🖍️Mike Barlow - Collected Quotes

"Applying data science principles to solve social problems and improve the lives of ordinary people seems like a logical idea, but it is by no means a given. Using data science to elevate the human condition won’t happen by accident; groups of people will have to envision it, develop the routine processes and underlying infrastructures required to make it practical, and then commit the time and energy necessary to make it all work." (Mike Barlow, "Learning to Love Data Science", 2015)

"Hollywood loves the myth of a lone scientist working late nights in a dark laboratory on a mysterious island, but the truth is far less melodramatic. Real science is almost always a team sport. Groups of people, collaborating with other groups of people, are the norm in science - and data science is no exception to the rule. When large groups of people work together for extended periods of time, a culture begins to emerge." (Mike Barlow, "Learning to Love Data Science", 2015)

"In other words, real-time denotes the ability to process data as it arrives, rather than storing the data and retrieving it at some point in the future. That’s the primary significance of the term - real-time means that you’re processing data in the present, rather than in the future." (Mike Barlow, "Learning to Love Data Science", 2015)

"The ability to manage large and complex sets of data hasn’t diminished the appetite for more size and greater speed. Every day it seems that a new technique or application is introduced that pushes the edges of the speed-size envelope even further." (Mike Barlow, "Learning to Love Data Science", 2015)

"The cultural component of big data is neither trivial nor free. It is not a list of 'feel-good' or 'fluffy' attributes that are posted on a corporate website. Culture (that is, people and processes) is integral and critical to the success of any new technology deployment or implementation." (Mike Barlow, "Learning to Love Data Science", 2015)

"The whole point of machine learning is automating the learning process itself, enabling the computer program to get better as it consumes more data, without requiring the continual intervention of a programmer." (Mike Barlow, "Learning to Love Data Science", 2015)

🖍️Peter C Bruce - Collected Quotes

"A popular misconception holds that the era of Big Data means the end of a need for sampling. In fact, the proliferation of data of varying quality and relevance reinforces the need for sampling as a tool to work efficiently with a variety of data, and minimize bias. Even in a Big Data project, predictive models are typically developed and piloted with samples." (Peter C Bruce & Andrew G Bruce, "Statistics for Data Scientists: 50 Essential Concepts", 2016)

"Do not confuse standard deviation (which measures the variability of individual data points) with standard error (which measures the variability of a sample metric)." (Peter C Bruce & Andrew G Bruce, "Statistics for Data Scientists: 50 Essential Concepts", 2016)

"In statistical theory, location and variability are referred to as the first and second moments of a distribution. The third and fourth moments are called skewness and kurtosis. Skewness refers to whether the data is skewed to larger or smaller values and kurtosis indicates the propensity of the data to have extreme values. Generally, metrics are not used to measure skewness and kurtosis; instead, these are discovered through visual displays [...]" (Peter C Bruce & Andrew G Bruce, "Statistics for Data Scientists: 50 Essential Concepts", 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)

"Moreover, data science (and business in general) is not so worried about statistical significance, but more concerned with optimizing overall effort and results." (Peter C Bruce & Andrew G Bruce, "Statistics for Data Scientists: 50 Essential Concepts", 2016)

"Statisticians often use the term estimates for values calculated from the data at hand, to draw a distinction between what we see from the data, and the theoretical true or exact state of affairs. Data scientists and business analysts are more likely to refer to such values as a metric. The difference reflects the approach of statistics versus data science: accounting for uncertainty lies at the heart of the discipline of statistics, whereas concrete business or organizational objectives are the focus of data science. Hence, statisticians estimate, and data scientists measure." (Peter C Bruce & Andrew G Bruce, "Statistics for Data Scientists: 50 Essential Concepts", 2016)

"The bootstrap does not compensate for a small sample size; it does not create new data, nor does it fill in holes in an existing data set. It merely informs us about how lots of additional samples would behave when drawn from a population like our original sample." (Peter C Bruce & Andrew G Bruce, "Statistics for Data Scientists: 50 Essential Concepts", 2016)

"The tension between oversmoothing and overfitting is an instance of the bias-variance tradeoff, an ubiquitous problem in statistical model fitting. Variance refers to the modeling error that occurs because of the choice of training data; that is, if you were to choose a different set of training data, the resulting model would be different. Bias refers to the modeling error that occurs because you have not properly identified the underlying real-world scenario; this error would not disappear if you simply added more training data. When a flexible model is overfit, the variance increases. You can reduce this by using a simpler model, but the bias may increase due to the loss of flexibility in modeling the real underlying situation." (Peter C Bruce & Andrew G Bruce, "Statistics for Data Scientists: 50 Essential Concepts", 2016)

"The variance, the standard deviation, mean absolute deviation, and median absolute deviation from the median are not equivalent estimates, even in the case where the data comes from a normal distribution. In fact, the standard deviation is always greater than the mean absolute deviation, which itself is greater than the median absolute deviation. Sometimes, the median absolute deviation is multiplied by a constant scaling factor (it happens to work out to 1.4826) to put MAD on the same scale as the standard deviation in the case of a normal distribution." (Peter C Bruce & Andrew G Bruce, "Statistics for Data Scientists: 50 Essential Concepts", 2016)

"When analysts and researchers use the term regression by itself, they are typically referring to linear regression; the focus is usually on developing a linear model to explain the relationship between predictor variables and a numeric outcome variable. In its formal statistical sense, regression also includes nonlinear models that yield a functional relationship between predictors and outcome variables. In the machine learning community, the term is also occasionally used loosely to refer to the use of any predictive model that produces a predicted numeric outcome (standing in distinction from classification methods that predict a binary or categorical outcome)." (Peter C Bruce & Andrew G Bruce, "Statistics for Data Scientists: 50 Essential Concepts", 2016)

🖍️Alessandro Negro - Collected Quotes

"A graph is a simple and quite old mathematical concept: a data structure consisting of a set of vertices (or nodes/points) and edges (or relationships/lines) that can be used to model relationships among a collection of objects." (Alessandro Negro, "Graph-Powered Machine Learning", 2021)

"A widely adopted technique for solving the data sparsity issue and the cold-start problem is based on graph representation, navigation, and processing. Graph navigation methods (like the pathfinding example [...]) and graph algorithms (such as PageRank) are applied to fill some gaps and create a denser representation of [a] dataset." (Alessandro Negro, "Graph-Powered Machine Learning", 2021)

"Deep learning approaches the problem of representation learning by introducing representations that are expressed in terms of other, simpler representations. In deep learning, the machine builds multiple levels of increasing complexity over the underlying simpler concepts." (Alessandro Negro, "Graph-Powered Machine Learning", 2021)

"GNNs are capable of generating representations of nodes that depend on the structure of the graph as well as on any feature information we have. These features could be nodes’ properties, relationship types, and relationship properties. That’s why GNNs could drive the final tasks to better results. These embeddings represent the input for tasks such as node classification, link prediction, and graph classification." (Alessandro Negro, "Graph-Powered Machine Learning", 2021)

"[...] graphs are extremely useful for encoding information, and data in graph format is increasingly plentiful. In many areas of machine learning - including natural language processing, computer vision, and recommendations - graphs are used to model local relationships between isolated data items (users, items, events, and so on) and to construct global structures from local information. Representing data as graphs is often a necessary step (and at other times only a desirable one) in dealing with problems arising from applications in machine learning or data mining." (Alessandro Negro, "Graph-Powered Machine Learning", 2021)

"Graphs are powerful structures useful not only for representing connected information, but also for supporting multiple types of analysis. Their simple data model, consisting of two basic concepts such as nodes and relationships, is flexible enough to store complex information. If you also store properties in nodes and relationships, it is possible to represent practically everything of any size." (Alessandro Negro, "Graph-Powered Machine Learning", 2021)

