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This paper analyzes the working or default assumptions researchers in the formal, statistical, and case study traditions typically hold regarding the sources of unexplained variance, the meaning of outliers, parameter values, human…

All scientific interpretations of statistical outputs depend on background (auxiliary) assumptions that are rarely delineated or explicitly interrogated. These include not only the usual modeling assumptions, but also deeper assumptions…

In an age of increasingly large data sets, investigators in many different disciplines have turned to clustering as a tool for data analysis and exploration. Existing clustering methods, however, typically depend on several nontrivial…

In recent years, specific evaluation metrics for time series anomaly detection algorithms have been developed to handle the limitations of the classical precision and recall. However, such metrics are heuristically built as an aggregate of…

The fundamental goal of information theory is to characterize complex operational tasks using efficiently computable information quantities, Shannon's capacity formula being the prime example of this. However, many tasks in quantum…

Unnormalized (or energy-based) models provide a flexible framework for capturing the characteristics of data with complex dependency structures. However, the application of standard Bayesian inference methods has been severely limited…

In any other circumstance, it might make sense to define the extent of the terrain (Data Science) first, and then locate and describe the landmarks (Principles). But this data revolution we are experiencing defies a cadastral survey. Areas…

The subject of features normalization plays an important central role in data representation, characterization, visualization, analysis, comparison, classification, and modeling, as it can substantially influence and be influenced by all of…

Empirical science needs to be based on facts and claims that can be reproduced. This calls for replicating the studies that proclaim the claims, but practice in most fields still fails to implement this idea. When such studies emerged in…

Most practical data science problems encounter missing data. A wide variety of solutions exist, each with strengths and weaknesses that depend upon the missingness-generating process. Here we develop a theoretical framework for training and…

Mixup is a data augmentation technique that creates new examples as convex combinations of training points and labels. This simple technique has empirically shown to improve the accuracy of many state-of-the-art models in different settings…

Despite alarm over the reliance of machine learning systems on so-called spurious patterns, the term lacks coherent meaning in standard statistical frameworks. However, the language of causality offers clarity: spurious associations are due…

Anomaly detection research works generally propose algorithms or end-to-end systems that are designed to automatically discover outliers in a dataset or a stream. While literature abounds concerning algorithms or the definition of metrics…

We propose a formal model for counterfactual estimation with unobserved confounding in "data-rich" settings, i.e., where there are a large number of units and a large number of measurements per unit. Our model provides a bridge between the…

Predictive inference is a fundamental task in statistics, traditionally addressed using parametric assumptions about the data distribution and detailed analyses of how models learn from data. In recent years, conformal prediction has…

The mathematical models used to capture features of complex, biological systems are typically non-linear, meaning that there are no generally valid simple relationships between their outputs and the data that might be used to validate them.…

Many algorithms have been recently proposed for causal machine learning. Yet, there is little to no theory on their quality, especially considering finite samples. In this work, we propose a theory based on generalization bounds that…

Scientific datasets play a crucial role in contemporary data-driven research, as they allow for the progress of science by facilitating the discovery of new patterns and phenomena. This mounting demand for empirical research raises…

Machine and Statistical learning techniques become more and more important for the analysis of psychological data. Four core concepts of machine learning are the bias variance trade-off, cross-validation, regularization, and basis…

Testing hypotheses is an issue of primary importance in the scientific research, as well as in many other human activities. Much clarification about it can be achieved if the process of learning from data is framed in a stochastic model of…