The mathematical foundations every ML practitioner needs. Linear algebra, calculus, probability, and optimization — then applied to regression, PCA, GMMs, and SVMs.
Systems of equations, matrices, vector spaces, linear independence, basis, rank, linear mappings.
Norms, inner products, distances, angles, orthogonal projections, rotations.
Determinants, eigenvalues, Cholesky, eigendecomposition, SVD, low-rank approximation.
Gradients, Jacobians, backpropagation, Hessians, Taylor series.
Probability spaces, Bayes' theorem, Gaussians, conjugacy, change of variables.
Gradient descent, Lagrange multipliers, convex optimization, duality.
Empirical risk minimization, parameter estimation, probabilistic modeling, model selection.
MLE, MAP, Bayesian linear regression, orthogonal projection interpretation.
Maximum variance, projection, eigenvector computation, latent variable perspective.
EM algorithm, responsibilities, latent variables, density estimation.
Separating hyperplanes, margin maximization, dual formulation, kernels.