"Graphs are useful for representing how things are either physically or logically linked in simple or complex structures. A graph in which we assign names and meanings to the edges and vertices becomes what is known as a network. In these cases, a graph is the mathematical model for describing a network, whereas a network is a set of relations between objects, which could include people, organizations, nations, items found in a Google search, brain cells, or electrical transformers." (Alessandro Negro, "Graph-Powered Machine Learning", 2021)

"Graphs can be used to model and analyze the relationships between entities as well as their properties. This aspect brings an additional dimension of information that graph-powered machine learning can harness for prediction and categorization. The schema flexibility provided by graphs also allows different models to coexist in the same dataset." (Alessandro Negro, "Graph-Powered Machine Learning", 2021)

"Graphs can support machine learning by doing what they do best: representing data in a way that is easily understandable and easily accessible. Graphs make all the necessary processes faster, more accurate, and much more effective. Moreover, graph algorithms are powerful tools for machine learning practitioners. Graph community detection algorithms can help identify groups of people, page rank can reveal the most relevant keywords in a text, and so on." (Alessandro Negro, "Graph-Powered Machine Learning", 2021)

"Graphs, with multiple node types and different types of relationships, are far from being a Euclidean space. This task is where graph neural networks (GNNs) comes in. GNNs are deep learning-based methods that operate on a graph domain to perform complex tasks such as node classification (the bot example), link prediction (the disease example), and so on. Due to its convincing performance, GNN has become a widely applied graph analysis method." (Alessandro Negro, "Graph-Powered Machine Learning", 2021)

"In many areas of machine learning, graphs are used to model local relationships between data elements and to build global structures from local information. Building graphs is sometimes necessary for dealing with problems arising from applications in machine learning or data mining, and at other times, it's helpful for managing data. It's important to note that the transformation from the original data to a graph data representation can always be performed in a lossless manner. The opposite is not always true." (Alessandro Negro, "Graph-Powered Machine Learning", 2021)

"One of the main goals of machine learning is to make sense of data and deliver some sort of predictive capability to the end user ([...] data analysis in general aims at extracting knowledge, insights, and finally wisdom from raw data sources, and prediction represents a small portion of possible uses). In this learning path, data visualization plays a key role because it allows us to access and analyze data from a different perspectiv." (Alessandro Negro, "Graph-Powered Machine Learning", 2021)

"The performance of machine learning algorithms, both in terms of accuracy and speed, is affected almost directly from the way in which we represent our training data and store our prediction model. The quality of algorithm prediction is as good as the quality of the training dataset. Data cleansing and feature selection, among other tasks, are mandatory if we would like to achieve a reasonable level of trust in the prediction. The speed at which the system provides prediction affects the usability of the entire product." (Alessandro Negro, "Graph-Powered Machine Learning", 2021)

"To compute the similarity between items, we must define a similarity measure. Cosine similarity is the standard metric in item-based recommendation approaches: it determines the similarity between two vectors by calculating the cosine of the angle between them In machine learning applications, this measure is often used to compare two text documents, which are represented as vectors of terms [...] prediction represents a small portion of possible uses). In this learning path, data visualization plays a key role because it allows us to access and analyze data from a different perspective." (Alessandro Negro, "Graph-Powered Machine Learning", 2021)

"Despite their effectiveness and advantages in supporting the development of intel-ligent systems, KGs haven’t been widely adopted for several reasons, including the following: (•) They are expensive to build and maintain in terms of time, effort, and money. (•) Intricate access patterns are required to navigate multiple hops. (•) Their results scatter information across multiple nodes and relationships." (Alessandro Negro, "Graph-Powered Machine Learning", 2021)

"A knowledge graph is an ever-evolving graph data structure composed of a set of typed entities, their attributes, and meaningful named rela-tionships. Built for a specific domain, it integrates both structured and unstructured data to craft knowledge for humans and machines." (Alessandro Negro, "Graph-Powered Machine Learning", 2021) 

"Generative artificial intelligence (GenAI), powered by large language models (LLMs) like Google’s Gemini and OpenAI’s GPT, has transformed how we work and live, revolutionizing business after business. Despite this success, generative AI falls short in domains where specific domain knowledge, high accuracy, and explainability are essential. And it has other significant limitations, including hallucinations and a lack of context and relations. This is where knowledge graphs (KGs) come in, provid-ing contextual information - such as experiences, environmental characteristics, cultural aspects, and social normsneeded to build the 'third wave of AI' for mission-critical applications." (Alessandro Negro et al, "Knowledge Graphs and LLMs in Action", 2026)

"Intelligent systems connect users to AI and ML to achieve meaningful objectives. An intelligent system is one in which intelligence evolves and improves over time, particularly when it improves by watching how users interact with the system.[...] The primary objective of the intelligent system is to support users in accomplishing complex tasks - not by replacing them, but by enhancing their decision-making capabilities. [...] An intelligent system must also have the ability to learn from user interactions and explicit feedback, as well as utilize contextual information. The system should contin-uously develop, use, and maintain an evolving knowledge base. This evolution is driven not only by data sources but also by ongoing interactions with users." (Alessandro Negro et al, "Knowledge Graphs and LLMs in Action", 2026)

"[...] KGs and LLMs can be the foundation for different types of reasoning, complementing each other in intelligent systems. We can use KGs for tasks that require precise, rule-based reasoning and explicit knowledge representation, and LLMs for tasks involving pattern recognition, context understanding, handling ambiguity or incomplete information, and reasoning about graph structures and their derived metrics. However, neither approach inherently possesses common-sense reasoning capabilities comparable to those of humans, and they often fail to make intuitive leaps or understand the implicit context that would be obvious to a person. These limitations underscore the importance of carefully considering the strengths and weaknesses of each approach when designing intelligent systems and potentially developing a powerful hybrid IAS." (Alessandro Negro et al, "Knowledge Graphs and LLMs in Action", 2026) 

"KGs are sophisticated graph structures that represent real-world entities (people, places, diseases, proteins), define meaningful connections between them, and provide context. KGs provide structured, explainable knowledge representation but are challenging to build and query; LLMs offer natural language processing capabilities but suffer from hallucinations, stale information, and a lack of domain-specific grounding. Together, they are a 'killer combination': LLMs can extract entities and relationships from unstructured text to build KGs more efficiently, providing more autonomous and powerful graph querying and analysis. Meanwhile, KGs provide reliable, up-to-date domain knowledge to ground LLM responses and prevent hallucinations." (Alessandro Negro et al, "Knowledge Graphs and LLMs in Action", 2026)

"Knowledge representation is the 'language' that AI systems use to structure, encode, and communicate information about the domain they are modelling. AI systems need it to reason or predict, and we use it to interpret the results they produce. The choice of how to represent knowledge can significantly affect the capabilities and limitations of the AI system." (Alessandro Negro et al, "Knowledge Graphs and LLMs in Action", 2026)

"Reasoning is the cognitive process of analyzing information, applying rules, and drawing conclusions based on evidence or premises. There are various types, such as deductive and inductive reasoning, each serving different purposes in problem-solving and decision-making. AI systems, particularly those combining KGs and LLMs, are increasingly adept at mimicking and even enhancing this fundamental cognitive skill." (Alessandro Negro et al, "Knowledge Graphs and LLMs in Action", 2026)

"The KG serves as the central reference for all structured and unstructured data related to a domain. Because a KG represents information by focusing on the meaning of data, users can overcome challenges related to data types, formats, and provenance, connecting information from multiple data sources. [...] A KG represents the core information and big picture of a domain. Humans can analyze, visualize, and query graph data to extract insights. Inference rules and machine learning algorithms are performed on top of the KG to infer new information not explicitly encoded within the KG. Analysts can use methods such as centrality and connectivity analysis to identify influential nodes, network analysis to detect the shortest path between nodes, and community analysis to recognize groups of similar nodes." (Alessandro Negro et al, "Knowledge Graphs and LLMs in Action", 2026) 

