeed. This is true despite formal arguments some have offered trying to prove the validity of some of these heuristics." (David H Wolpert, "The lack of a priori distinctions between learning algorithms", Neural Computation Vol. 8(7), 1996)

"[...] an algorithm’s average performance is determined by how 'aligned' it is with the underlying probability distribution over optimization problems on which it is run." (David H Wolpert & William G Macready, "No free lunch theorems for optimization", IEEE Transactions on Evolutionary Computation 1 (1), 1997)

"[...] despite the NFL theorems, algorithms can have a priori distinctions that hold even if nothing is specified concerning the optimization problems. In particular, we show that there can be 'head-to-head' minimax distinctions between a pair of algorithms, i.e., that when considering one function at a time ,a pair of algorithms may be distinguishable, even if they are not when one looks over all functions." (David H Wolpert & William G Macready, "No free lunch theorems for optimization", IEEE Transactions on Evolutionary Computation 1 (1), 1997)

"The NFL theorems do not directly address minimax properties of search. For example, say we are considering two deterministic algorithms a1 and a2. It may very well be that there exist cost functions such that a1’s histogram is much better (according to some appropriate performance measure) than a2’s, but no cost functions for which the reverse is true. For the NFL theorem to be obeyed in such a scenario, it would have to be true that there are many more f for which a2’s histogram is better than a1’s than vice-versa, but it is only slightly better for all those f. For such a scenario, in a certain sense a1 has better 'head-to-head' minimax behavior than a2; there are f for which a1 beats a2 badly, but none for which a1 does substantially worse than a2." (David H Wolpert & William G Macready, "No free lunch theorems for optimization", IEEE Transactions on Evolutionary Computation 1 (1), 1997)

"[...] the NFL theorems mean that if an algorithm does particularly well on average for one class of problems then it must do worse on average over the remaining problems. In particular, if an algorithm performs better than random search on some class of problems then in must perform worse than random search on the remaining problems. Thus comparisons reporting the performance of a particular algorithm with a particular parameter setting on a few sample problems are of limited utility. While such results do indicate behavior on the narrow range of problems considered, one should be very wary of trying to generalize those results to other problems." (David H Wolpert & William G Macready, "No free lunch theorems for optimization", IEEE Transactions on Evolutionary Computation 1 (1), 1997)

"[...] if you have a general optimization involving uncertainty and very little prior knowledge, the situation is rather hopeless. Due to the NFL theorem, you cannot do any better than a blind search. Each blind search evaluation will be very expensive, with no hope of future improvement, theoretical or otherwise. And the number of performance searches required to get anywhere is simply too large. Neither time nor theoretical or technological progress are on your side. No grand optimization algorithm to end all algorithms is possible." (Yu-Chi Ho, "The no free lunch theorem and the human-machine interface", IEEE Control Systems Magazine, 1999)

"The No Free Lunch (NFL) theorem […] tells us that without any structural assumptions on an optimization problem, no algorithm can perform better on average than blind search." (Yu-Chi Ho, "The no free lunch theorem and the human-machine interface", IEEE Control Systems Magazine, 1999)

"[...] a general-purpose universal optimization strategy is theoretically impossible, and the only way one strategy can outperform another is if it is specialized to the specific problem under consideration." (Yu-Chi Ho & David L Pepyne, "Simple explanation of the no-free-lunch theorem and its implications", Journal of Optimization Theory and Applications 115, 2002)

"Because No Free Lunch is a well-known concept, researchers are increasingly interested in finding function classes that are well matched to their algorithms. The determination of an algorithm–class pairing is generally approximated by testing the algorithm on one of a number of benchmark functions, then generalizing the results by distilling various defining characteristics of those benchmarks." (Christopher K Monson, "No Free Lunch, Bayesian Inference, and Utility: A Decision-Theoretic Approach to Optimization", [thesis] 2006)

"Because No Free Lunch theorems dictate that no optimization algorithm can be considered more efficient than any other when considering all possible functions, the desired function class plays a prominent role in the model. In particular, this provides a tractable way to answer the traditionally difficult question of what algorithm is best matched to a particular class of functions. Among the benefits of the model are the ability to specify the function class in a straightforward manner, a natural way to specify noisy or dynamic functions, and a new source of insight into No Free Lunch theorems for optimization." (Christopher K Monson, "No Free Lunch, Bayesian Inference, and Utility: A Decision-Theoretic Approach to Optimization", [thesis] 2006)

"No Free Lunch dictates that any algorithm may be deceived, a difficulty to which the inference algorithm is not immune." (Christopher K Monson, "No Free Lunch, Bayesian Inference, and Utility: A Decision-Theoretic Approach to Optimization", [thesis] 2006)

