Theoretical Foundations of Machine Learning Questions

Covers the mathematical and theoretical building blocks that underpin modern machine learning and artificial intelligence. Key areas include probability theory and Bayesian reasoning such as conditional probability, Bayes theorem, expectation and variance, and probabilistic inference; linear algebra and matrix analysis including eigenvalues, eigenvectors, matrix decompositions, matrix norms, rank, and geometric intuitions; optimization and calculus topics such as gradient descent, stochastic optimization, convexity, Lagrange multipliers, partial derivatives, the chain rule, and properties of optimization landscapes; and related theoretical themes such as information theory and approximation concepts. Candidates should be able to connect these foundations to algorithm behavior, model expressivity, convergence properties, and practical design decisions.