Mathematical Foundations of Data Science

Review of eigenvalues and eigenvectors. Fundamental subspaces, matrix factorization techniques, principal components and best low-rank matrices; the structure of neural nets for deep learning. Convergence concepts and limit theorems in probability, basic inequalities of probability, tail bounds, the concentration of measures phenomena, empirical process. Maximum likelihood estimation, regularized regression, the Lasso and its variations. Optimization methods, gradient descent, stochastic gradient descent, convolutional neural nets.