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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 Bayesian Machine Learning

Prerequisites: Strong foundation in machine learning concepts, probability theory, calculus, and linear algebra. Proficiency in Python and experience with standard machine learning libraries (e.g., NumPy, SciPy, Scikit-learn, TensorFlow/PyTorch) are required.

Level: Advanced

What You'll Learn

Advanced Inference Implementation
Implement and diagnose complex MCMC algorithms (Metropolis-Hastings, Gibbs, HMC) and Variational Inference methods (CAVI, SVI).
Sophisticated Bayesian Modeling
Formulate, build, and critique advanced Bayesian models including Gaussian Processes, Probabilistic Graphical Models, and Bayesian Neural Networks.
Uncertainty Quantification
Accurately represent and interpret model uncertainty using Bayesian approaches.
Model Selection and Comparison
Apply advanced techniques for comparing Bayesian models and evaluating their performance.
Scalable Bayesian Methods
Understand and apply techniques for scaling Bayesian inference to larger datasets.

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