Stats 102B Matrix Computation and Optimization for Statistics

Course description:
Introduction to matrix computation and optimization methods for statistical theory and applications. Main topics include
1) Vectors and vector spaces: inner products, norms, geometrical properties, variance and covariance of vectors;
2) Matrix computations: trace, determinant, linear operators, self-adjoint operators, quadratic forms, eigenanalysis;
3) Gradient-based optimization: gradient and the Hessian, stationary points, the Lagrangian, Newton's method;
4) Applications in statistics: multivariate normal distributions, principal components, singular value decomposition.

Lectures: MWF 1-1:50pm, PAB 1749.  Discussion session: Th 1-1:50pm, WGYoung 4216.
Instructor: Qing Zhou (zhou@stat.ucla.edu), Office Hour: Wed 4pm ¨C 5:30pm, MS 8979.
TA:
Ryan Rosario (rosario@stat.ucla.edu), Office Hour: Thu 12-1pm, MS 8105H.

Text book:

Gentle, JE (2007) Matrix algebra: Theory, computations and applications in statistics. Springer.

Syllabus

Lecture Notes:    1    2    3    4    5    6    7    8    9    10

Homework:

Hw1: P37-38, 2.2, 2.3, 2.4, 2.7, 2.10.
Hw2: P38-39, 2.11, 2.14, 2.15, 2.16, 2.17.
Hw3: Download.
Hw4: Download.
Hw5: Download.
Hw6: Download.
Hw7: Download.
Hw8: Download.

Solutions:    Hw1    Hw2    Hw3    Hw4    Hw5    Hw6