Variational Autoencoders: Advanced Techniques and Representation Learning
Chapter 1: Foundations of Probabilistic Generative Models and Representation Learning
Probabilistic Models: An Advanced Perspective
Latent Variable Models: Theory and Formulation
Core Principles of Representation Learning
Evaluating Representation Quality: Metrics and Methodologies
Autoencoders Revisited: Limitations for Generative Tasks
Information Theory in Representation Learning
Chapter 2: Variational Autoencoders: Mathematical Deep Dive
VAE Derivation: Variational Inference
The Evidence Lower Bound (ELBO) Formulation
The Reparameterization Trick
KL Divergence in VAEs: Role and Interpretation
VAE Encoder and Decoder Network Design
Common VAE Training Difficulties
Analysis of VAE Objective Functions
Hands-on Practical: VAE Implementation and Diagnostics
Chapter 3: Advanced VAE Architectures and Modifications
Conditional VAEs (CVAEs) for Controlled Generation
Hierarchical VAEs for Complex Data Structures
Vector Quantized VAEs (VQ-VAEs)
Autoregressive Decoders in VAEs
Normalizing Flows for Flexible Priors and Posteriors
Beta-VAEs for Disentangled Representations
FactorVAEs and Total Correlation VAEs (TCVAEs)
Hands-on Practical: Implementing Advanced VAE Architectures
Chapter 4: Inference Techniques and Amortization in VAEs
Amortized Variational Inference: Strengths and Weaknesses
Limitations of Mean-Field Approximations
Structured Variational Inference in VAEs
Importance Weighted Autoencoders (IWAEs)
Auxiliary Variables and Semi-Amortized Variational Inference
Variational Inference with Implicit Models
Adversarial Variational Bayes (AVB)
Practice: Implementing IWAEs and Advanced Inference
Chapter 5: Disentangled Representation Learning with VAEs
Defining Disentanglement: Formulations and Difficulties
Metrics for Quantifying Disentanglement
The Influence of KL Regularization on Disentanglement
Information Bottleneck Theory and VAEs for Disentanglement
Adversarial Training for Disentanglement
Group-Theoretic Approaches to Disentanglement
Identifiability and Limitations in Disentanglement Learning
Hands-on Practical: Training and Evaluating Disentangled VAEs
Chapter 6: VAEs for Sequential and Structured Data
Recurrent VAEs (RVAEs) for Time Series Modeling
VAEs with Attention Mechanisms for Sequences
Graph VAEs for Structured Data Representation
VAEs in Natural Language Processing
Temporal VAEs for Video and Dynamic Systems
Connections between State-Space Models and VAEs
Practice: Implementing VAEs for Sequential Data
Chapter 7: Advanced Topics and Extensions of VAEs
Semi-Supervised Learning with VAEs
VAEs for Anomaly Detection and Out-of-Distribution Detection
Generative Adversarial Networks (GANs) vs. VAEs: A Comparative Analysis
Hybrid Models: VAE-GANs and Adversarial Autoencoders (AAEs)
VAEs in Model-Based Reinforcement Learning
Denoising VAEs and Input Perturbation Robustness
Advanced Optimization Strategies for VAEs
Hands-on Practical: Exploring Hybrid VAE-GAN Architectures
Normalizing Flows for Flexible Priors and Posteriors
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- Variational Inference with Normalizing Flows, Danilo Jimenez Rezende, Shakir Mohamed, 2015 Proceedings of the 32nd International Conference on Machine Learning (ICML) - Introduces normalizing flows for variational inference, proposing planar and radial flows to build more expressive approximate posteriors in VAEs.
- Improving Variational Inference with Inverse Autoregressive Flows, Diederik P. Kingma, Tim Salimans, Rafal Jozefowicz, Xi Chen, Ilya Sutskever, Max Welling, 2016 Advances in Neural Information Processing Systems, Vol. 29 (NeurIPS) DOI: 10.48550/arXiv.1606.04934 - Introduces inverse autoregressive flows (IAF) to create flexible posterior distributions, allowing efficient sampling and exact log-probability computation.
- Density estimation using Real NVP, Laurent Dinh, Jascha Sohl-Dickstein, Samy Bengio, 2017 International Conference on Learning Representations (ICLR) DOI: 10.48550/arXiv.1605.08803 - Presents Real NVP, a type of coupling layer flow that allows for both efficient density estimation and sampling, suitable for high-dimensional data.
- Masked Autoregressive Flow for Density Estimation, George Papamakarios, Theo Pavlakou, Iain Murray, 2017 Advances in Neural Information Processing Systems, Vol. 30 (NeurIPS) DOI: 10.48550/arXiv.1705.07057 - Details masked autoregressive flows (MAF) for density estimation, where log-probability evaluation is efficient while sampling is sequential.