Lecturer: Valentin Polishchuk (email)
Text: Schaum's Outline (any edition is fine)
Suggested grading: 6 credits (finished in ~1/2year) = Problem Sets solved + Several topics presented + In-class tests (pen&paper: closed books, closed notes, no internet). Other options may be negotiated
Applications to ML (mostly taught by Kien Huynh)
List of topics needed for the ML presentation
Vectors and geometric interpretation of data points
Dot products, angles, orthogonality, cosine similarity
Linear combinations, span, linear independence, rank
Matrices as linear transformations; matrix products as dot products; composition of linear maps
Linear vs. affine maps; hyperplanes, half-spaces, distance from a point to a hyperplane
Systems of linear equations and least-squares approximation
Orthogonal projections onto subspaces
Eigenvalues and eigenvectors; spectral theorem for symmetric matrices
Quadratic forms and maximizing xᵀAx on the unit sphere
Variance, covariance matrices, principal directions of variation
Аny topic not covered by the time ML is taught, will be covered during ML teaching
Topics in ML (tentative)
PCA, factor analysis
linear / least-squares regression (incl. sketching, see, e.g., these videos)
basic neural network
attention model
SVM (time-permitting)