Probabilistic Graphical Model

This page contains resources about Probabilistic Graphical Models, Probabilistic Machine Learning and Probabilistic Models, including Latent Variable Models.

Graphical Models do not necessarily follow Bayesian Methods, but they are named after Bayes' Rule. Bayesian and Non-Bayesian (Frequentist) Methods can either be used.

A distinction should be made between Models and Methods (which might be applied on or using these Models).

Subfields and Concepts

See Category:Probabilistic Graphical Models for some of its subfields.

• Bayesian Networks (directed graphical models) - not  necessarily following a "Bayesian" approach
  • Artificial Neural Network
    • Feedforward Nerual Network (Directed Acyclic Graph)
    • Recurrent Neural Network (Directed Cyclic Graph)
  • Naive Bayes classifier (generative model)
    • Bayesian Naive Bayes
    • Tree Augmented Naive Bayes
  • Logistic Regression (discriminative model)
  • Gaussian Bayes Network / Gaussian Belief Net / Directed Gaussian Graphical Model
  • Dynamic Bayesian Network (used for Sequential Data / Time Series)
    • Hidden Markov Model (HMM)
    • Linear Dynamical System / State Space Model
      • Kalman filter / Linear Gaussian State Space Model
  • Deep Belief Network
  • Hierarchical Bayesian Model
  • Stochastic Computation Graph
  • Factor Analyzer
  • Auto-Regressive Network / Fully-visible Bayes Network (FVBN)
  • Variational Autoencoder (VAE)
• Markov Random Fields (undirected graphical models)
  • Gibbs Random Field
  • Gaussian MRF / Undirected Gaussian Graphical Model
  • Lattice Model
    • Potts Model
    • Ising Model
  • Hopfield Network
  • Boltzmann Machine
    • Restricted Boltzmann Machine
  • Conditional Random Field
  • Structural Support Vector Machine
  • Deep Boltzmann Machine
  • Associative Markov Network
  • Maximum Entropy (Maxent) Model
  • Structural Support Vector Machine (SSVM) / Max Margin Markov Network (M3net)
  • Factor Graph
• Stochastic Models (Stochastic Processes, Random Fields, ...)
• Latent Variable Models (i.e. Partially Observed Probabilistic Models)
  • Continuous Latent Variable Models
    • Factor Analyzer
    • Gaussian Process Latent Variable Model (GPLVM)
    • Gauss-Markov Process
    • State Space Model
      • Kalman filter / Linear Gaussian SSM
  • Discrete Latent Variable Models
    • Latent Dirichlet Allocation
    • Hidden Markov Model
    • Mixture Model
      • Bayesian Model
      • Non-Bayesian Model
• Mixed Networks (i.e. both deterministic and probabilistic)
• Chain Graph / Mixed Graph (i.e. both directed and undirected edges)
• Structure Learning
  • PC Algorithm
  • Network Scoring
  • Chow-Liu Trees
  • Minimal I-Map
  • Bayesian Model Selection
  • Annealed Importance Sampling
  • Sparsity promoting priors / Sparsity inducing priors
    • L2-regularization / Bayesian Ridge Regression / Gaussian prior
    • L1-regularization / Bayesian LASSO / Laplace prior
    • Spike and Slab / Bernoulli-Gaussian prior
• Inference in graphical models / Probabilistic Inference
  • Exact Inference / Exact Marginalization
    • Enumeration
    • Variable Elimination Algorithm / Bucket Elimination
    • Sum-Product Algorithm / Belief Propagation / Sum-Product Message Passing / Factor Graph propagation
    • Max-Product Algorithm / Max-Product Belief Propagation / Max-Sum Algorithm
    • Conditioning
    • Junction Tree Algorithm / Clique Tree Propagation
    • Forward-Backward Algorithm (used for HMM)
    • Baum-Welch Algorithm (used for HMM)
    • Viterbi Algorithm (used for HMM)
  • Approximate Inference
    • Deterministic / Structural: Variational Bayesian Inference (as Optimization)
    • Stochastic: Monte Carlo Inference / Sampling Inference / Particle-based Inference
    • Laplace Approximation

Online Courses

Video Lectures

• Probabilistic Graphical Models by Daphne Koller
• Machine Learning, Probability and Graphical Models by Sam Roweis  - VideoLectures.Net
• Graphical Models by Zoubin Ghahramani - VideoLectures.Net
• Graphical Models by Cedric Archambeau - VideoLectures.Net
• Introduction to Graphical Models for Data Mining by Arindam Banerjee - VideoLectures.Net
• Bayesian Learning by Zoubin Ghahramani - VideoLectures.Net
• Graphical modelling and Bayesian structural learning by Peter Green - VideoLectures.Net
• Graphical Models by Christian Borgelt - VideoLectures.Net
• Learning Bayesian Networks by Richard E. Neapolitan - VideoLectures.Net
• Machine Learning, Probability and Graphical Models by Sam Roweis - VideoLectures.Net
• Probabilistic Graphical Models by Sam Roweis - VideoLectures.Net

