Lectures in course MGT-448: Statistical inference and machine learning

Covers the basics of probability theory, including definitions, calculations, and important concepts for statistical inference and machine learning.

Covers supervised learning with gradient descent algorithms and their statistical justification.

Covers random variables, probability functions, expectations, variances, and joint distributions.

Covers exponential family distributions, natural parameters, sufficient statistics, and logistic regression.

Explores the statistical justification of Least Squares and Generalized Linear Models.

Explores Newton's method for optimization, emphasizing the role of the Hessian matrix.

Explains the Armijo rule for setting step size in optimization methods.

Introduces convex sets and functions, discussing minimizers, optimality conditions, and characterizations, along with examples and key inequalities.

Explains how gradient descent converges to a function's minimum at a rate of 1 over k.

Explores strong convexity's role in faster convergence rates for optimization algorithms.

Explores the convergence of gradient descent for strongly convex functions and the importance of regularization in preventing overfitting.

Explores generative learning, class priors, and maximum likelihood estimation in classification models.

Explores generative learning algorithms, decision rules, and Gaussian distribution properties in machine learning.

Covers Gaussian discriminant analysis, log-likelihood, supervised learning, and logistic regression.

Covers the Naive Bayes algorithm with Gaussian Discriminant Analysis.

Explores logistic regression for predicting vegetation proportions in the Amazon region through remote sensing data analysis.

Covers the Naive Bayes assumption, Gaussian Discriminant Analysis, ML estimates, and Kernel trick.

Covers the concept of Least Mean Squares (LMs) with features and iterative updates.

Covers logistic regression, likelihood function, Newton's method, and classification error estimation.