"Traditional paradigms build systems for specific purposes with structured, homogeneous databases. This approach works for tailored needs but is impractical for complex domains that need to adapt to user characteristics and integrate heterogeneous data. KGs capture connections, enabling relationship discovery through graph pattern matching and traversal. Both the Resource Description Framework (RDF) and Labeled Property Graphs (LPGs) provide machine-readable formats that humans can interpret. KGs emphasize rich, meaningful data representations usable by both humans and machines, enabling a paradigm shift where intelligent behavior is encoded in a unique source of truth." (Alessandro Negro et al, "Knowledge Graphs and LLMs in Action", 2026)

🖍️Pedro Domingos - Collected Quotes

"A learner that uses Bayes’ theorem and assumes the effects are independent given the cause is called a Naïve Bayes classifier. That’s because, well, that’s such a naïve assumption." (Pedro Domingos, "The Master Algorithm", 2015)

"An algorithm is not just any set of instructions: they have to be precise and unambiguous enough to be executed by a computer. [...] The computer has to know how to execute the algorithm all the way down to turning specific transistors on and off." (Pedro Domingos, "The Master Algorithm", 2015)

"As so often happens in computer science, we’re willing to sacrifice efficiency for generality." (Pedro Domingos, "The Master Algorithm", 2015)

"Believe it or not, every algorithm, no matter how complex, can be reduced to just these three operations: AND, OR, and NOT." (Pedro Domingos, "The Master Algorithm", 2015)

"Designing an algorithm is not easy. Pitfalls abound, and nothing can be taken for granted. Some of your intuitions will turn out to have been wrong, and you’ll have to find another way. On top of designing the algorithm, you have to write it down in a language computers can understand, like Java or Python (at which point it’s called a program). Then you have to debug it: find every error and fix it until the computer runs your program without screwing up. But once you have a program that does what you want, you can really go to town." (Pedro Domingos, "The Master Algorithm", 2015)

"Dimensionality reduction is essential for coping with big data—like the data coming in through your senses every second. A picture may be worth a thousand words, but it’s also a million times more costly to process and remember. [...] A common complaint about big data is that the more data you have, the easier it is to find spurious patterns in it. This may be true if the data is just a huge set of disconnected entities, but if they’re interrelated, the picture changes." (Pedro Domingos, "The Master Algorithm", 2015)

"Every algorithm has an input and an output: the data goes into the computer, the algorithm does what it will with it, and out comes the result. Machine learning turns this around: in goes the data and the desired result and out comes the algorithm that turns one into the other. Learning algorithms - also known as learners - are algorithms that make other algorithms. With machine learning, computers write their own programs, so we don’t have to." (Pedro Domingos, "The Master Algorithm", 2015)

"In machine learning, knowledge is often in the form of statistical models, because most knowledge is statistical [...] Machine learning is a kind of knowledge pump: we can use it to extract a lot of knowledge from data, but first we have to prime the pump." (Pedro Domingos, "The Master Algorithm", 2015)

"Learning is forgetting the details as much as it is remembering the important parts." (Pedro Domingos, "The Master Algorithm", 2015)

"Machine learning takes many different forms and goes by many different names: pattern recognition, statistical modeling, data mining, knowledge discovery, predictive analytics, data science, adaptive systems, self-organizing systems, and more. Each of these is used by different communities and has different associations. Some have a long half-life, some less so." (Pedro Domingos, "The Master Algorithm", 2015)

"Our beliefs are based on our experience, which gives us a very incomplete picture of the world, and it's easy to jump to false conclusions." (Pedro Domingos, "The Master Algorithm", 2015)

"People often think computers are all about numbers, but they’re not. Computers are all about logic." (Pedro Domingos, "The Master Algorithm", 2015)

"Science’s predictions are more trustworthy, but they are limited to what we can systematically observe and tractably model. Big data and machine learning greatly expand that scope. Some everyday things can be predicted by the unaided mind, from catching a ball to carrying on a conversation. Some things, try as we might, are just unpredictable. For the vast middle ground between the two, there’s machine learning." (Pedro Domingos, "The Master Algorithm", 2015)

"To make progress, every field of science needs to have data commensurate with the complexity of the phenomena it studies. [...] With big data and machine learning, you can understand much more complex phenomena than before. In most fields, scientists have traditionally used only very limited kinds of models, like linear regression, where the curve you fit to the data is always a straight line. Unfortunately, most phenomena in the world are nonlinear. [...] Machine learning opens up a vast new world of nonlinear models." (Pedro Domingos, "The Master Algorithm", 2015)

"Today we routinely learn models with millions of parameters, enough to give each elephant in the world his own distinctive wiggle. It’s even been said that data mining means 'torturing the data until it confesses'." (Pedro Domingos, "The Master Algorithm", 2015)

"Traditionally, the only way to get a computer to do something - from adding two numbers to flying an airplane - was to write down an algorithm explaining how, in painstaking detail. But machine-learning algorithms, also known as learners, are different: they figure it out on their own, by making inferences from data. And the more data they have, the better they get. Now we don’t have to program computers; they program themselves." (Pedro Domingos, "The Master Algorithm", 2015)

"Whoever has the best algorithms and the most data wins. A new type of network effect takes hold: whoever has the most customers accumulates the most data, learns the best models, wins the most new customers, and so on in a virtuous circle (or a vicious one, if you’re the competition)." (Pedro Domingos, "The Master Algorithm", 2015)

🖍️Richard Levins - Collected Quotes

"A mathematical model is neither an hypothesis nor a theory. Unlike the scientific hypothesis, a model is not verifiable directly by experiment. For all models are both true and false. Almost any plausible proposed relation among aspects of nature is likely to be true in the sense that it occurs (although rarely and slightly). Yet all models leave out a lot and are in that sense false, incomplete, inadequate. The validation of a model is not that it is ' 'true" but that it generates good testable hypotheses relevant to important problems. A model may be discarded in favor of a more powerful one, but it usually is simply outgrown when the live issues are not any longer those for which it was designed." (Richard Levins, "The Strategy of Model Building in Population Biology", American Scientist 54(4), 1966)

"For population genetics, a population is specified by the frequencies of genotypes without reference to the age distribution, physiological state as a reflection of past history, or population density. A single population or species is treated at a time, and evolution is usually assumed to occur in a constant environment. Population ecology, on the other hand, recognizes multispecies systems, describes populations in terms of their age distributions, physiological states, and densities. The environment is allowed to vary but the species are treated as genetically homogeneous, so that evolution is ignored." (Richard Levins, "The Strategy of Model Building in Population Biology", American Scientist 54(4), 1966)

"It is of course desirable to work with manageable models which maximize generality, realism, and precision toward the overlapping but not identical goals of understanding, predicting, and modifying nature. But this cannot be done. Therefore, several alternative strategies have evolved: (1) Sacrifice generality to realism and precision. (2) Sacrifice realism to generality and precision. (3) Sacrifice precision to realism and generality." (Richard Levins, "The strategy of model building in population biology", American Scientist Vol. 54 (4), 1966) 

"The multiplicity of models is imposed by the contradictory demands of a complex, heterogeneous nature and a mind that can only cope with few variables at a time; by the contradictory desiderata of generality, realism, and precision; by the need to understand and also to control; even by the opposing esthetic standards which emphasize the stark simplicity and power of a general theorem as against the richness and the diversity of living nature. These conflicts are irreconcilable. Therefore, the alternative approaches even of contending schools are part of a larger mixed strategy. But the conflict is about method, not nature, for the individual models, while they are essential for understanding reality, should not be confused with that reality itself." (Richard Levins, "The Strategy of Model Building in Population Biology", American Scientist 54(4), 1966)

"The validation of a model is not that it is 'true' but that it generates good testable hypotheses relevant to important problems." (Richard Levins, "The Strategy of Model Building in Population Biology", American Scientist 54(4), 1966)

"[…] truth is the intersection of independent lies." (Richard Levins, "The Strategy of Model Building in Population Biology", 1966)