Lecture Notes

• Probabilistic Graphical Models by Sargur Srihari
• Probabilistic Graphical Models by David Sontag
• Probabilistic Graphical Models by Andreas Krause
• Probabilistic Graphical Models by Eric Xing
• Probabilistic Graphical Models Course by Sargur Srihari
• Foundations of Graphical Models by David M. Blei
• Probabilistic Models of Discrete Data by David M. Blei
• Probabilistic Modelling and Reasoning by Amos Storkey
• COS597C: Advanced Methods in Probabilistic Modeling BY David M. Blei
• CS228: Probabilistic Graphical Models by Stefano Ermon
• Statistical Methods for Machine Learning and Data Mining by Russ Salakhutdinov
• Statistical Methods for Machine Learning and Data Mining by Radford Neal
• CSC 2541: Topics in Machine Learning: Bayesian Methods for Machine Learning by Radford Neal
• CSE 515T: Bayesian Methods in Machine Learning by Roman Garnett
• CS 281A/Stat 241A: Statistical Learning Theory - Probabilistic Graphical Models by Michael Jordan
• Unsupervised Learning by Lester Mackey
• Unsupervised Learning by Zoubin Ghahramani
• Probabilistic and Unsupervised Learning by Maneesh Sahani - Gatsby
• Approximate Inference and Learning in Probabilistic Models by Maneesh Sahani - Gatsby
• Probabilistic Machine Learning by Carl Edward Rasmussen
• Machine Learning by Kevin Murphy
• Topics in multivariate analysis: Probabilistic graphical models
• Advanced Statistical Machine Learning by Stefanos Zafeiriou
•  Statistical Methods in Computer Science by Su-In Lee
•  Inference in Graphical Models by Sewoong Oh
•  COS513: Foundations of Probabilistic Modeling
• Probabilistic reasoning and statistical inference by Daniel Lassiter
• Data Mining and Machine Learning by Dino Sejdinovic
• Advanced Topics in Statistical Machine Learning by Dino Sejdinovic
• Statistical Data Mining and Machine Learning by Dino Sejdinovic

Books and Book Chapters

• Jordan, M. I. (TBA) An Introduction to Probabilistic Graphical Models. (draft)
• Bellot, D. (2016). Learning Probabilistic Graphical Models in R. Packt Publishing.
• Pfeffer, A. (2016). Practical probabilistic programming. Manning Publications Co.
• Koduvely, H. M. (2015). Learning Bayesian Models with R. Packt Publishing.
• Theodoridis, S. (2015). Machine Learning: A Bayesian and Optimization Perspective. Academic Press.
• Hastie, T., Tibshirani, R., & Wainwright, M. (2015). "Chapter 9: Graphs and Model Selection". Statistical learning with sparsity: the lasso and generalizations. CRC Press.
• Davidson-Pilon, C. (2015). Bayesian Methods for Hackers: Probabilistic Programming and Bayesian Inference. Addison-Wesley Professional.
• Ankan, A., & Panda, A. (2015). Mastering Probabilistic Graphical Models Using Python. Packt Publishing Ltd.
• Nagarajan, R., Scutari, M., & Lèbre, S. (2013). Bayesian Networks in R. Springer, 122, 125-127.
• Barber, D. (2012). Bayesian Reasoning and Machine Learning. Cambridge University Press.
• Murphy, K. P. (2012). Machine Learning: A Probabilistic Perspective. MIT Press.
• Duda, R. O., Hart, P. E., & Stork, D. G. (2012). Pattern Classification. John Wiley & Sons.
• Neal, R. M. (2012). Bayesian learning for neural networks. Springer Science & Business Media.
• Russell, S. J., & Norvig, P. (2010). "Part IV: Uncertain knowledge and reasoning". Artificial Intelligence: A Modern Approach. Prentice Hall.
• Alpaydin, E. (2010). "Chapter 16: Graphical Models". Introduction to machine learning. MIT Press.
• Koller, D., & Friedman, N. (2009). Probabilistic Graphical Models. MIT Press.
• Darwiche, A. (2009). Modeling and reasoning with Bayesian networks. Cambridge University Press.
• Borgelt, C., Steinbrecher, M., & Kruse, R. R. (2009). Graphical Models - Representations for Learning, Reasoning and Data Mining. John Wiley & Sons.
• Theodoridis, S., Pikrakis, A., Koutroumbas, K., & Cavouras, D. (2008). "Chapter 9: Context-dependent Classification". Pattern Recognition. 4th Ed. Academic Press.
• Wainwright, M. J., & Jordan, M. I. (2008). Graphical models, exponential families, and variational inference. Foundations and Trends® in Machine Learning, 1(1-2), 1-305.
• Bishop, C. M. (2006). "Chapter 8. Graphical Models". Pattern Recognition and Machine Learning. Springer. pp. 359–422.
• Jordan, M. I. (2003). An Introduction to Probabilistic Graphical Models.
• Jordan, M. I., & Sejnowski, T. J. (Ed.). (2001). Graphical models: Foundations of neural computation. MIT Press.
• Cowell, R. G., D., A. Philip, L., Steffen L., & Spiegelhalter, D. J. (1999). Probabilistic Networks and Expert Systems. Springer.
• Lauritzen, S. L. (1996). Graphical Models. Oxford University Press.
• Jensen, F. (1996). An Introduction to Bayesian Networks. Springer.
• Pearl, J. (1988). Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann.
• Jordan, M. I. (Ed.). (1998). Learning in graphical models. Kluwer Academic Publishers.

