"The preliminary examination of most data is facilitated by the use of diagrams. Diagrams prove nothing, but bring outstanding features readily to the eye; they are therefore no substitutes for such critical tests as may be applied to the data, but are valuable in suggesting such tests, and in explaining the conclusions founded upon them." (Sir Ronald A Fisher, "Statistical Methods for Research Workers", 1925)
"Every bit of knowledge we gain and every conclusion we draw about the universe or about any part or feature of it depends finally upon some observation or measurement. Mankind has had again and again the humiliating experience of trusting to intuitive, apparently logical conclusions without observations, and has seen Nature sail by in her radiant chariot of gold in an entirely different direction." (Oliver J Lee, "Measuring Our Universe: From the Inner Atom to Outer Space", 1950)
"Probability is the mathematics of uncertainty. Not only do we constantly face situations in which there is neither adequate data nor an adequate theory, but many modem theories have uncertainty built into their foundations. Thus learning to think in terms of probability is essential. Statistics is the reverse of probability (glibly speaking). In probability you go from the model of the situation to what you expect to see; in statistics you have the observations and you wish to estimate features of the underlying model." (Richard W Hamming, "Methods of Mathematics Applied to Calculus, Probability, and Statistics", 1985)
"Complexity is not an objective factor but a subjective one. Supersignals reduce complexity, collapsing a number of features into one. Consequently, complexity must be understood in terms of a specific individual and his or her supply of supersignals. We learn supersignals from experience, and our supply can differ greatly from another individual's. Therefore there can be no objective measure of complexity." (Dietrich Dorner, "The Logic of Failure: Recognizing and Avoiding Error in Complex Situations", 1989)
"Formulation of a mathematical model is the first step in the process of analyzing the behaviour of any real system. However, to produce a useful model, one must first adopt a set of simplifying assumptions which have to be relevant in relation to the physical features of the system to be modelled and to the specific information one is interested in. Thus, the aim of modelling is to produce an idealized description of reality, which is both expressible in a tractable mathematical form and sufficiently close to reality as far as the physical mechanisms of interest are concerned." (Francois Axisa, "Discrete Systems" Vol. I, 2001)
"Graphical displays are often constructed to place principal focus on the individual observations in a dataset, and this is particularly helpful in identifying both the typical positions of data points and unusual or influential cases. However, in many investigations, principal interest lies in identifying the nature of underlying trends and relationships between variables, and so it is often helpful to enhance graphical displays in ways which give deeper insight into these features. This can be very beneficial both for small datasets, where variation can obscure underlying patterns, and large datasets, where the volume of data is so large that effective representation inevitably involves suitable summaries." (Adrian W Bowman, "Smoothing Techniques for Visualisation" [in "Handbook of Data Visualization"], 2008)
"It is impossible to construct a model that provides an entirely accurate picture of network behavior. Statistical models are almost always based on idealized assumptions, such as independent and identically distributed (i.i.d.) interarrival times, and it is often difficult to capture features such as machine breakdowns, disconnected links, scheduled repairs, or uncertainty in processing rates." (Sean Meyn, "Control Techniques for Complex Networks", 2008)
"In order to deal with these phenomena, we abstract from details and attempt to concentrate on the larger picture - a particular set of features of the real world or the structure that underlies the processes that lead to the observed outcomes. Models are such abstractions of reality. Models force us to face the results of the structural and dynamic assumptions that we have made in our abstractions." (Bruce Hannon and Matthias Ruth, "Dynamic Modeling of Diseases and Pests", 2009)
"Despite the enormous success of deep learning, relatively little is understood theoretically about why these techniques are so successful at feature learning and compression." (Pankaj Mehta & David J Schwab, "An exact mapping between the Variational Renormalization Group and Deep Learning", 2014)
"A predictive model overfits the training set when at least some of the predictions it returns are based on spurious patterns present in the training data used to induce the model. Overfitting happens for a number of reasons, including sampling variance and noise in the training set. The problem of overfitting can affect any machine learning algorithm; however, the fact that decision tree induction algorithms work by recursively splitting the training data means that they have a natural tendency to segregate noisy instances and to create leaf nodes around these instances. Consequently, decision trees overfit by splitting the data on irrelevant features that only appear relevant due to noise or sampling variance in the training data. The likelihood of overfitting occurring increases as a tree gets deeper because the resulting predictions are based on smaller and smaller subsets as the dataset is partitioned after each feature test in the path." (John D Kelleher et al, "Fundamentals of Machine Learning for Predictive Data Analytics: Algorithms, Worked Examples, and Case Studies", 2015)
