Minimum Divergence Methods In Statistical Machine Learning

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Minimum Divergence Methods In Statistical Machine Learning

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Author : Shinto Eguchi
language : en
Publisher: Springer Nature
Release Date : 2022-03-14

Minimum Divergence Methods In Statistical Machine Learning written by Shinto Eguchi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-14 with Mathematics categories.

This book explores minimum divergence methods of statistical machine learning for estimation, regression, prediction, and so forth, in which we engage in information geometry to elucidate their intrinsic properties of the corresponding loss functions, learning algorithms, and statistical models. One of the most elementary examples is Gauss's least squares estimator in a linear regression model, in which the estimator is given by minimization of the sum of squares between a response vector and a vector of the linear subspace hulled by explanatory vectors. This is extended to Fisher's maximum likelihood estimator (MLE) for an exponential model, in which the estimator is provided by minimization of the Kullback-Leibler (KL) divergence between a data distribution and a parametric distribution of the exponential model in an empirical analogue. Thus, we envisage a geometric interpretation of such minimization procedures such that a right triangle is kept with Pythagorean identity in the sense of the KL divergence. This understanding sublimates a dualistic interplay between a statistical estimation and model, which requires dual geodesic paths, called m-geodesic and e-geodesic paths, in a framework of information geometry. We extend such a dualistic structure of the MLE and exponential model to that of the minimum divergence estimator and the maximum entropy model, which is applied to robust statistics, maximum entropy, density estimation, principal component analysis, independent component analysis, regression analysis, manifold learning, boosting algorithm, clustering, dynamic treatment regimes, and so forth. We consider a variety of information divergence measures typically including KL divergence to express departure from one probability distribution to another. An information divergence is decomposed into the cross-entropy and the (diagonal) entropy in which the entropy associates with a generative model as a family of maximum entropy distributions; the cross entropy associates with a statistical estimation method via minimization of the empirical analogue based on given data. Thus any statistical divergence includes an intrinsic object between the generative model and the estimation method. Typically, KL divergence leads to the exponential model and the maximum likelihood estimation. It is shown that any information divergence leads to a Riemannian metric and a pair of the linear connections in the framework of information geometry. We focus on a class of information divergence generated by an increasing and convex function U, called U-divergence. It is shown that any generator function U generates the U-entropy and U-divergence, in which there is a dualistic structure between the U-divergence method and the maximum U-entropy model. We observe that a specific choice of U leads to a robust statistical procedure via the minimum U-divergence method. If U is selected as an exponential function, then the corresponding U-entropy and U-divergence are reduced to the Boltzmann-Shanon entropy and the KL divergence; the minimum U-divergence estimator is equivalent to the MLE. For robust supervised learning to predict a class label we observe that the U-boosting algorithm performs well for contamination of mislabel examples if U is appropriately selected. We present such maximal U-entropy and minimum U-divergence methods, in particular, selecting a power function as U to provide flexible performance in statistical machine learning.

Minimum Gamma Divergence For Regression And Classification Problems

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Author : Shinto Eguchi
language : en
Publisher: Springer Nature
Release Date : 2025-03-11

Minimum Gamma Divergence For Regression And Classification Problems written by Shinto Eguchi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-11 with Mathematics categories.

This book introduces the gamma-divergence, a measure of distance between probability distributions that was proposed by Fujisawa and Eguchi in 2008. The gamma-divergence has been extensively explored to provide robust estimation when the power index γ is positive. The gamma-divergence can be defined even when the power index γ is negative, as long as the condition of integrability is satisfied. Thus, the authors consider the gamma-divergence defined on a set of discrete distributions. The arithmetic, geometric, and harmonic means for the distribution ratios are closely connected with the gamma-divergence with a negative γ. In particular, the authors call the geometric-mean (GM) divergence the gamma-divergence when γ is equal to -1. The book begins by providing an overview of the gamma-divergence and its properties. It then goes on to discuss the applications of the gamma-divergence in various areas, including machine learning, statistics, and ecology. Bernoulli, categorical, Poisson, negative binomial, and Boltzmann distributions are discussed as typical examples. Furthermore, regression analysis models that explicitly or implicitly assume these distributions as the dependent variable in generalized linear models are discussed to apply the minimum gamma-divergence method. In ensemble learning, AdaBoost is derived by the exponential loss function in the weighted majority vote manner. It is pointed out that the exponential loss function is deeply connected to the GM divergence. In the Boltzmann machine, the maximum likelihood has to use approximation methods such as mean field approximation because of the intractable computation of the partition function. However, by considering the GM divergence and the exponential loss, it is shown that the calculation of the partition function is not necessary, and it can be executed without variational inference.

Information Theory And Statistical Learning

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Author : Frank Emmert-Streib
language : en
Publisher: Springer Science & Business Media
Release Date : 2009

Information Theory And Statistical Learning written by Frank Emmert-Streib and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Computers categories.

This interdisciplinary text offers theoretical and practical results of information theoretic methods used in statistical learning. It presents a comprehensive overview of the many different methods that have been developed in numerous contexts.

Geometric Science Of Information

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Author : Frank Nielsen
language : en
Publisher: Springer Nature
Release Date : 2023-07-31

Geometric Science Of Information written by Frank Nielsen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-31 with Computers categories.

This book constitutes the proceedings of the 6th International Conference on Geometric Science of Information, GSI 2023, held in St. Malo, France, during August 30-September 1, 2023. The 125 full papers presented in this volume were carefully reviewed and selected from 161 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications. The papers are organized in the following topics: geometry and machine learning; divergences and computational information geometry; statistics, topology and shape spaces; geometry and mechanics; geometry, learning dynamics and thermodynamics; quantum information geometry; geometry and biological structures; geometry and applications.

