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Stochastic noise in Machine Learning

Objectives

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

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

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

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Syllabus

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  1. 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

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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.

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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

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