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
Black Box Variational Inference (BBVI)
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- Black Box Variational Inference, Rajesh Ranganath, Sean Gerrish, David Blei, 2014 Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics (AISTATS), Vol. 33 - This foundational paper introduces Black Box Variational Inference (BBVI), providing a general framework for variational inference that bypasses the need for analytical gradient derivations, relying instead on Monte Carlo estimation. It is the direct source for the section's core topic.
- Auto-Encoding Variational Bayes, Diederik P. Kingma, Max Welling, 2013 International Conference on Learning Representations (ICLR) Workshop Track DOI: 10.48550/arXiv.1312.6114 - This seminal work, while introducing Variational Autoencoders, popularized the reparameterization trick (also known as the pathwise derivative estimator) as a low-variance method for estimating gradients in variational inference, making it highly relevant to the detailed explanation of this technique.
- Automatic Differentiation Variational Inference, Alp Kucukelbir, Dustin Tran, Robert R. Ma, Adeline Yu, Andrew Gelman, 2017 Journal of Machine Learning Research (JMLR), Vol. 18 (Journal of Machine Learning Research) DOI: 10.5555/3122009.3122010 - This paper elaborates on Automatic Differentiation Variational Inference (ADVI), a practical implementation of BBVI that leverages modern automatic differentiation tools within probabilistic programming languages like Stan. It demonstrates how the general BBVI framework is applied in practice.