WAIC and WBIC with Python Stan : 100 Exercises for Building Logic / Joe Suzuki.

Format:

Book

Author/Creator:

Suzuki, Joe, author.

Language:

English

Subjects (All):

Bayesian statistical decision theory.

Logic, Symbolic and mathematical.

Physical Description:

1 online resource (249 pages)

Edition:

First edition.

Place of Publication:

Singapore : Springer Nature Singapore Pte Ltd, [2023]

Summary:

Master the art of machine learning and data science by diving into the essence of mathematical logic with this comprehensive textbook. This book focuses on the widely applicable information criterion (WAIC), also described as the Watanabe-Akaike information criterion, and the widely applicable Bayesian information criterion (WBIC), also described as the Watanabe Bayesian information criterion. The book expertly guides you through relevant mathematical problems while also providing hands-on experience with programming in Python and Stan. Whether you're a data scientist looking to refine your model selection process or a researcher who wants to explore the latest developments in Bayesian statistics, this accessible guide will give you a firm grasp of Watanabe Bayesian Theory. The key features of this indispensable book include: A clear and self-contained writing style, ensuring ease of understanding for readers at various levels of expertise. 100 carefully selected exercises accompanied by solutions in the main text, enabling readers to effectively gauge their progress and comprehension. A comprehensive guide to Sumio Watanabe's groundbreaking Bayes theory, demystifying a subject once considered too challenging even for seasoned statisticians. Detailed source programs and Stan codes that will enhance readers' grasp of the mathematical concepts presented. A streamlined approach to algebraic geometry topics in Chapter 6, making Bayes theory more accessible and less daunting. Embark on your machine learning and data science journey with this essential textbook and unlock the full potential of WAIC and WBIC today!

Contents:

Intro

Preface: Sumio Watanabe-Spreading the Wonder of Bayesian Theory

One-Point Advice for Those Who Struggle with Math

Features of This Series

Contents

1 Overview of Watanabe's Bayes

1.1 Frequentist Statistics

1.2 Bayesian Statistics

1.3 Asymptotic Normality of the Posterior Distribution

1.4 Model Selection

1.5 Why are WAIC and WBIC Bayesian Statistics?

1.6 What is ``Regularity''

1.7 Why is Algebraic Geometry Necessary for Understanding WAIC and WBIC?

1.8 Hironaka's Desingularization, Nothing to Fear

1.9 What is the Meaning of Algebraic Geometry's λ in Bayesian Statistics?

2 Introduction to Watanabe Bayesian Theory

2.1 Prior Distribution, Posterior Distribution, and Predictive Distribution

2.2 True Distribution and Statistical Model

2.3 Toward a Generalization Without Assuming Regularity

2.4 Exponential Family

3 MCMC and Stan

3.1 MCMC and Metropolis-Hastings Method

3.2 Hamiltonian Monte Carlo Method

3.3 Stan in Practice

3.3.1 Binomial Distribution

3.3.2 Normal Distribution

3.3.3 Simple Linear Regression

3.3.4 Multiple Regression

3.3.5 Mixture of Normal Distributions

4 Mathematical Preparation

4.1 Elementary Mathematics

4.1.1 Matrices and Eigenvalues

4.1.2 Open Sets, Closed Sets, and Compact Sets

4.1.3 Mean Value Theorem and Taylor Expansion

4.2 Analytic Functions

4.3 Law of Large Numbers and Central Limit Theorem

4.3.1 Random Variables

4.3.2 Order Notation

4.3.3 Law of Large Numbers

4.3.4 Central Limit Theorem

4.4 Fisher Information Matrix

5 Regular Statistical Models

5.1 Empirical Process

5.2 Asymptotic Normality of the Posterior Distribution

5.3 Generalization Loss and Empirical Loss

6 Information Criteria

6.1 Model Selection Based on Information Criteria

6.2 AIC and TIC

6.3 WAIC.

6.4 Free Energy, BIC, and WBIC

7 Algebraic Geometry

7.1 Algebraic Sets and Analytical Sets

7.2 Manifold

7.3 Singular Points and Their Resolution

7.4 Hironaka's Theorem

7.5 Local Coordinates in Watanabe Bayesian Theory

8 The Essence of WAIC

8.1 Formula of State Density

8.2 Generalization of the Posterior Distribution

8.3 Properties of WAIC

8.4 Equivalence with Cross-Validation-Like Methods

9 WBIC and Its Application to Machine Learning

9.1 Properties of WBIC

9.2 Calculation of the Learning Coefficient

9.3 Application to Deep Learning

9.4 Application to Gaussian Mixture Models

9.5 Non-informative Prior Distribution

References

Index.

Notes:

Includes bibliographical references and index.

Description based on print version record.

ISBN:

981-9938-41-4