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Course

MATH-412: Statistical machine learning

Lectures in this course (49)

Kernel Methods: Representer Theorem and SVM Applications

Explores the Representer Theorem, SVM applications, smoothness measurement, kernel combinations, and scalability in kernel methods.

Decision and regression trees

Explores decision and regression trees, impurity measures, learning algorithms, and implementations, including conditional inference trees and tree pruning.

Bagging and Random Forests

Covers ensembling, bagging, random forests, variable importance, and OOB cross-validation in machine learning.

Linear Regression Basics: ERM Perspective

Introduces linear regression basics from an empirical risk minimization perspective, covering the square loss, data preprocessing, and gradient computation.

Boosting: Adaboost Algorithm

Covers boosting with a focus on the Adaboost algorithm, forward stagewise additive modeling, and gradient tree boosting.

K-means Algorithm: Demo

Introduces the k-means algorithm for clustering data points based on centroids and iterative updates.

K-means and Gaussian Mixture Model

Introduces K-means clustering, the Gaussian mixture model, Jensen's inequality, and the EM algorithm.

Derivation of EM for the GMM

Covers the derivation of the EM algorithm for the Gaussian Mixture Model.

End of the M-step derivation

Covers the derivation of the M-step for mu_k and Sigma_k, focusing on key quantities and matrices.

Gaussian Mixture Model: EM final form

Explains the E-step and M-step calculations in the Gaussian Mixture Model, including the pseudocode of the EM algorithm.

Untitled

Neural Networks and Deep Learning

Covers formal neuron models, activation functions, and approximation results for neural networks.

Training Neural Networks

Covers the training of neural networks using stochastic gradient descent, chain rules, gradients computation, weight decay, and dropout.

Convolutional Neural Networks

Explores convolutional neural networks, covering convolution, cross-correlation, max pooling, layer structure, and examples like LeNet5 and AlexNet.

Theoretical Properties of Linear Regression Estimator

Covers the theoretical properties of the linear regression estimator, including the hat matrix and the Gauss-Markov theorem.

Learning with Deep Neural Networks

Explores the success and challenges of deep learning, including overfitting, generalization, and the impact on various domains.

Rademacher Complexity Control: Empirical Risk

Discusses statistical learning theory, Rademacher complexity, and empirical process control for estimation error.

Proof for Rademacher Control

Presents a proof for Rademacher control of the expected estimation error, focusing on empirical process control.

High probability learning guarantees

Explores Talagrand's lemma, Rademacher complexity bounds, and high probability guarantees in learning.

McDiarmid Inequality: Insights and Applications

Explores the McDiarmid inequality and its implications in probability theory, focusing on writing variations and key concepts.