"Unlike the theory, models are restricted by technical considerations to a few components at a time, even in systems which are complex. Thus a satisfactory theory is usually a cluster of models. These models are related to each other in several ways : as coordinate alternative models for the same set of phenomena, they jointly produce robust theorems; as complementary models they can cope with different aspects of the same problem and give complementary as well as overlapping results; as hierarchically arranged 'nested' models, each provides an interpretation of the sufficient parameters of the next higher level where they are taken as given." (Richard Levins, "The Strategy of Model Building in Population Biology", American Scientist 54(4), 1966)

"Parts and wholes evolve in consequence of their relationship, and the relationship itself evolves. These are the properties of things that we call dialectical: that one thing cannot exist without the other, that one acquires its properties from its relation to the other, that the properties of both evolve as a consequence of their interpenetration."  (Richard Levins & Richard C Lewontin, "The Dialectical Biologist", 1985)

"The organism cannot be regarded as simply the passive object of autonomous internal and external forces; it is also the subject of its own evolution." (Richard Levins & Richard C Lewontin, "The Dialectical Biologist", 1985)

"We believe that science, in all its sense, is a social process that both causes and is caused by social organisation."  (Richard Levins & Richard C Lewontin, "The Dialectical Biologist", 1985)

🖍️Amit Ray - Collected Quotes

"Artificial intelligence is defined as the branch of science and technology that is concerned with the study of software and hardware to provide machines the ability to learn insights from data and the environment, and the ability to adapt in changing situations with high precision, accuracy and speed." (Amit Ray, "Compassionate Artificial Intelligence", 2018)

"Artificial Intelligence is not just learning patterns from data, but understanding human emotions and its evolution from its depth and not just fulfilling the surface level human requirements, but sensitivity towards human pain, happiness, mistakes, sufferings and well-being of the society are the parts of the evolving new AI systems." (Amit Ray, "Compassionate Artificial Intelligence", 2018)

"Quantum Machine Learning is defined as the branch of science and technology that is concerned with the application of quantum mechanical phenomena such as superposition, entanglement and tunneling for designing software and hardware to provide machines the ability to learn insights and patterns from data and the environment, and the ability to adapt automatically to changing situations with high precision, accuracy and speed." (Amit Ray, "Quantum Computing Algorithms for Artificial Intelligence", 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)

"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)

"You can't understand depth of science, unless you challenge the published scientific data." (Amit Ray)

🖍️Aleksander Molak - Collected Quotes

"An important concept in complexity science is emergence – a phenomenon in which we can observe certain properties at the system level that cannot be observed at its constituent parts’ level. This property is sometimes described as a system being more than the sum of its parts." (Aleksander Molak, "Causal Inference and Discovery in Python", 2023)

"Any time you run regression analysis on arbitrary real-world observational data, there’s a significant risk that there’s hidden confounding in your dataset and so causal conclusions from such analysis are likely to be (causally) biased." (Aleksander Molak, "Causal Inference and Discovery in Python", 2023)

"Expert knowledge is a term covering various types of knowledge that can help define or disambiguate causal relations between two or more variables. Depending on the context, expert knowledge might refer to knowledge from randomized controlled trials, laws of physics, a broad scope of experiences in a given area, and more." (Aleksander Molak, "Causal Inference and Discovery in Python", 2023)

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

"In summary, the relationship between different branches of contemporary machine learning and causality is nuanced. That said, most broadly adopted machine learning models operate on rung one, not having a causal world model." (Aleksander Molak, "Causal Inference and Discovery in Python", 2023)

"'Let the data speak'" is a catchy and powerful slogan, but [...] data itself is not always enough. It’s worth remembering that in many cases 'data cannot speak for themselves' and we might need more information than just observations to address some of our questions." (Aleksander Molak, "Causal Inference and Discovery in Python", 2023)

"Matching is a family of methods for estimating causal effects by matching similar observations (or units) in the treatment and non-treatment groups. The goal of matching is to make comparisons between similar units in order to achieve as precise an estimate of the true causal effect as possible." (Aleksander Molak, "Causal Inference and Discovery in Python", 2023)

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

"Non-linear associations are also quantifiable. Even linear regression can be used to model some non-linear relationships. This is possible because linear regression has to be linear in parameters, not necessarily in the data. More complex relationships can be quantified using entropy-based metrics such as mutual information. Linear models can also handle interaction terms. We talk about interaction when the model’s output depends on a multiplicative relationship between two or more variables." (Aleksander Molak, "Causal Inference and Discovery in Python", 2023)

"The basic goal of causal inference is to estimate the causal effect of one set of variables on another. In most cases, to do it accurately, we need to know which variables we should control for. [...] to accurately control for confounders, we need to go beyond the realm of pure statistics and use the information about the data-generating process, which can be encoded as a (causal) graph. In this sense, the ability to translate between graphical and statistical properties is central to causal inference." (Aleksander Molak, "Causal Inference and Discovery in Python", 2023)

"The causal interpretation of linear regression only holds when there are no spurious relationships in your data. This is the case in two scenarios: when you control for a set of all necessary variables (sometimes this set can be empty) or when your data comes from a properly designed randomized experiment." (Aleksander Molak, "Causal Inference and Discovery in Python", 2023)

"The first level of creativity [for evaluating causal models] is to use the refutation tests [...] The second level of creativity is available when you have access to historical data coming from randomized experiments. You can compare your observational model with the experimental results and try to adjust your model accordingly. The third level of creativity is to evaluate your modeling approach on simulated data with known outcomes. [...] The fourth level of creativity is sensitivity analysis." (Aleksander Molak, "Causal Inference and Discovery in Python", 2023)

"[...] the modularity assumption states that when we perform a (perfect) intervention on one variable in the system, the only structural change that takes place in this system is the removal of this variable’s incoming edges (which is equivalent to the modification of its structural equation) and the rest of the system remains structurally unchanged." (Aleksander Molak, "Causal Inference and Discovery in Python", 2023)

