Stochastic noise in Machine Learning
Objectives

Study different types of stochastic noise as well as their interpretations as an error of various algorithms in machine learning.

Study stochastic process theory, as well as its applications to data science, with mathematical formality.

Invite the student to different directions where stochastic processes are necessary such as Game Theory, Reinforcement Learning and Stochastic Calculus.
Syllabus

Complements to Probability Theory

Kolmogorov axiomatization

Independence

Random Variables

Hope and other moments

Joint probabilities

Covariance

Law of the big numbers

Central limit theorem
2. Linear regressions and Gaussian noise

Definition of overfitting

Ridge regularization
3. Noise and Martingales

Formal definitions

Applications to biology Branching processes

Polya Urns

Derivatives Calculation

Invitation to stochastic calculation
4. Time series and white noise
 Moving averages

White noise

An invitation to ARIMA and Garch.
5. Markov chains and noise

Basic definitions

Discreet examples

Examples from graph theory

Limit measures

Monte Carlo method

Invitation to Reinforcement Learning and game theory