Scholarly Articles

• Ghahramani, Z. (2015). Probabilistic machine learning and artificial intelligence. Nature, 521(7553), 452-459.
• Larranaga, P., & Moral, S. (2011). Probabilistic graphical models in artificial intelligence. Applied soft computing, 11(2), 1511-1528.
• Airoldi, E. M. (2007). Getting Started in Probabilistic Graphical Models. PLoS Computational Biology, 3(12), e252.
• Wainwright, M. J., & Jordan, M. I. (2008). Graphical Models, Exponential Families, and Variational Inference. Foundations and Trends® in Machine Learning, 1(1-2), 1-305.
• Koller, D., Friedman, N., Getoor, L., & Taskar, B. (2007). 2 Graphical Models in a Nutshell. Statistical Relational Learning, 13.
• Silva, R., Scheine, R., Glymour, C., & Spirtes, P. (2006). Learning the structure of linear latent variable models. Journal of Machine Learning Research, 7(Feb), 191-246.
• Frey, B. J., & Jojic, N. (2005). A comparison of algorithms for inference and learning in probabilistic graphical models. IEEE Transactions on pattern analysis and machine intelligence, 27(9), 1392-1416.
• Ghahramani, Z. (2004). Unsupervised learning. In Advanced lectures on machine learning (pp. 72-112). Springer.
• Jordan, M. I. (2004). Graphical Models. Statistical Science, 140-155.
• Jordan, M. I., & Weiss, Y. (2002). Graphical models: Probabilistic inference.The handbook of brain theory and neural networks, 490-496.

Tutorials

• Graphical Models: Structure Learning by David Heckermann
• Graphical Models: Parameter Learning by Zoubin Ghahramani
• Heckerman's Bayes Net Learning Tutorial
• A Brief Introduction to Graphical Models and Bayesian Networks by Kevin Murphy
• An Introduction to Graphical Models by Michael Jordan
• Bayesian Modelling in Machine Learning: A Tutorial Review
• Bayesian Methods for Machine Learning - NIPS 2004
• Probabilistic Modelling, Machine Learning, and the Information Revolution by Zoubin Ghahramani - 2012
• Graphical Models by Zoubin Ghahramani - MLSS 2012
• Graphical Models Lectures - 2015
• An Introduction to Probabilistic Modeling by Oliver Stegle and Karsten Borgwardt
• Probabilistic reasoning and statistical inference by Daniel Lassiter

Software

• Edward: A library for probabilistic modeling, inference, and criticism - Python with TensorFlow
• Edward2 - Python with TensorFlow
• InferPy - Python with Edward
• Pyro - Python with PyTorch
• pgmpy - Python
• PyJAGS - Python
• Stan - Python (PyStan) and R (RStan) interfaces
• PyMC3 - Python
• PRMLT - MATLAB Toolbox for the book of PRML by C. Bishop
• pmtk3 - Probabilistic Modeling Toolkit for MLPP book by Murphy in Matlab/Octave (3rd edition)
• pyprobml - Python code for MLPP book by K. Murphy
• BRMLtoolbox - MATLAB and Julia code for the BRML book by D. Barber
• PyBRML - Python code for the BRML book by D. Barber
• Bayesian Probabilistic Matrix Factorization - MATLAB
• Mens X Machina PGM Toolbox - MATLAB
• UGM (undirected graphical models) - MATLAB
• Module libpgm - Python
• Graphical Models Toolkit (GMTK)
• Bayesian Modeling and Monte Carlo Methods
• SamIam
• BNT - Bayes Net Toolbox in MATLAB
• libDAI - C++
• OpenGM - C++
• Infer.NET - Developed by Microsoft Research
• OpenBUGS - Bayesian Inference Using Gibbs Sampling

See also

• Bayesian Machine Learning
• Bayesian Nonparametrics
• Estimation Theory
• Statistical Learning Theory
• Probability Theory
• Control Theory

Other Resources

• Comparison of software toolkits
• Probabilistic Graphical Models wiki
• Easier Plate Notation in Python using Daft - Python
• Graphical Models - Notebook
• Probabilistic: Definition, Models and Theory Explained - Statistics How To
• Graphical Models - Zoubin Ghahramani