🖍️Manfred Drosg - Collected Quotes

"A histogram consists of the outline of bars of equal width and appropriate length next to each other. By connecting the frequency values at the position of the nominal values (the midpoints of the intervals) with straight lines, a frequency polygon is obtained. Attaching classes with frequency zero at either end makes the area (the integral) under the frequency polygon equal  to that under the histogram." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"A valid digit is not necessarily a significant digit. The significance of numbers is a result of its scientific context." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"[myth:] Accuracy is more important than precision. For single best estimates, be it a mean value or a single data value, this question does not arise because in that case there is no difference between accuracy and precision. (Think of a single shot aimed at a target.) Generally, it is good practice to balance precision and accuracy. The actual requirements will differ from case to case." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"Any scientific data without (a stated) uncertainty is of no avail. Therefore the analysis and description of uncertainty are almost as important as those of the data value itself . It should be clear that the uncertainty itself also has an uncertainty – due to its nature as a scientific quantity – and so on. The uncertainty of an uncertainty is generally not determined." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"As uncertainties of scientific data values are nearly as important as the data values themselves, it is usually not acceptable that a best estimate is only accompanied by an estimated uncertainty. Therefore, only the size of nondominant uncertainties should be estimated. For estimating the size of a nondominant uncertainty we need to find its upper limit, i.e., we want to be as sure as possible that the uncertainty does not exceed a certain value." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"Before best estimates are extracted from data sets by way of a regression analysis, the uncertainties of the individual data values must be determined.In this case care must be taken to recognize which uncertainty components are common to all the values, i.e., those that are correlated (systematic)." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"Before discarding a data point one should investigate the possible reasons for this faulty data value." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"Correlation analysis can help us find the size of the formal relation between two properties. An equidirectional variation is present if we observe high values of one variable together with high values of the other variable (or low ones combined with low ones). In this case there is a positive correlation. If high values are combined with low values and low values with high values, the variation is counterdirectional, and the correlation is negative." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"[myth:] Counting can be done without error. Usually, the counted number is an integer and therefore without (rounding) error. However, the best estimate of a scientifically relevant value obtained by counting will always have an error. These errors can be very small in cases of consecutive counting, in particular of regular events, e.g., when measuring frequencies." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"Due to the theory that underlies uncertainties an infinite number of data values would be necessary to determine the true value of any quantity. In reality the number of available data values will be relatively small and thus this requirement can never be fully met; all one can get is the best estimate of the true value." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"For linear dependences the main information usually lies in the slope. It is obvious that those points that lie far apart have the strongest influence on the slope if all points have the same uncertainty. In this context we speak of the strong leverage of distant points; when determining the parameter “slope” these distant points carry more effective weight. Naturally, this weight is distinct from the “statistical” weight usually used in regression analysis." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"For some scientific data the true value cannot be given by a constant or some straightforward mathematical function but by a probability distribution or an expectation value. Such data are called probabilistic. Even so, their true value does not change with time or place, making them distinctly different from  most statistical data of everyday life." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"If there is an outlier there are two possibilities: The model is wrong– after all, a theory is the basis on which we decide whether a data point is an outlier (an unexpected value) or not. The value of the data point is wrong because of a failure of the apparatus or a human mistake. There is a third possibility, though: The data point might not be an actual  outlier, but part of a (legitimate) statistical fluctuation." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"In error analysis the so-called 'chi-squared' is a measure of the agreement between the uncorrelated internal and the external uncertainties of a measured functional relation. The simplest such relation would be time independence. Theory of the chi-squared requires that the uncertainties be normally distributed. Nevertheless, it was found that the test can be applied to most probability distributions encountered in practice." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"In many cases systematic errors are interpreted as the systematic difference between nature (which is being questioned by the experimenter in his experiment) and the model (which is used to describe nature). If the model used is not good enough, but the measurement result is interpreted using this model, the final result (the interpretation) will be wrong because it is biased, i.e., it has a systematic deviation (not uncertainty). If we do not use the best model (the best theory) available for the description of a certain phenomenon this procedure is just wrong. It has nothing to do with an uncertainty." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"In science we try to explain reality by using models (theories). This is necessary because reality itself is too complex. So we need to come up with a model for that aspect of reality we want to understand – usually with the help of mathematics. Of course, these models or theories can only be simplifications of that part of reality we are looking at. A model can never be a perfect description of reality, and there can never be a part of reality perfectly mirroring a model." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"It is also inevitable for any model or theory to have an uncertainty (a difference between model and reality). Such uncertainties apply both to the numerical parameters of the model and to the inadequacy of the model as well. Because it is much harder to get a grip on these types of uncertainties, they are disregarded, usually." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"It is important that uncertainty components that are independent of each other are added quadratically. This is also true for correlated uncertainty components, provided they are independent of each other, i.e., as long as there is no correlation between the components." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"It is important to pay heed to the following detail: a disadvantage of logarithmic diagrams is that a graphical integration is not possible, i.e., the area under the curve (the integral) is of no relevance." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"It is the aim of all data analysis that a result is given in form of the best estimate of the true value. Only in simple cases is it possible to use the data value itself as result and thus as best estimate." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"It is the nature of an uncertainty that it is not known and can never be known, whether the best estimate is greater or less than the true value." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"Outliers or flyers are those data points in a set that do not quite fit within the rest of the data, that agree with the model in use. The uncertainty of such an outlier is seemingly too small. The discrepancy between outliers and the model should be subject to thorough examination and should be given much thought. Isolated data points, i.e., data points that are at some distance from the bulk of the data are not outliers if their values are in agreement with the model in use." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"[myth:] Random errors can always be determined by repeating measurements under identical conditions. […] this statement is true only for time-related random errors ." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"[myth:] Systematic errors can be determined inductively. It should be quite obvious that it is not possible to determine the scale error from the pattern of data values." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"The fact that the same uncertainty (e.g., scale uncertainty) is uncorrelated if we are dealing with only one measurement, but correlated (i.e., systematic) if we look at more than one measurement using the same instrument shows that both types of uncertainties are of the same nature. Of course, an uncertainty keeps its characteristics (e.g., Poisson distributed), independent of the fact whether it occurs only once or more often." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"To fulfill the requirements of the theory underlying uncertainties, variables with random uncertainties must be independent of each other and identically distributed. In the limiting case of an infinite number of such variables, these are called normally distributed. However, one usually speaks of normally distributed variables even if their number is finite." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

🖍️Aldo Marzullo - Collected Quotes

"[...] a graph is a mathematical model that is used for describing relationships between entities. However, each complex network presents intrinsic properties. Such properties can be measured by particular metrics, and each measure may characterize one or several local and global aspects of the graph." (Aldo Marzullo et al, "Graph Machine Learning" 2nd Ed., 2025)

"A point of caution when dealing with projections: be aware of the dimension of the projected graph.  In certain cases, such as the one we are considering here, projection may create extremely large numbers of edges, which makes the graph hard to be analyzed." (Aldo Marzullo et al, "Graph Machine Learning" 2nd Ed., 2025)

"A small-world network is characterized by a high clustering coefficient and a short average path length, meaning that most nodes can be reached from any other node through a small number of intermediate connections. This structure often mirrors real-world social networks, where individuals are typically connected through a few mutual acquaintances, allowing for rapid information dissemination." (Aldo Marzullo et al, "Graph Machine Learning" 2nd Ed., 2025)

"Although creating simple subgraphs and merging them is a way to generate new graphs of increasing complexity, networks may also be generated by means of probabilistic models   and/or generative models that let a graph grow by itself. Such graphs usually share   interesting properties with real networks and have long been used to create benchmarks and synthetic graphs, especially in times when the amount of data available was not as overwhelming as today." (Aldo Marzullo et al, "Graph Machine Learning" 2nd Ed., 2025)

"As with many other deep learning-based approaches, another major challenge is in interpretability. While knowledge graphs provide a structured and transparent way to store relationships, LLMs operate as a black box, making it difficult to understand how specific outputs are generated. [...] Data alignment is also a key issue, as structured knowledge graphs and unstructured text data must be carefully preprocessed to ensure consistency.  Differences in data formats, ontology mismatches, and information redundancy can create inefficiencies when integrating these two paradigms. Developing robust pipelines that seamlessly connect graph-based insights with LLM-generated text remains an open challenge." (Aldo Marzullo et al, "Graph Machine Learning" 2nd Ed., 2025)

"Assortativity is used to quantify the tendency of nodes being connected to similar nodes, which can impact the network’s ability to withstand failures or 'attacks'. High assortativity indicates that nodes of similar degrees are more likely to be connected, leading to a resilient structure where the failure of some nodes does not significantly disrupt overall connectivity. Conversely, networks with low assortativity tend to have nodes connecting with dissimilar degrees, making them more vulnerable to targeted attacks on high-degree nodes [...]" (Aldo Marzullo et al, "Graph Machine Learning" 2nd Ed., 2025)

"Besides allowing us to compress a sparse representation into a denser vector, autoencoders are also widely used to process a signal in order to filter out noise and extract only a relevant (characteristic) signal. This can be very useful in many applications, especially when identifying anomalies and outliers." (Aldo Marzullo et al, "Graph Machine Learning" 2nd Ed., 2025)

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

"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)

"Graph analytics is generally very effective in clustering users, merchants, and communities to provide an effective implementation of behavior analytics. On the other hand, second-party fraud can be identified with the implementation of monitoring employee behavior, as well as compliance checks. Graph analytics can indeed be useful for these use cases. Similar to the first-party models, employee behavior can also be analyzed using graph machine learning, although the dataset may need to encode a number of other sources of information besides transactional data. From a compliance standpoint, process mining techniques that still rely on a graph representation of the various procedural steps/pathways can be effective in identifying fraudulent behavior or non-compliant processes. Finally, third-party fraud, especially in the form of phishing attacks, can also be addressed using graph machine learning. In this context, understanding the network from which the phishing attack comes as well as the URLs being used (which can also benefit from a graph representation) can be critical for building an effective phishing classifier." (Aldo Marzullo et al, "Graph Machine Learning" 2nd Ed., 2025)

