Markov Chain Monte Carlo: Theory, Applications and Interdisciplinary Problems

January, 2021

Schedule

5-630PM, Wednesday and Saturdays.

Meetings

  1. Intro to Markov Chains and the MCMC Method (by Girish)
    Shuffling Cards Analysis | Fundamental Theorem of Convergence of MCs

  2. Uniform Sampling and Approximate Counting (by Girish)
    MC for Knapsack | Reduction from Counting to Sampling

  3. Coupling of Markov Chains (by Athreya)
    Analysis of Random Walk on Hypercube using Coupling

  4. Spectral Graph Theory and MCs (by Shantanu)
    Eigenvalues and MCs | Conductance and Second largest eigenvalue

  5. Path Coupling (by Athreya)
    Examples the Hypercube Random Walk, Colorings

Projects

1. Lifted Sampling of PGMs

2. Energy Based Models for Generative Models in ML

3. MCMC for Combinatorial Sampling and Approximate Counting

4. MCMC in Computer Graphics

5. MCMC for Random Colorings with Applications in Statistical Physics

6. Markov Chains for Transportation Problems

7. Bayesian Modeling for Ranking and Match making in Gaming Systems

Misc

Participants

  • TANMAY SINHA
  • Aditya Morolia
  • Chaitanya Kharyal
  • Shantanu Das
  • Rohan Sharma
  • ABHINAV VAISHYA
  • SHREEVIGNESH SURIYANARAYANAN
  • Prajwal Krishna
  • Athreya Chandramouli