Lectures

Lecture Jan 12: Introduction

Lecture Jan 14: Statistical learning, estimators, Markov and Chebyshev inequalities. PDF

Lecture Jan 19: Confidence intervals, weak convergence, L2 convergence. PDF

Lecture Jan 21: Bias-variance trade-off. PDF

Lecture Jan 27: The Central Limit Theorem. PDF

Lecture Jan 29: The Method of Moments estimator. PDF

Lecture Feb 3: Consistency of the MLE Estimator. Reimann & Lebesgue integration. PDF

Lecture Feb 5: Lebesgue integral, measurable functions, Borel sets, sigma fields. PDF

Lecture Feb 10: Convergence of random variables, measure continuity, liminf and limsup. PDF

Lecture Feb 12: Borel-Cantelli Lemma and the Strong Law of Large Numbers. PDF

Lecture Feb 24: Boltzmann machines, Gibbs fields, graphical models and pattern completion. PDF

Lecture Feb 26: Parameters estimation for restricted Boltzmann machines, Younes algorithm and contrastive divergence. PDF

Lecture March 3: More on RBMs and deep belief networks. PDF

Lecture March 5: Gaussian and Beta RBMs. Rao Blackwellization for RBMs. PDF

Lecture March 17: Stochastic approximation and Robins-Monro. PDF

Lecture March 19: More on stochastic approximation, averaging and momemtum. PDF

Lecture March 24: PDF

Lecture March 26: Lyapunov functions and convergence of stochastic approximation. PDF

Lecture March 31: Martingales and conditional expectation. PDF

Lecture Apr 2: Martingales, filtrations and Doob-Kolmogorov's inequality. PDF

Lecture Apr 9: Martingale convergence theorem and Hoeffding inequality. PDF