"Graphs are mathematical structures that are used for describing relationships between entities, and they are used almost everywhere." (Aldo Marzullo et al, "Graph Machine Learning" 2nd Ed., 2025)

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

"Machine learning is a subset of artificial intelligence that aims to provide systems with the ability to learn and improve from data. It has achieved impressive results in many different applications, especially where it is difficult or unfeasible to explicitly define rules to solve a specific task." (Aldo Marzullo et al, "Graph Machine Learning" 2nd Ed., 2025)

"Most of the complexity indeed arises from the presence of entities that appear only once or very few times, but still generate cliques within the graph. Such entities are not very informative to capture patterns and provide insights. Besides, they are possibly strongly affected by statistical variability. On the other hand, we should focus on strong correlations that are supported by larger occurrences and provide more reliable statistical results." (Aldo Marzullo et al, "Graph Machine Learning" 2nd Ed., 2025)

"Overfitting is one of the main problems that affect machine learning practitioners. It can occur due to several reasons. Some of the reasons can be as follows: The dataset can be ill-defined or not sufficiently representative of the task. In this case, adding more data could help to mitigate the problem. The mathematical model used for addressing the problem is too powerful for the task. In this case, proper constraints can be added to the loss function in order to reduce the model’s 'power'. Such constraints are called regularization terms.(Aldo Marzullo et al, "Graph Machine Learning" 2nd Ed., 2025)

"RAG is a framework that combines the strengths of traditional information retrieval systems with the generative capabilities of LLMs. In this setup, an LLM is augmented with a retrieval component that fetches relevant information from external data sources, such as knowledge bases or databases, to produce more accurate and contextually relevant responses. This method enhances the LLM’s output by grounding it in authoritative, up-to-date information." (Aldo Marzullo et al, "Graph Machine Learning" 2nd Ed., 2025)

"Reinforcement learning is used for training machine learning agents to make a sequence of decisions. The artificial intelligence algorithm faces a game-like situation, where the agent gets penalties or rewards based on the actions performed The goal of the agent is to understand how to act in order to maximize rewards and minimize penalties". (Aldo Marzullo et al, "Graph Machine Learning" 2nd Ed., 2025)

"The concept of temporal graphs is useful in all the real-world problems that can be represented as a graph, where the nodes and edges of the graph may change over time. For example, temporal graphs are extensively applied in modeling social networks. By capturing the evolving relationships between individuals, temporal graphs enable a more accurate representation of social dynamics. This is particularly useful for predicting changes in friendships, community structures, and the information diffusion over time." (Aldo Marzullo et al, "Graph Machine Learning" 2nd Ed., 2025)

"The label spreading algorithm is another semi-supervised shallow embedding algorithm.  It was built in order to overcome one big limitation of the label propagation method: the   initial labeling. Indeed, according to the label propagation algorithm, the initial labels cannot be modified in the training process and, in each iteration, they are forced to be equal to their original value. This constraint could generate incorrect results when the initial labeling is affected by errors or noise. As a consequence, the error will be propagated in all nodes of the input graph." (Aldo Marzullo et al, "Graph Machine Learning" 2nd Ed., 2025)

"The main difference between unsupervised and supervised embedding methods essentially lies in the task they attempt to solve. Indeed, if unsupervised shallow embedding algorithms try to learn a good graph, node, or edge representation in order to understand the underlying structure, the supervised algorithms try to find the best solution for a prediction task such as node classification, label prediction, or graph classification." (Aldo Marzullo et al, "Graph Machine Learning" 2nd Ed., 2025)

🖍️Jesús Rogel-Salazar - Collected Quotes

"[...] a data scientist role goes beyond the collection and reporting on data; it must involve looking at a business The role of a data scientist goes beyond the collection and reporting on data. application or process from multiple vantage points and determining what the main questions and follow-ups are, as well as recommending the most appropriate ways to employ the data at hand." (Jesús Rogel-Salazar, "Data Science and Analytics with Python", 2017)

"High-bias models typically produce simpler models that do not overfit and in those cases the danger is that of underfitting. Models with low-bias are typically more complex and that complexity enables us to represent the training data in a more accurate way. The danger here is that the flexibility provided by higher complexity may end up representing not only a relationship in the data but also the noise. Another way of portraying the bias-variance trade-off is in terms of complexity v simplicity." (Jesús Rogel-Salazar, "Data Science and Analytics with Python", 2017) 

"In terms of characteristics, a data scientist has an inquisitive mind and is prepared to explore and ask questions, examine assumptions and analyse processes, test hypotheses and try out solutions and, based on evidence, communicate informed conclusions, recommendations and caveats to stakeholders and decision makers." (Jesús Rogel-Salazar, "Data Science and Analytics with Python", 2017)

"Munging, or wrangling data is actually the most time-consuming task in the data science workflow. [...] Data preparation is key to the extraction of valuable insight and although some may prefer to concentrate only on the much more fun modelling part, the fact that you get to know your dataset inside out while munging it implies that any new or follow-up questions can probably be attained with less effort." (Jesús Rogel-Salazar, "Data Science and Analytics with Python", 2017)

"The tension between bias and variance, simplicity and complexity, or underfitting and overfitting is an area in the data science and analytics process that can be closer to a craft than a fixed rule. The main challenge is that not only is each dataset different, but also there are data points that we have not yet seen at the moment of constructing the model. Instead, we are interested in building a strategy that enables us to tell something about data from the sample used in building the model." (Jesús Rogel-Salazar, "Data Science and Analytics with Python", 2017)

"One important thing to bear in mind about the outputs of data science and analytics is that in the vast majority of cases they do not uncover hidden patterns or relationships as if by magic, and in the case of predictive analytics they do not tell us exactly what will happen in the future. Instead, they enable us to forecast what may come. In other words, once we have carried out some modelling there is still a lot of work to do to make sense out of the results obtained, taking into account the constraints and assumptions in the model, as well as considering what an acceptable level of reliability is in each scenario." (Jesús Rogel-Salazar, "Data Science and Analytics with Python", 2017)

🖍️Francis Galton - Collected Quotes

"A visual image is the most perfect form of mental representation wherever the shape, position, and relations of objects in space are concerned. It is of importance in every handicraft and profession where design is required." (Francis Galton, "Mental Imagery" [in "Inquiries into Human Faculty and Development"] 1883)

"The object of statistical science is to discover methods of condensing information concerning large groups of allied facts into brief and compendious expressions suitable for discussion. The possibility of doing this is based on the constancy and continuity with which objects of the same species are found to vary." (Sir Francis Galton, "Inquiries into Human Faculty and Its Development, Statistical Methods", 1883) 

"It is always well to retain a clear geometric view of the facts when we are dealing with statistical problems, which abound with dangerous pitfalls, easily overlooked by the unwary, while they are cantering gaily along upon their arithmetic." (Sir Francis Galton, "Natural Inheritance", 1889)

"It is difficult to understand why statisticians commonly limit their inquiries to Averages, and do not revel in more comprehensive views. […] An Average is but a solitary fact, whereas if a single other fact be added to it, an entire Normal Scheme, which nearly corresponds to the observed one, starts potentially into existence. Some people hate the very name of statistics, but I find them full of beauty and interest. Whenever they are not brutalised, but delicately handled by the higher methods, and are warily interpreted, their power of dealing with complicated phenomena is extraordinary. They are the only tools by which an opening can be cut through the formidable thicket of difficulties that bars the path of those who pursue the Science of man." (Sir Francis Galton, "Natural Inheritance", 1889)

"It is difficult to understand why statisticians commonly limit their inquiries to Averages, and do not revel in more comprehensive views. Their souls seem as dull to the charm of variety as that of the native of one of our flat English counties, whose retrospect of Switzerland was that, if its mountains could be thrown into its lakes, two nuisances would be got rid of at once. An Average is but a solitary fact, whereas if a single other fact be added to it, an entire Normal Scheme, which nearly corresponds to the observed one, starts potentially into existence." (Sir Francis Galton, "Natural Inheritance", 1889)

