Applied Probability & Statistics

Stochastic Processes

  • Bernoulli Process: definition, number of successes, distribution of inter-intervals, examples
  • Poisson Process: definition, inter-arrival time, number of arrivals, merging & splitting, examples
  • Space-time continuous  stochastic processes: Langevin equation, Path integral, Fokker Planck, examples (Brownian motion, first passage, Kramers escape problem)
  • Advanced example: Queuing theory

Stochastic Optimization

  • Stochastic Optimal Control (continuous space & time)
  • Markov Decision Process (discrete space & time)

Applied Statistics (Graphical Models and Neural Networks)

  • Inference, Counting, Sampling and Optimization  (problem formulation on example of Ising Model – undirected graphical models). Overview of variational and stochastic Methods
  • Directed Graphical Models. Neural Networks. Supervised, unsupervised. Reinforcement Learning. Deterministic/Stochastic – formulations and basic ideas.