Probability for Machine Learning

following notes were taken by attending Mathematics for Machine Learning — Ulrike von Luxburg, 2020/21, an amazing course offered by University of Tubingen

• Probability Theory 1: Introduction to Probability Measures

• Probability Theory 2: Different Types of Probability Measures

• Probability Theory 3: Lebesgue Decomposition and Singular Decomposition

• Probability Theory 4: Cumulative Distribution Function

• Probability Theory 5: Random Variables

• Probability Theory 6+8: Conditional Probability and Independence

• Probability Theory 7: Bayes Theorem

• Probability Theory 9: Expectation (discrete case)

• Probability Theory 10: Variance, covariance, correlation (discrete case)

• Probability Theory 11: Expectation and covariance (general case)

• Probability Theory 12: Markov and Chebyshev inequality

• Probability theory 13: Example distributions: binomial, poisson, multivariate normal

• Probability theory 14: Convergence of random variables

• Probability theory 15: Borel-Cantelli

• Probability theory 16: Law of large numbers, Central limit theorem

• Probability theory 17: Concentration inequalities

• Probability theory 18: Product space and joint distribution

• Probability theory 19: Marginal distribution

• Probability theory 20: Conditional distribution

• Probability theory 21: Conditional expectation