"[Statistics] are the only tools by which an opening can be cut through the formidable thicket of difficulties that bars the path of those who pursue the Science of man." (Sir Francis Galton, "Natural Inheritance", 1889)

"Every statistician wants now and then to test the practical value of some theoretical process, it may be of smoothing, or of interpola- tion, or of obtaining a measure of variability, or of making some particular deduction or inference." (Francis Galton, Nature vol. 42, [letter] 1890)

"It is now beginning to be generally understood, even by merely practical statisticians, that there is truth in the theory that all variability is much the same kind." (Francis Galton, "Kinship and Correlation", North American Review Vol. 150 (11), 1890)

"Reflection soon made it clear to me that not only were the two new problems identical in principle with the old one of kinship which I had already solved, but that all three of them were no more than special cases of a much more general problem - namely, that of Correlation." (Francis Galton,"Kinship and Correlation", 1890) 

"It had appeared from observation, and it was fully confirmed by this theory, that such a thing existed as an 'Index of Correlation', that is to say, a fraction, now commonly written T, that connects with close approximation every value of the deviation on the part of the subject, with the average of all the associated deviations of the Relative [...]" (Francis Galton, "Memories of My Life", 1908)

"[Statistics are] the only tools by which an opening can be cut through the formidable thicket of difficulties that bars the path of those who pursue the Science of Man." (Sir Ronald Galton)

More quotes from the author at quotablemath.blogspot.com. 

🖍️Frederick Mosteller - Collected Quotes

"As usual we may make the errors of I) rejecting the null hypothesis when it is true, II) accepting the null hypothesis when it is false. But there is a third kind of error which is of interest because the present test of significance is tied up closely with the idea of making a correct decision about which distribution function has slipped furthest to the right. We may make the error of III) correctly rejecting the null hypothesis for the wrong reason." (Frederick Mosteller, "A k-Sample Slippage Test for an Extreme Population", The Annals of Mathematical Statistics 19, 1948)

"Errors of the third kind happen in conventional tests of differences of means, but they are usually not considered, although their existence is probably recognized. It seems to the author that there may be several reasons for this among which are 1) a preoccupation on the part of mathematical statisticians with the formal questions of acceptance and rejection of null hypotheses without adequate consideration of the implications of the error of the third kind for the practical experimenter, 2) the rarity with which an error of the third kind arises in the usual tests of significance." (Frederick Mosteller, "A k-Sample Slippage Test for an Extreme Population", The Annals of Mathematical Statistics 19, 1948)

"For many purposes graphical accuracy is sufficient. The speed of graphical processes, and more especially the advantages of visual presentation in pointing out facts or clues which might otherwise be overlooked, make graphical analysis very valuable." (Frederick Mosteller & John W Tukey, "The Uses and Usefulness of Binomial Probability Paper?", Journal of the American Statistical Association 44, 1949)

"If significance tests are required for still larger samples, graphical accuracy is insufficient, and arithmetical methods are advised. A word to the wise is in order here, however. Almost never does it make sense to use exact binomial significance tests on such data - for the inevitable small deviations from the mathematical model of independence and constant split have piled up to such an extent that the binomial variability is deeply buried and unnoticeable. Graphical treatment of such large samples may still be worthwhile because it brings the results more vividly to the eye." (Frederick Mosteller & John W Tukey, "The Uses and Usefulness of Binomial Probability Paper?", Journal of the American Statistical Association 44, 1949)

"Scientific and technological advances have made the world we live in complex and hard to understand. […] Science itself shows the same growing complexity. We often hear that 'one man can no longer cover a broad enough field' and that 'there is too much narrow specialization'. And yet these complexities must be met - and resolved. At all levels, decisions must be made which involve consideration of more than a single field." (Frederick Mosteller et al, "The Education of a Scientific Generalist", Science 109,1949)

"Mathematical models for empirical phenomena aid the development of a science when a sufficient body of quantitative information has been accumulated. This accumulation can be used to point the direction in which models should be constructed and to test the adequacy of such models in their interim states. Models, in turn, frequently are useful in organizing and interpreting experimental data and in suggesting new directions for experimental research." (Robert R. Bush & Frederick Mosteller, "A Mathematical Model for Simple Learning", Psychological Review 58, 1951)

"Almost any sort of inquiry that is general and not particular involves both sampling and measurement […]. Further, both the measurement and the sampling will be imperfect in almost every case. We can define away either imperfection in certain cases. But the resulting appearance of perfection is usually only an illusion." (Frederick Mosteller et al, "Principles of Sampling", Journal of the American Statistical Association Vol. 49 (265), 1954)

"Because representativeness is inherent in the sampling plan and not in the particular sample at hand, we can never make adequate use of sample results without some measure of how well the results of this particular sample are likely to agree with the results of other samples which the same sampling plan might have provided. The ability to assess stability fairly is as important as the ability to represent the population fairly. Modern sampling plans concentrate on both." (Frederick Mosteller et al, "Principles of Sampling", Journal of the American Statistical Association Vol. 49 (265), 1954)

"By sampling we can learn only about collective properties of populations, not about properties of individuals. We can study the average height, the percentage who wear hats, or the variability in weight of college juniors [...]. The population we study may be small or large, but there must be a population - and what we are studying must be a population characteristic. By sampling, we cannot study individuals as particular entities with unique idiosyncrasies; we can study regularities (including typical variabilities as well as typical levels) in a population as exemplified by the individuals in the sample." (Frederick Mosteller et al, "Principles of Sampling", Journal of the American Statistical Association Vol. 49 (265), 1954)

"In many cases general probability samples can be thought of in terms of (1) a subdivision of the population into strata, (2) a self-weighting probability sample in each stratum, and (3) combination of the stratum sample means weighted by the size of the stratum." (Frederick Mosteller et al, "Principles of Sampling", Journal of the American Statistical Association Vol. 49 (265), 1954)

"That which can be and should be representative is the sampling plan, which includes the manner in which the sample was drawn (essentially a specification of what other samples might have been drawn and what the relative chances of selection were for any two possible samples) and how it is to be analyzed. [...] It is clear that many [...] groups fail to be represented in any particular sample, yet this is not a criticism of that sample. Representation is not, and should not be, by groups. It is, and should be, by individuals as members of the sampled population. Representation is not, and should not be, in any particular sample. It is, and should be, in the sampling plan." (Frederick Mosteller et al, "Principles of Sampling", Journal of the American Statistical Association Vol. 49 (265), 1954)

"The main purpose of a significance test is to inhibit the natural enthusiasm of the investigator." (Frederick Mosteller, "Selected Quantitative Techniques", 1954)

"We must emphasize that such terms as 'select at random', 'choose at random', and the like, always mean that some mechanical device, such as coins, cards, dice, or tables of random numbers, is used." (Frederick Mosteller et al, "Principles of Sampling", Journal of the American Statistical Association Vol. 49 (265), 1954)

"We have made the sampling plan representative, not by giving each individual an equal chance to enter the sample and then weighting them equally, but by a more noticeable process of compensation, where those individuals very likely to enter the sample are weighted less, while those unlikely to enter are weighted more when they do appear. The net result is to give each individual an equal chance of affecting the (weighted) sample mean." (Frederick Mosteller et al, "Principles of Sampling", Journal of the American Statistical Association Vol. 49 (265), 1954)

"We realize that if someone just 'grabs a handful', the individuals in the handful almost always resemble one another (on the average) more than do the members of a simple random sample. Even if the 'grabs' [sampling] are randomly spread around so that every individual has an equal chance of entering the sample, there are difficulties. Since the individuals of grab samples resemble one another more than do individuals of random samples, it follows (by a simple mathematical argument) that the means of grab samples resemble one another less than the means of random samples of the same size. From a grab sample, therefore, we tend to underestimate the variability in the population, although we should have to overestimate it in order to obtain valid estimates of variability of grab sample means by substituting such an estimate into the formula for the variability of means of simple random samples. Thus using simple random sample formulas for grab sample means introduces a double bias, both parts of which lead to an unwarranted appearance of higher stability." (Frederick Mosteller et al, "Principles of Sampling", Journal of the American Statistical Association Vol. 49 (265), 1954)

