Monte Carlo Methods

Monte Carlo methods form a family of stochastic approximation techniques, and are widely used in fields spanning Physics, Statistics and Finance. It is also a principal tool for statistical inference in ML. The module will cover Markov chains and Monte Carlo methods. These include Metropolis-Hastings methods, Gibbs sampling and collapsed Gibbs sampling, with applications to topic modelling and non-parametric Bayesian inference. Topics like importance sampling, slice sampling and exact sampling will also be included. Inference techniques for normalising constants (model scores), annealing and thermodynamic integration will also be covered.

Upon completion of the module the student will be able to:

  • apply practical tools to construct Markov chain Monte Carlo algorithms for statistical inference in ML problems;
  • analyse and apply those tools with an insight into their strengths and limitations;
  • formulate and interpret the mathematical theory underlying Monte Carlo methods;
  • discuss recent developments in Monte Carlo approaches, from both a theoretical and practical viewpoint.