Diffusion Generative Models: From Theory To Practice
Bahman Moraffah, Springer
This book investigates the rapidly evolving field of diffusion generative models, which have gained prominence for their capability in probabilistic modeling and data synthesis. By intertwining stochastic processes with deep learning techniques, diffusion models provide a versatile framework for producing high-quality samples across various domains such as images, text, and audio. This book begins with an exploration of the fundamental concepts underlying diffusion models, shedding light on their probabilistic foundations and the key elements of stochastic processes and Bayesian inference. It then navigates through the deep learning intricacies of these models, examining the neural network architectures and training methodologies employed. Additionally, the book discusses essential sampling techniques and inference methods for generating realistic samples and efficiently estimating model parameters. This book highlights the latest advancements in diffusion generative modeling, underscoring its scalability, interpretability, and capacity for uncertainty modeling. This book also covers a range of applications for diffusion models, such as image generation, text synthesis, audio synthesis, and biology, and evaluates metrics for assessing the quality of generated samples. This comprehensive overview aims to be a valuable resource for researchers and practitioners seeking to grasp the theoretical underpinnings and practical applications of diffusion generative modeling.
Contents:
Introduction
Mathematical Background and Principles Underlying Diffusion Models
Exploring Generative Modeling Techniques
Diving into the Depths: Understanding Diffusion Generative Models
Building Bridges: Exploring the Foundations of Diffusion Models
Beyond the Horizon: Advancements in Diffusion Models
Training and Inference: Techniques and Tricks
Architectural Variants of Diffusion Models
From Theory to Practice: Applications
Challenges and Future Directions
Appendix A: Datasets Used in Generative Modeling
Appendix B: Metrics Used for Training and Sampling
Appendix C: Summary of Techniques and Applications
Appendix D: Gumbel-Softmax Technique
Probability, Statistics, and Random Processes with Applications in Learning Theory
Bahman Moraffah
Probability theory provides a principled, practical, mathematical approach to learning theory. This book provides the fundamental background for doing research in machine learning, engineering, and statistics. It provides a unified treatment of theoretical and practical aspects of probability theory. The treatment is comprehensive and self-contained with many applications, targeted at researchers and students in machine learning, engineering, and applied statistics.
Contents:
Part I: Probability Theory
Probability Space
Continuous and Discrete Random Variables
Multiple Random Variables
Parametric Point Estimation
Probability Theory: Applications
Convergence and Asymptotic Behavior
Part II: Random Processes
Part III: Applications in Learning Theory
Probability and its Application in Machine Learning
Bootstrap and Monte Carlo Resampling Methods
Information Geometry and its Applications in Machine Learning
Bayesian Modeling and Inference: A Bayesian Approach to Machine Learning
Bahman Moraffah
It provides a comprehensive treatment of advanced learning theory. It spans a wide range of statistical tools from frequentists to Bayesian. This book extensively emphasizes the advances in machine learning theory from a Bayesian perspective. This book can be used for an advanced graduate course in Bayesian statistics.
Contents:
Theory of Point Estimation
Likelihood and first order methods such as MLE
Delta method
Asymptotic statistics
M and Z estimators
U statistics
Empirical processes
L-Stattiitcs
Parametric minimax theory
Expectation-minimization algorithm to compute
Introduction to nonparametric Statistics
Concentration of measure
Density estimation
Minimax theory
Statistical Decision Theory: A frequentist Approach
Bootstrap
Information Geometry
Regression
Introduction to Bayesian Statistics
Bayesian statistics: introduction and example — Bayes rule, Exchangeability, posterior, inference, marginalization
Singel parameter estimation
Multi- parameter estimation
Choice of prior
Frequentist property of Bayesian modeling
Advanced Posterior Computation
Markov chain Monte Carlo method
Gibbs sampling — efficient Gibbs sampling
Metropolis-Hastings algorithm
Building MC algorithm
Variational Bayes
Hierarchical Modeling
Mixture Model
Robust inference
Bayesian Regression
Bayesian Decision theory
Poisson Processes
Bayesian nonparametrics I
Dirichlet process – gamma process
Hierarchical Dirichlet process
Dependent Dirichlet process
Two-parameter Poisson-Dirichlet process
Bayesian nonparametrics II
Beta processes, stick-breaking, and power law
Indian Buffett process
Hierarchical Indian buffet proceses
Bayesian nonparametric III
Completely random measure
Normalized random measure
Kingman paintbox
Feature allocation and paintbox
Truncated random measure
Bayesian Nonparametrics IV
Bayesian Network and Causal Inference
Undirected graphical model
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