Probabilistic Graphical Models

Probabilistic Graphical Models


Jiří Materna


  • basic knowledge of programing in Python
  • high school level of mathematics


This course is intended for people interested in Bayesian networks and probabilistic programming. At the beginning of the course, the theoretical part will lead to a practical example of topic modeling using Latent Dirichlet Allocation and its non-parametric extension, including hyperparameter estimation. By completing this course, the participants should be able to design and implement their own simple Bayesian networks for various problems.


  • Bayesian networks
  • Model representation
  • Generative vs. discriminative models
  • Statistical inference in Bayesian networks
    • Variational inference
    • Sampling
      • Rejection sampling
      • Markov Chain Monte Carlo
      • Metropolis-Hastings sampling
      • Gibbs sampling
  • Probability distributions
    • Binomial and multinomial distributions
    • Beta and Dirichlet distributions
    • Gamma distribution
  • Probabilistic programming languages
  • Practical example with topic modeling
    • Latent Semantic Analysis
    • Probabilistic Latent Semantic Analysis
    • Latent Dirichlet Allocation
  • Non-Parametric topic modelling
    • Dirichlet process
    • Chinese restaurant process and Stick breaking process
    • Non-parametric LDA
  • Hyperparameter estimation