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Utkir A Rozikov: Gibbs Measures In
Machine Learning

Gibbs Measures In Machine Learning

This book is the first one that shows how to accurately and efficiently solve time-varying problems in real-time or online using continuous- or discrete-time zeroing dynamics. The authors provide a comprehensive treatment of the theory of both static and dynamic neural networks. They develop, analyze, model, simulate, and compare zeroing dynamics models for the online solution of numerous time-varying problems, such as root finding, nonlinear equation solving, matrix inversion, matrix square root finding, quadratic optimization, and inequality solving.

Neural networks and neural dynamics are powerful approaches for the online solution of mathematical problems arising in many areas of science, engineering, and business. Compared with conventional gradient neural networks that only deal with static problems of constant coefficient matrices and vectors, the authors’ new method called zeroing dynamics solves time-varying problems. Zeroing Dynamics, Gradient Dynamics, and Newton Iterations is the first book that shows how to accurately and efficiently solve time-varying problems in real-time or online using continuous- or discrete-time zeroing dynamics. The book brings together research in the developing fields of neural networks, neural dynamics, computer mathematics, numerical algorithms, time-varying computation and optimization, simulation and modeling, analog and digital hardware, and fractals.The authors provide a comprehensive treatment of the theory of both static and dynamic neural networks. Readers will discover how novel theoretical results have been successfully applied to many practical problems. The authors develop, analyze, model, simulate, and compare zeroing dynamics models for the online solution of numerous time-varying problems, such as root finding, nonlinear equation solving, matrix inversion, matrix square root finding, quadratic optimization, and inequality solving.

Zeroing Dynamics, Gradient Dynamics, and Newton Iterations

Causal Inference and Machine Learning

While the field of Deep Learning has been advancing at frightening speeds during the last ten years, we do not have a plausible theoretical explanation of its success yet. One can safely say that Deep Learning works, but nobody really understands why. Nevertheless, starting around five years before now, a decent number of theoretical papers specifically concerning neural nets started to emerge at top machine learning venues. This makes us think that the core of Deep Learning theory has already started to crystallize.The goal of the present book is to present these core concepts of Deep Learning theory to readers so that they could directly dive into recent papers of this area. For this purpose, each chapter elaborates a simple model or a classical result in details first and then discusses possible generalizations and more recent developments of the same idea.We have to warn the reader that the present book is not a mathematical manuscript. Not all results here are stated as formal theorems and not all theorems are provided with complete and rigorous proofs. Many of the theorems of the book are proven up to some technical lemmas, while for some there is only a proof sketch. This conforms with the main idea of the book: present and illustrate concepts rather than reproduce all the results.The book, in its present form, covers the following topics: uniform generalization bounds, PAC-bayesian generalization bounds, double descent phenomena, infinitely-wide networks, implicit bias of gradient descent, loss landscape, gradient descent convergence guarantees, and initialization strategies.

Elements Of Deep Learning Theory

Lectures On Quantum State Estimation

Algorithms have become the key organizer through which power is enacted in our society. A huge amount of data regarding our daily routines are monitored and analyzed to make recommendations that manage, control, and lead our behaviors in everyday life. AI, Humans, and Misinformation: How Does AI Alter Human Behavior and How Do Humans Influence Algorithmic Misinformation? is a guide to understanding the dynamics of AI and misinformation in human contexts by addressing meaningful questions-How does AI alter human behavior and how do humans influence algorithmic decision-making? In answering these questions, this book examines the role of misinformation, disinformation, and fake news, and shows readers how to develop AI methods and algorithms that combat misinformation by using AI design choices that provide users and developers alike with meaningful control over AI. This book brings together various perspectives on algorithms into an integrated conceptual framework, and provides a broad socio-technical analysis, addressing critical and ethical issues of misinformation and fake news. The book offers a compelling insight into the misinformation phenomenon and the future of AI-based society. Readers will find an integrated technical analysis of the logic and social implications of algorithmic processes. Reporting from the cutting edge of critical technical methods and research, the result is useful and constructive for developing the relations between algorithms and humans. This is an imperative methodology for understanding what is at stake as industry and government use AI to reshape the world.

Decoding Bias, Algorithms, and Trust

Minds, Machines, and Misinformation

Why Not Nonlinear Algebra: Math, Science, Applications And Funding

This unique compendium develops a general approach to building models of economic and financial processes, with a focus on statistical learning techniques that scale to large data sets. It introduces the key elements of a parametric statistical model: likelihood, prior, and posterior, and show how to use them to make predictions.The book covers classical techniques such as multiple regression and the Kalman filter in a clear, accessible style that has been popular with students, but also includes detailed treatments of state-of-the-art models, highlighting tree-based methods, support vector machines and kernel methods, deep learning, and reinforcement learning. Theories are supplemented by real-world examples.This reference text is useful for undergraduate, graduate and even PhD students in quantitative finance, and also to practitioners who are facing the reality that data science and machine learning are disrupting the industry.

Statistical Machine Learning With Applications In Finance

Dynamics and Astrophysics of Galaxies

An Introduction to String Algorithms

Scaling (zooming in or out) is taking a close or distant view of an object. Infinite scaling (the scaling parameter tends to zero or infinity) may lead to a limit which is self-similar and much simpler than the original object. For instance, the classical Donsker's theorem says that all weakly dependent stationary processes with finite variance scale to Brownian motion at large scales. In the case of a random field indexed by two-dimensional parameter, both types of scaling can be anisotropic, meaning that the horizontal and vertical axes are scaled at different rate determined by the ratio γ&gt;0 of the scaling exponents along the axes. The natural questions under such scaling are whether the scaling limits exist for any γ&gt;0, and what are these limits are. The book tries to answer these questions. It introduces the concept of scaling transition and discusses its existence for a natural class of planar random fields including Gaussian, linear and some nonlinear ones. The scaling limits are identified and exhibit a surprising trichitomy at a critical point γ0, with 'unbalanced' limits having unusual path properties and dependence structure along one of the coordinate axes. Scaling transition occurs in applied sciences (telecommunications and econometrics) when aggregating independent processes with long-range dependence in which case 'unbalanced' limits are classical Gaussian or stable random fields.

Anisotropic Scaling Of Random Fields With Long-range Dependence: Scaling Limits Of Random Fields With Applications

The book is devoted to contemporary variance reduction methods for Monte Carlo and Markov Chain (MCMC) with Machine Learning and Finance applications. We present new approaches based on martingale representations, and Stein control variates besides the standard techniques. In addition, the book focuses on developing new variance reduction algorithms in MCMC and their theoretical analysis. Readers will find numerical examples that illustrate all proposed algorithms.

Advanced Variance Reduction Techniques For Mcmc

Gibbs Measures In Machine Learning

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