Mathematics of Uncertainty

Mathematics of Uncertainty

  1. Basic Concepts from Statistics
    i. Distibution of random variables
    ii. Moments and cumulants
    iii. Probabilistic inequalities
    iv. Random variables from one to many
    v. Information theoretic view on randomness
  2. Stochastic Processes
    i. Bernoulli processes (discrete space, discrete time)
    ii. Poisson processes (discrete space, continuous time)
    iii. Stochastic processes which are continuous in space-time
    iv. Markov processes (discrete space, discrete time)
    v. Stochastic optimal control: Markov Decision Process
    vi. Queuing networks (bonus)
  3. Elements of Inference and Learning
    i. Statistical inference: sampling and stochastic algorithms
    ii. Statistical inference: general relations, calculus of variations and trees
    iii. Theory of learning: sufficient statistics and maximum likelihood
    iv. Function approximation with neural networks
    v. Reinforcement learning​​​​​​​