Probabilistic Graphical Models (EN)

Description

This course is intended for people interested in Bayesian networks and probabilistic programming.

The theoretical part at the beginning of the course 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.

Contents

• 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

Prerequisites

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