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 Variational Families
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- Variational Inference: A Review for Statisticians, David M. Blei, Alp Kucukelbir, Jon D. McAuliffe, 2017 Journal of the American Statistical Association, Vol. 112 (Taylor & Francis Ltd.) DOI: 10.1080/01621459.2017.1285773 - Provides a comprehensive overview of variational inference, including the limitations of mean-field approximations and an introduction to more advanced methods.
- Variational Inference with Normalizing Flows, Danilo Jimenez Rezende, Shakir Mohamed, 2015 International Conference on Machine Learning (ICML) DOI: 10.48550/arXiv.1505.05770 - Introduces the concept of normalizing flows for constructing flexible variational distributions, detailing planar and radial flow transformations.
- Normalizing Flows for Probabilistic Modeling and Inference, George Papamakarios, Eric Nalisnick, Danilo Jimenez Rezende, Shakir Mohamed, Balaji Lakshminarayanan, 2021 Journal of Machine Learning Research, Vol. 22 (JMLR, Inc.) DOI: 10.5555/3540209.3540212 - A comprehensive review of normalizing flows, covering their theoretical foundations, various architectures (including autoregressive and coupling flows), and applications in probabilistic modeling and inference.