Mathematics of Uncertainty
- 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 - 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) - 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