Adversarial Machine Learning

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Author : Aneesh Sreevallabh Chivukula
language : en
Publisher: Springer Nature
Release Date : 2023-03-06

Adversarial Machine Learning written by Aneesh Sreevallabh Chivukula and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-06 with Computers categories.

A critical challenge in deep learning is the vulnerability of deep learning networks to security attacks from intelligent cyber adversaries. Even innocuous perturbations to the training data can be used to manipulate the behaviour of deep networks in unintended ways. In this book, we review the latest developments in adversarial attack technologies in computer vision; natural language processing; and cybersecurity with regard to multidimensional, textual and image data, sequence data, and temporal data. In turn, we assess the robustness properties of deep learning networks to produce a taxonomy of adversarial examples that characterises the security of learning systems using game theoretical adversarial deep learning algorithms. The state-of-the-art in adversarial perturbation-based privacy protection mechanisms is also reviewed. We propose new adversary types for game theoretical objectives in non-stationary computational learning environments. Proper quantification of the hypothesis set in the decision problems of our research leads to various functional problems, oracular problems, sampling tasks, and optimization problems. We also address the defence mechanisms currently available for deep learning models deployed in real-world environments. The learning theories used in these defence mechanisms concern data representations, feature manipulations, misclassifications costs, sensitivity landscapes, distributional robustness, and complexity classes of the adversarial deep learning algorithms and their applications. In closing, we propose future research directions in adversarial deep learning applications for resilient learning system design and review formalized learning assumptions concerning the attack surfaces and robustness characteristics of artificial intelligence applications so as to deconstruct the contemporary adversarial deep learning designs. Given its scope, the book will be of interest to Adversarial Machine Learning practitioners and Adversarial Artificial Intelligence researchers whose work involves the design and application of Adversarial Deep Learning.

Algebraic Methods In Statistics And Probability Ii

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Author : Marlos A. G. Viana
language : en
Publisher: American Mathematical Soc.
Release Date : 2010

Algebraic Methods In Statistics And Probability Ii written by Marlos A. G. Viana and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.

A decade after the publication of Contemporary Mathematics Vol. 287, the present volume demonstrates the consolidation of important areas, such as algebraic statistics, computational commutative algebra, and deeper aspects of graphical models. --

Probability Models

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Author :
language : en
Publisher: Elsevier
Release Date : 2024-10-24

Probability Models written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-24 with Mathematics categories.

Probability Models, Volume 51 in the Handbook of Statistics series, highlights new advances in the field, with this new volume presenting interesting chapters on Stein's methods, Probabilities and thermodynamics third law, Random Matrix Theory, General tools for understanding fluctuations of random variables, An approximation scheme to compute the Fisher-Rao distance between multivariate normal distributions, Probability Models Applied to Reliability and Availability Engineering, Backward stochastic differential equation– Stochastic optimization theory and viscous solution of HJB equation, and much more.Additional chapters cover Probability Models in Machine Learning, The recursive stochastic algorithm, randomized urn models and response-adaptive randomization in clinical trials, Random matrix theory: local laws and applications, KOO methods and their high-dimensional consistencies in some multivariate models, Fourteen Lectures on Inference for Stochastic Processes, and A multivariate cumulative damage model and some applications. - Provides the latest information on probability models - Offers outstanding and original reviews on a range of probability models research topics - Serves as an indispensable reference for researchers and students alike

Linguistically Motivated Statistical Machine Translation

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Author : Deyi Xiong
language : en
Publisher: Springer
Release Date : 2015-02-11

Linguistically Motivated Statistical Machine Translation written by Deyi Xiong and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-11 with Language Arts & Disciplines categories.

This book provides a wide variety of algorithms and models to integrate linguistic knowledge into Statistical Machine Translation (SMT). It helps advance conventional SMT to linguistically motivated SMT by enhancing the following three essential components: translation, reordering and bracketing models. It also serves the purpose of promoting the in-depth study of the impacts of linguistic knowledge on machine translation. Finally it provides a systematic introduction of Bracketing Transduction Grammar (BTG) based SMT, one of the state-of-the-art SMT formalisms, as well as a case study of linguistically motivated SMT on a BTG-based platform.

Integration Of Machine Learning And Computer Simulation In Solving Complex Physiological And Medical Questions

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Author : Nicole Y. K. Li-Jessen
language : en
Publisher: Frontiers Media SA
Release Date : 2022-08-01

Integration Of Machine Learning And Computer Simulation In Solving Complex Physiological And Medical Questions written by Nicole Y. K. Li-Jessen and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-01 with Science categories.

Sensor Signal And Information Processing Ii

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Author : Wai Lok Woo
language : en
Publisher: MDPI
Release Date : 2020-12-29

Sensor Signal And Information Processing Ii written by Wai Lok Woo and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-29 with Technology & Engineering categories.

In the current age of information explosion, newly invented technological sensors and software are now tightly integrated with our everyday lives. Many sensor processing algorithms have incorporated some forms of computational intelligence as part of their core framework in problem solving. These algorithms have the capacity to generalize and discover knowledge for themselves and learn new information whenever unseen data are captured. The primary aim of sensor processing is to develop techniques to interpret, understand, and act on information contained in the data. The interest of this book is in developing intelligent signal processing in order to pave the way for smart sensors. This involves mathematical advancement of nonlinear signal processing theory and its applications that extend far beyond traditional techniques. It bridges the boundary between theory and application, developing novel theoretically inspired methodologies targeting both longstanding and emergent signal processing applications. The topic ranges from phishing detection to integration of terrestrial laser scanning, and from fault diagnosis to bio-inspiring filtering. The book will appeal to established practitioners, along with researchers and students in the emerging field of smart sensors processing.