"That the complexity of the problem is inherently tied to the flexibility of the representation of the prior serves to clarify part of No Free Lunch, especially the proof that problem difficulties cannot be ranked in the absence of a specific algorithm: it is not, in fact, the choice of algorithm that makes ranking possible among problems, but the choice of representation." (Christopher K Monson, "No Free Lunch, Bayesian Inference,and Utility: A Decision Theoretic Approach to Optimization", [thesis] 2006)

"The No Free Lunch work is a framework that addresses the core aspects of search, focusing on the connection between fitness functions and effective search algorithms. The central importance of this connection is demonstrated by the No Free Lunch theorem, which states that, averaged over all problems, all search algorithms perform equally. This result implies that if we are comparing a genetic algorithm to some other algorithm (e.g., simulated annealing, or even random search) and the genetic algorithm to some other algorithm (e.g., simulated annealing, or even random search) performs better for some class of problems, then the other algorithm necessarily performs better on problems outside the class. Thus it is essential to incorporate knowledge of the problem into the search algorithm." (S N Sivanandam & S N Deepa, "Introduction to Genetic Algorithms", 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)

"Methods perform well if the conditions of their derivation are met, with no method capable of covering all possible conditions. More strongly put, each good method has a domain on which it may be best, and different methods have different domains so the task is to characterize those domains and then figure out which domain a given problem’s solution is likely to be in. This of course, is extraordinarily difficult in its own right." (Bertrand Clarke et al, "Principles and Theory for Data Mining and Machine Learning", 2009)

"The well-known 'No Free Lunch' theorem indicates that there does not exist a pattern classification method that is inherently superior to any other, or even to random guessing without using additional information. It is the type of problem, prior information, and the amount of training samples that determine the form of classifier to apply. In fact, corresponding to different real-world problems, different classes may have different underlying data structures. A classifier should adjust the discriminant boundaries to fit the structures which are vital for classification, especially for the generalization capacity of the classifier." (Hui Xue et al, "SVM: Support Vector Machines", 2009)

"Another important fact, having impact on EA [Evolutionary Algorithm] use is so called No Free Lunch Theorem (NFLT) [...]. Main idea of this theorem is that there is no ideal algorithm which would be able to solve any problem. Simply, if there are for example two algorithms A and B, then for certain subset of possible problems is more suitable algorithms A and for another subset algorithm B. All those subsets can be of course totally disconnected, or/and overlapped." (Ivan Zelinka & Hendrik Richter, "Evolutionary Algorithms for Chaos Researchers", Studies in Computational Intelligence Vol. 267, 2010)

"Each learning algorithm dictates a certain model that comes with a set of assumptions. This inductive bias leads to error if the assumptions do not hold for the data. Learning is an ill-posed problem and with finite data, each algorithm converges to a different solution and fails under different circumstances. The performance of a learner may be fine-tuned to get the highest possible accuracy on a validation set, but this finetuning is a complex task and still there are instances on which even the best learner is not accurate enough. The idea is that there may be another base-learner learner that is accurate on these. By suitably combining multiple base learners then, accuracy can be improved." (Ethem Alpaydin, "Introduction to Machine Learning" 2nd Ed, 2010)

"The problem of comparing classifiers is not at all an easy task. There is no single classifier that works best on all given problems, phenomenon related to the 'No-free-lunch' metaphor, i.e., each classifier (’restaurant’) provides a specific technique associated with the corresponding costs (’menu’ and ’price’ for it). It is hence up to us, using the information and knowledge at hand, to find the optimal trade-off." (Florin Gorunescu, "Data Mining Concepts, Models and Techniques", 2011)

"As a consequence of the no free lunch theorem, we need to develop many different types of models, to cover the wide variety of data that occurs in the real world. And for each model, there may be many different algorithms we can use to train the model, which make different speed-accuracy-complexity tradeoffs." (Kevin P Murphy, "Machine Learning: A Probabilistic Perspective", 2012)

"Much of machine learning is concerned with devising different models, and different algorithms to fit them. We can use methods such as cross validation to empirically choose the best method for our particular problem. However, there is no universally best model - this is sometimes called the no free lunch theorem. The reason for this is that a set of assumptions that works well in one domain may work poorly in another." (Kevin P Murphy, "Machine Learning: A Probabilistic Perspective", 2012)

"The validity of NFL theorems largely depends on the validity of their fundamental assumptions. However, whether these assumptions are valid in practice is another question. Often, these assumptions are too stringent, and thus free lunches are possible." (Xin-She Yang, "Free Lunch or No Free Lunch: That is not Just a Question?", 2012)

"The idea of feature learning is to automate the process of finding a good representation of the input space. As mentioned before, the No-Free-Lunch theorem tells us that we must incorporate some prior knowledge on the data distribution in order to build a good feature representation." (Shai Shalev-Shwartz & Shai Ben-David, "Understanding Machine Learning: From Theory to Algorithms", 2014)