"Bayesian networks provide a more flexible representation for encoding the conditional independence assumptions between the features in a domain. Ideally, the topology of a network should reflect the causal relationships between the entities in a domain. Properly constructed Bayesian networks are relatively powerful models that can capture the interactions between descriptive features in determining a prediction." (John D Kelleher et al, "Fundamentals of Machine Learning for Predictive Data Analytics: Algorithms, worked examples, and case studies", 2015)
"Bayesian networks use a graph-based representation to encode the structural relationships - such as direct influence and conditional independence - between subsets of features in a domain. Consequently, a Bayesian network representation is generally more compact than a full joint distribution (because it can encode conditional independence relationships), yet it is not forced to assert a global conditional independence between all descriptive features. As such, Bayesian network models are an intermediary between full joint distributions and naive Bayes models and offer a useful compromise between model compactness and predictive accuracy." (John D Kelleher et al, "Fundamentals of Machine Learning for Predictive Data Analytics: Algorithms, worked examples, and case studies", 2015)
"Decision trees are also discriminative models. Decision trees are induced by recursively partitioning the feature space into regions belonging to the different classes, and consequently they define a decision boundary by aggregating the neighboring regions belonging to the same class. Decision tree model ensembles based on bagging and boosting are also discriminative models." (John D Kelleher et al, "Fundamentals of Machine Learning for Predictive Data Analytics: Algorithms, Worked Examples, and Case Studies", 2015)
"There are two kinds of mistakes that an inappropriate inductive bias can lead to: underfitting and overfitting. Underfitting occurs when the prediction model selected by the algorithm is too simplistic to represent the underlying relationship in the dataset between the descriptive features and the target feature. Overfitting, by contrast, occurs when the prediction model selected by the algorithm is so complex that the model fits to the dataset too closely and becomes sensitive to noise in the data." (John D Kelleher et al, "Fundamentals of Machine Learning for Predictive Data Analytics: Algorithms, Worked Examples, and Case Studies", 2015)
"The power of deep learning models comes from their ability to classify or predict nonlinear data using a modest number of parallel nonlinear steps4. A deep learning model learns the input data features hierarchy all the way from raw data input to the actual classification of the data. Each layer extracts features from the output of the previous layer." (N D Lewis, "Deep Learning Made Easy with R: A Gentle Introduction for Data Science", 2016)
"[...] adding nonlinear features to the representation of our data can make linear models much more powerful. However, often we don’t know which features to add, and adding many features (like all possible interactions in a 100-dimensional feature space) might make computation very expensive. Luckily, there is a clever mathematical trick that allows us to learn a classifier in a higher-dimensional space without actually computing the new, possibly very large representation. This is known as the kernel trick, and it works by directly computing the distance (more precisely, the scalar products) of the data points for the expanded feature representation, without ever actually computing the expansion." (Andreas C Müller & Sarah Guido, "Introduction to Machine Learning with Python: A Guide for Data Scientists", 2017)
"Decision trees are important for a few reasons. First, they can both classify and regress. It requires literally one line of code to switch between the two models just described, from a classification to a regression. Second, they are able to determine and share the feature importance of a given training set." (Russell Jurney, "Agile Data Science 2.0: Building Full-Stack Data Analytics Applications with Spark", 2017)
"Decision trees have two advantages over many of the algorithms [...]: the resulting model can easily be visualized and understood by nonexperts (at least for smaller trees), and the algorithms are completely invariant to scaling of the data. As each feature is processed separately, and the possible splits of the data don’t depend on scaling, no preprocessing like normalization or standardization of features is needed for decision tree algorithms. In particular, decision trees work well when you have features that are on completely different scales, or a mix of binary and continuous features. The main downside of decision trees is that even with the use of pre-pruning, they tend to overfit and provide poor generalization performance. Therefore, in most applications, the ensemble methods we discuss next are usually used in place of a single decision tree." (Andreas C Müller & Sarah Guido, "Introduction to Machine Learning with Python: A Guide for Data Scientists", 2017)
