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There has been a lot of recent interest in adopting machine learning methods for scientific and engineering applications. This has in large part been inspired by recent successes and advances in the domains of Natural Language Processing…
Learning representations of data is an important problem in statistics and machine learning. While the origin of learning representations can be traced back to factor analysis and multidimensional scaling in statistics, it has become a…
This graduate textbook on machine learning tells a story of how patterns in data support predictions and consequential actions. Starting with the foundations of decision making, we cover representation, optimization, and generalization as…
Topological data analysis has emerged as a powerful tool for extracting the metric, geometric and topological features underlying the data as a multi-resolution summary statistic, and has found applications in several areas where data…
This study has the purpose of addressing four questions that lie at the base of the probability theory and statistics, and includes two main steps. As first, we conduct the textual analysis of the most significant works written by eminent…
What is Statistics? Opinions vary. In fact, there is a continuous spectrum of attitudes toward statistics ranging from pure theoreticians, proving asymptotic efficiency and searching for most powerful tests, to wild practitioners, blindly…
Machine Learning algorithms have had a profound impact on the field of computer science over the past few decades. These algorithms performance is greatly influenced by the representations that are derived from the data in the learning…
The aim of this textbook is to provide students with basic knowledge of stochastic models that may apply to telecommunications research areas, such as traffic modelling, resource provisioning and traffic management. These study areas are…
This book collects the lectures about graph theory and its applications which were given to students of mathematical departments of Moscow State University and Peking University. Graph theory is a very wide field with a lot of applications…
Ensuring that analyses performed on a dataset are representative of the entire population is one of the central problems in statistics. Most classical techniques assume that the dataset is independent of the analyst's query and break down…
Over 300 sequences and many unsolved problems and conjectures related to them are presented herein. These notions, definitions, unsolved problems, questions, theorems corollaries, formulae, conjectures, examples, mathematical criteria, etc.…
Deep learning has arguably achieved tremendous success in recent years. In simple words, deep learning uses the composition of many nonlinear functions to model the complex dependency between input features and labels. While neural networks…
In distributional or average-case analysis, the goal is to design an algorithm with good-on-average performance with respect to a specific probability distribution. Distributional analysis can be useful for the study of general-purpose…
In the footsteps of the book \textit{Measure Theory and Integration By and For the Learner} of our series in Probability Theory and Statistics, we intended to devote a special volume of the very probabilistic aspects of the first cited…
Statistical estimation in many contemporary settings involves the acquisition, analysis, and aggregation of datasets from multiple sources, which can have significant differences in character and in value. Due to these variations, the…
How can we make sense of large-scale recordings of neural activity across learning? Theories of neural network learning with their origins in statistical physics offer a potential answer: for a given task, there are often a small set of…
Statistics comes in two main flavors: frequentist and Bayesian. For historical and technical reasons, frequentist statistics has dominated data analysis in the past; but Bayesian statistics is making a comeback at the forefront of science.…
Statistically sound pattern discovery harnesses the rigour of statistical hypothesis testing to overcome many of the issues that have hampered standard data mining approaches to pattern discovery. Most importantly, application of…
Statistical thermodynamics has a universal appeal that extends beyond molecular systems, and yet, as its tools are being transplanted to fields outside physics, the fundamental question, \textit{what is thermodynamics?}, has remained…
The theory of statistical learning has focused on variational objectives expressed on functions. In this note, we discuss motivations to write similar objectives on measures, in particular to discuss out-of-distribution generalization and…