Advanced Bayesian Machine Learning
Chapter 1: Revisiting Bayesian Foundations
Probabilistic Modeling Principles
Bayes' Theorem in High Dimensions
Subjectivity and Objectivity in Prior Selection
Information Theory Connection: Entropy and KL Divergence
Computational Challenges in Bayesian Inference
Advanced Model Checking and Criticism
Chapter 2: Markov Chain Monte Carlo Methods
Principles of Monte Carlo Integration
Markov Chain Theory for MCMC
Metropolis-Hastings Algorithm Variants
Gibbs Sampling for Conditional Structures
Hamiltonian Monte Carlo (HMC) Mechanics
The No-U-Turn Sampler (NUTS)
Diagnosing MCMC Convergence and Performance
Hands-on Practical: Implementing Advanced MCMC
Chapter 3: Variational Inference Techniques
Optimization as Inference: The VI Perspective
Deriving the Evidence Lower Bound (ELBO)
Mean-Field Approximation Details
Coordinate Ascent Variational Inference (CAVI)
Stochastic Variational Inference (SVI) for Large Data
Black Box Variational Inference (BBVI)
Advanced Variational Families
Comparing MCMC and VI Strengths
Hands-on Practical: Scalable Variational Inference
Chapter 4: Gaussian Processes
Bayesian Non-parametric Modeling Introduction
Defining Gaussian Processes: Priors Over Functions
Covariance Functions (Kernels): Properties and Selection
Gaussian Process Regression Formulation
Hyperparameter Marginal Likelihood Optimization
Gaussian Process Classification Techniques
Approximations for Scalable Gaussian Processes
Hands-on Practical: Gaussian Process Modeling
Chapter 5: Advanced Topics in Probabilistic Graphical Models
Bayesian Networks: Structure Learning
Parameter Learning in Bayesian Networks
Advanced Inference in PGMs: Junction Tree Algorithm
Approximate Inference in Large PGMs
Latent Dirichlet Allocation (LDA): Bayesian Formulation
Inference for LDA: Collapsed Gibbs Sampling
Inference for LDA: Variational Bayes
Hands-on Practical: Topic Modeling with LDA
Chapter 6: Bayesian Deep Learning
Motivation for Bayesian Deep Learning
Bayesian Neural Networks (BNNs): Priors over Weights
Inference Challenges in BNNs
MCMC Methods for BNNs (e.g., Stochastic Gradient HMC)
Variational Inference for BNNs (e.g., Bayes by Backprop)
Uncertainty Estimation in BNNs
Variational Autoencoders (VAEs) as Probabilistic Models
Dropout as Approximate Bayesian Inference
Practical Training and Evaluation of BNNs
Hands-on Practical: Building a Bayesian Neural Network
Advanced Inference in PGMs: Junction Tree Algorithm
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- Probabilistic Graphical Models: Principles and Techniques, Daphne Koller and Nir Friedman, 2009 (The MIT Press) - Provides comprehensive coverage of PGM theory, including detailed explanations of the Junction Tree algorithm.
- Bayesian Networks and Decision Graphs, Finn V. Jensen, Thomas D. Nielsen, 2007 (Springer) DOI: 10.1007/978-0-387-68282-2 - A classic textbook offering a thorough treatment of exact inference in Bayesian networks, including the Junction Tree algorithm.
- CS228: Probabilistic Graphical Models (Autumn 2023-2024 Course Materials - Lecture 10: Junction Tree Algorithm), Volodymyr Kuleshov, Stefano Ermon, 2022 - Provides clear explanations and algorithmic details of the Junction Tree algorithm as part of a highly regarded PGM course.
- Local Computations with Probabilities on Graphical Structures and their Application to Expert Systems, Steffen L. Lauritzen and David J. Spiegelhalter, 1988 Journal of the Royal Statistical Society, Series B (Methodological), Vol. 50 (Blackwell Publishing for the Royal Statistical Society) DOI: 10.1111/j.2517-6161.1988.tb01720.x - Foundational paper introducing local computation on graphical models, which underpins the Junction Tree algorithm for exact inference.