Probabilistic graphical models (PGMs) are sub-area of machine learning and statistics. PGMs are a framework for representing independence assumptions of random variables in probability distributions. Broadly, the study of PGMs includes the study of algorithms for learning and inference for these complex probability distributions. PGMs have applications in machine learning, statistics, natural language processing, speech recognition, computer vision, robotics, and other areas. Topics include Bayesian Networks, Hidden Markov Models (HMMs), Conditional Random Fields (CRFs), Markov Random Fields (MRFs), Variational Inference and Bayesian Non-parametrics.

• Sometimes PGMS are covered in the UCSC course CSE 290C (when Lisa Geetoor teaches it)
• Course at CMU: Probabilistic Graphical Models Spring 2020 Lectures with videos
• Best overview tutorial: CS228 Lecture Notes
• Tutorial on Probabilistic Graphical Models
• Book Chapter: Graphical Models in a Nutshell
• Paper: A Tutorial on Deep Latent Variable Models of Natural Language

• Bayesian Networks
• Markov Random Fields
  • Bert Huang's Video
• Factor Graphs

• Belief Propagation
  • Book chapter
  • Matt Gormley's slides
  • Bert Huang's Video Talks about relation of BP and Lagrangian relaxation at the end.

• Kschischang et al 1998 - Factor Graphs and The Sum-Product Algorithm The paper that introduced factor graphs
• Finkel et al 2005 - Incorporating Non-local Information into Information Extraction Systems by Gibbs Sampling

• Bach et al 2017 - Hinge-Loss Markov Random Fields and Probabilistic Soft Logic
• Chiang & Riley 2020 - Factor Graph Grammars

See also recent advances in HMMs and CRFs.

• Kim et al 2017 - Structured Attention Networks
• Thai et al 2018 - Embedded-State Latent Conditional Random Fields for Sequence Labeling
• Wang et al 2019 - Second-Order Semantic Dependency Parsing with End-to-End Neural Networks Uses loopy BP and variational inference
• Wang & Cho 2019 - BERT has a Mouth, and It Must Speak:BERT as a Markov Random Field Language Model WARNING: Mistake in this paper, it's not an MRF
• Gao & Gormley 2020 - Training for Gibbs Sampling on Conditional Random Fields with Neural Scoring Factors (basically adapted Finkel et al 2005 to the neural era)
• Lee et al 2020 - On the Discrepancy between Density Estimation and Sequence Generation Uses latent variables for fast non-autoregressive generation
• Srivastava et al 2020 - Robustness to Spurious Correlations via Human Annotations

• Conditional Random Field
• Probabilistic Logic