"Extracting good features is the most important thing for getting your analysis to work. It is much more important than good machine learning classifiers, fancy statistical techniques, or elegant code. Especially if your data doesn’t come with readily available features (as is the case with web pages, images, etc.), how you reduce it to numbers will make the difference between success and failure." (Field Cady, "The Data Science Handbook", 2017)
"Feature extraction is also the most creative part of data science and the one most closely tied to domain expertise. Typically, a really good feature will correspond to some real‐world phenomenon. Data scientists should work closely with domain experts and understand what these phenomena mean and how to distill them into numbers." (Field Cady, "The Data Science Handbook", 2017)
"Learning a decision tree means learning the sequence of if/else questions that gets us to the true answer most quickly. In the machine learning setting, these questions are called tests (not to be confused with the test set, which is the data we use to test to see how generalizable our model is). Usually data does not come in the form of binary yes/no features as in the animal example, but is instead represented as continuous features [...]. The tests that are used on continuous data are of the form 'Is feature i larger than value a?'" (Andreas C Müller & Sarah Guido, "Introduction to Machine Learning with Python: A Guide for Data Scientists", 2017)
"Variables which follow symmetric, bell-shaped distributions tend to be nice as features in models. They show substantial variation, so they can be used to discriminate between things, but not over such a wide range that outliers are overwhelming." (Steven S Skiena, "The Data Science Design Manual", 2017)
"The idea behind deeper architectures is that they can better leverage repeated regularities in the data patterns in order to reduce the number of computational units and therefore generalize the learning even to areas of the data space where one does not have examples. Often these repeated regularities are learned by the neural network within the weights as the basis vectors of hierarchical features." (Charu C Aggarwal, "Neural Networks and Deep Learning: A Textbook", 2018)
"We humans are reasonably good at defining rules that check one, two, or even three attributes (also commonly referred to as features or variables), but when we go higher than three attributes, we can start to struggle to handle the interactions between them. By contrast, data science is often applied in contexts where we want to look for patterns among tens, hundreds, thousands, and, in extreme cases, millions of attributes." (John D Kelleher & Brendan Tierney, "Data Science", 2018)
"Feature extraction is a way to distill large volumes of data and attributes down to a set of representative descriptive attributes. The process derives numerical values (fea‐ tures) for distinctive characteristics or patterns in input data so that we can differentiate categories in other data. It’s used when data is difficult for a model to analyze directly perhaps because of size, format, or the need for incidental comparisons. Feature selection is the process of determining the subset of extracted features that are most important or influential to a target goal. It’s used to surface predictive importance as well as for efficiency." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019
"Using graphs for connected feature extraction can significantly improve our predictions. The ideal graph features and algorithms vary depending on the attributes of the data, including the network domain and graph shape. We suggest first considering the predictive elements within your data and testing hypotheses with different types of connected features before fine-tuning." (Mark Needham & Amy E Hodler, "Graph Algorithms: Practical Examples in Apache Spark and Neo4j", 2019)
"Any machine learning model is trained based on certain assumptions. In general, these assumptions are the simplistic approximations of some real-world phenomena. These assumptions simplify the actual relationships between features and their characteristics and make a model easier to train. More assumptions means more bias. So, while training a model, more simplistic assumptions = high bias, and realistic assumptions that are more representative of actual phenomena = low bias." (Imran Ahmad, "40 Algorithms Every Programmer Should Know", 2020)
"Smoothing and aggregating can help us see important features and relationships, but when we have only a handful of observations, smoothing techniques can be misleading. With just a few observations, we prefer rug plots over histograms, box plots, and density curves, and we use scatterplots rather than smooth curves and density contours. This may seem obvious, but when we have a large amount of data, the amount of data in a subgroup can quickly dwindle. This phenomenon is an example of the curse of dimensionality." (Sam Lau et al, "Learning Data Science: Data Wrangling, Exploration, Visualization, and Modeling with Python", 2023)
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