"Weighing a sample appropriately is no more fudging the data than is correcting a gas volume for barometric pressure." (Frederick Mosteller et al, "Principles of Sampling", Journal of the American Statistical Association Vol. 49 (265), 1954)

"A primary goal of any learning model is to predict correctly the learning curve - proportions of correct responses versus trials. Almost any sensible model with two or three free parameters, however, can closely fit the curve, and so other criteria must be invoked when one is comparing several models." (Robert R Bush & Frederick Mosteller, "A Comparison of Eight Models?", Studies in Mathematical Learning Theory, 1959)

"A satisfactory prediction of the sequential properties of learning data from a single experiment is by no means a final test of a model. Numerous other criteria - and some more demanding - can be specified. For example, a model with specific numerical parameter values should be invariant to changes in independent variables that explicitly enter in the model." (Robert R Bush & Frederick Mosteller,"A Comparison of Eight Models?", Studies in Mathematical Learning Theory, 1959)

"In the testing of a scientific model or theory, one rarely has a general measure of goodness-of-fit, a universal yardstick by which one accepts or rejects the model. Indeed, science does not and should not work this way; a theory is kept until a better one is found. One way that science does work is by comparing two or more theories to determine their relative merits in handling relevant data."(Robert R Bush & Frederick Mosteller, "A Comparison of Eight Models?", Studies in Mathematical Learning Theory, 1959)

"In a problem, the great thing is the challenge. A problem can be challenging for many reasons: because the subject matter is intriguing, because the answer defies unsophisticated intuition, because it illustrates an important principle, because of its vast generality, because of its difficulty, because of a clever solution, or even because of the simplicity or beauty of the answer." (Frederick Mosteller, "Fifty Challenging Problems in Probability with Solutions", 1965)

"Using data from the population as it stands is a dangerous substitute for testing." (Frederick Mosteller & Gale Mosteller, "New Statistical Methods in Public Policy. Part I: Experimentation", Journal of Contemporary Business 8, 1979)

"Although we often hear that data speak for themselves, their voices can be soft and sly." (Frederick Mosteller, "Beginning Statistics with Data Analysis", 1983)

"The law of truly large numbers states: With a large enough sample, any outrageous thing is likely to happen." (Frederick Mosteller, "Methods for Studying Coincidences", Journal of the American Statistical Association Vol. 84, 1989)

"It is easy to lie with statistics, but easier to lie without them [...]" (Frederick Mosteller)

🖍️Abi Aryan - Collected Quotes

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

"Agentic workflows break when the logic is messy - if, say, the plans don’t decompose or memory is poorly structured. However, infrastructure-level LLM applications introduce even more failure points and complexity. If the protocols don’t sync with each other, or the data flows start leaking, or the model boundaries are unclear... there are far too many failure points to count. While most people have been jumping on the bandwagon to adopt MCPs or A2A, very few are equipped to handle the LLMOps issues these tools introduce." (Abi Aryan, "LLMOps: Managing Large Language Models in Production", 2025)

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

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

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

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

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

"LLM deployment failures often trace back not to the model itself, but to the prompts it receives. In production environments, prompts are rarely fixed, handcrafted snippets. Instead, they are dynamically generated, assembled from templates, and parameterized based on upstream data sources or evolving user state. This dynamism introduces complexity and variability that can subtly undermine the system’s performance if not carefully managed." (Abi Aryan, "LLMOps: Managing Large Language Models in Production", 2025)

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

"LLMs excel at understanding context and making associations among words, phrases, and concepts to provide relevant information based on the input query or prompt. While structured knowledge bases rely on humancurated data, LLMs can  automatically extract knowledge from unstructured text. When trained on diverse textual sources, they can process a vast amount of information without explicit human intervention. However, this also introduces a challenge, as the model can learn biased or incorrect information from the training data." (Abi Aryan, "LLMOps: Managing Large Language Models in Production", 2025)

"[...] prompt engineering, the science and art of crafting the text inputs that are sent to the models. Prompt updates can significantly improve or degrade the user experience. But prompt engineering is iterative and can be difficult to master and document, especially with closed-source LLMs." (Abi Aryan, "LLMOps: Managing Large Language Models in Production", 2025)

"Prompt injection is a security vulnerability that is specific to AI systems, especially LLM systems, in which malicious users try to manipulate prompts to make a model behave in a certain unintended way. They may try to get it to leak data, execute unauthorized tasks (especially with agentic systems), or ignore constraints. This is possible because LLMs are typically encapsulated inside applications using metaprompts, which are developer-created instructions that define the model’s behavior. Metaprompts usually contain safeguard instructions, such as 'do not use curse words', and placeholders where the input submitted by the user is pasted. The user’s input is combined with the metaprompts into a larger prompt that then goes to the model." (Abi Aryan, "LLMOps: Managing Large Language Models in Production", 2025)

"Semantic Kernel is a framework designed to simplify integrating LLMs into applications that require dynamic knowledge, reasoning, and state tracking. It’s particularly useful when you want to build complex, modular AI systems that can interact with external APIs, knowledge bases, or decision-making processes. Semantic Kernel focuses on building more flexible AI systems that can handle a variety of tasks beyond just generating text. It allows for modularity, enabling developers to easily combine different components - such as embeddings, prompt templates, and custom functions - in a cohesive manner." (Abi Aryan, "LLMOps: Managing Large Language Models in Production", 2025)

"The simplest form of an agent is little more than a wrapped prompt. It takes an input, does some local reasoning, returns an output, and exits. There’s no memory, no iteration, no 

feedback loop. These are useful when the task is bounded, like generating a SQL query, converting a paragraph to a tweet, or answering a direct question. But single-step agents 

are brittle. They assume everything is known up front. They can’t handle surprises or partial failures. You’ll quickly outgrow them when tasks involve multiple actions or require state tracking." (Abi Aryan, "LLMOps: Managing Large Language Models in Production", 2025)

"There are three techniques for model domain adaptation: prompt engineering, RAG, and fine-tuning. Strictly speaking, RAG is a form of dynamic prompt engineering where developers use a retrieval system to add content to an existing prompt, but RAG systems are used so often that it’s worth discussing them separately. One critical difference with fine-tuning is that you must have access to the model’s weights, information that is usually not available with cloud-based, proprietary LLMs." (Abi Aryan, "LLMOps: Managing Large Language Models in Production", 2025)

"These user-controlled templates are pre-engineered prompt structures that can be presented to the model as part of the context or decision-making path. Prompts help guide the model’s behavior using predefined instructions, formats, strategies. They can encapsulate common workflows suggest best practices for using tools and resourceseffective." (Abi Aryan, "LLMOps: Managing Large Language Models in Production", 2025)

"Vector databases are designed to store and index highdimensional embeddings - dense numeric vectors that capture the semantic meaning of text, images, audio, or other content. Instead of looking for exact matches, they use approximate nearest neighbor (ANN) algorithms to return the items whose vectors lie closest to a query vector in that multidimensional space. This makes them the engine behind semantic search, recommendation systems, image-or-audio similarity matching, and retrieval augmented generation (RAG) pipelines that supply LLM prompts with relevant context in milliseconds." (Abi Aryan, "LLMOps: Managing Large Language Models in Production", 2025)

"With MCP, a model no longer has to guess what’s possible. Instead, it can discover tools, query data sources, and select prompts - all in real time, all through a shared protocol. This means a model doesn’t just generate responses; it acts, it calls tools, it gathers context, and it learns how to interact with the outside world in a modular,controlled way." (Abi Aryan, "LLMOps: Managing Large Language Models in Production", 2025)