## Lectures

Lecture Jan 12: Introduction

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

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

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Lecture Jan 21: Bias-variance trade-off.

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Lecture Jan 27: The Central Limit Theorem.

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Lecture Jan 29: The Method of Moments estimator.

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

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

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

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

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

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

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

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

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Lecture March 17: Stochastic approximation and Robins-Monro.

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

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Lecture March 24:

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

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Lecture March 31: Martingales and conditional expectation.

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

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Lecture Apr 9: Martingale convergence theorem and Hoeffding inequality.

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