"We emphasize that while there are some common techniques for feature learning one may want to try, the No-Free-Lunch theorem implies that there is no ultimate feature learner. Any feature learning algorithm might fail on some problem. In other words, the success of each feature learner relies (sometimes implicitly) on some form of prior assumption on the data distribution. Furthermore, the relative quality of features highly depends on the learning algorithm we are later going to apply using these features." (Shai Shalev-Shwartz & Shai Ben-David, "Understanding Machine Learning: From Theory to Algorithms", 2014)

"Choosing an appropriate classification algorithm for a particular problem task requires practice: each algorithm has its own quirks and is based on certain assumptions. To restate the 'No Free Lunch' theorem: no single classifier works best across all possible scenarios. In practice, it is always recommended that you compare the performance of at least a handful of different learning algorithms to select the best model for the particular problem; these may differ in the number of features or samples, the amount of noise in a dataset, and whether the classes are linearly separable or not." (Sebastian Raschka, "Python Machine Learning", 2015)

"Learning theory claims that a machine learning algorithm can generalize well from a finite training set of examples. This seems to contradict some basic principles of logic. Inductive reasoning, or inferring general rules from a limited set of examples, is not logically valid. To logically infer a rule describing every member of a set, one must have information about every member of that set." (Ian Goodfellow et al, "Deep Learning", 2015)

"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)

"The no free lunch theorem implies that we must design our machine learning algorithms to perform well on a specific task. We do so by building a set of preferences into the learning algorithm. When these preferences are aligned with the learning problems we ask the algorithm to solve, it performs better." (Ian Goodfellow et al, "Deep Learning", 2015)

"The 'No free lunch' theorem demonstrates that it is not possible to find one algorithm behaving better for any problem. On the other hand, we know that we can work with different degrees of knowledge of the problem which we expect to solve, and that it is not the same to work without knowledge of the problem (hypothesis of the 'no free lunch' theorem) than to work with partial knowledge about the problem, knowledge that allows us to design algorithms with specific characteristics which can make them more suitable to solve of the problem." (Salvador García et al, "Data Preprocessing in Data Mining", 2015)

"Roughly stated, the No Free Lunch theorem states that in the lack of prior knowledge (i.e. inductive bias) on average all predictive algorithms that search for the minimum classification error (or extremum over any risk metric) have identical performance according to any measure." (N D Lewis, "Deep Learning Made Easy with R: A Gentle Introduction for Data Science", 2016)

"However, because ML algorithms are biased to look for different types of patterns, and because there is no one learning bias across all situations, there is no one best ML algorithm. In fact, a theorem known as the 'no free lunch theorem' states that there is no one best ML algorithm that on average outperforms all other algorithms across all possible data sets." (John D Kelleher & Brendan Tierney, "Data Science", 2018)

"The no free lunch theorems set limits on the range of optimality of any method. That is, each methodology has a ‘catchment area’ where it is optimal or nearly so. Often, intuitively, if the optimality is particularly strong then the effectiveness of the methodology falls off more quickly outside its catchment area than if its optimality were not so strong. Boosting is a case in point: it seems so well suited to binary classification that efforts to date to extend it to give effective classification (or regression) more generally have not been very successful. Overall, it remains to characterize the catchment areas where each class of predictors performs optimally, performs generally well, or breaks down." (Bertrand S Clarke & Jennifer L. Clarke, "Predictive Statistics: Analysis and Inference beyond Models", 2018)

"The No Free Lunch theorems prove that under a uniform distribution over induction problems (search problems or learning problems), all induction algorithms perform equally.  […] the importance of the theorems arises by using them to analyze scenarios involving non-uniform distributions, and to compare different algorithms, without any assumption about the distribution over problems at all. In particular, the theorems prove that anti-cross-validation (choosing among a set of candidate algorithms based on which has worst out-of-sample behavior) performs as well as cross-validation, unless one makes an assumption - which has never been formalized - about how the distribution over induction problems, on the one hand, is related to the set of algorithms one is choosing among using (anti-)cross validation, on the other. In addition, they establish strong caveats concerning the significance of the many results in the literature which establish the strength of a particular algorithm without assuming a particular distribution." (David H Wolpert, "What is important about the No Free Lunch theorems?", 2020)

"A well-known theorem called the 'no free lunch' theorem proves exactly what we anecdotally witness when designing and building learning systems. The theorem states that any bias-free learning system will perform no better than chance when applied to arbitrary problems. This is a fancy way of stating that designers of systems must give the system a bias deliberately, so it learns what’s intended. As the theorem states, a truly bias- free system is useless." (Erik J Larson, "The Myth of Artificial Intelligence: Why Computers Can’t Think the Way We Do", 2021)