EE 270 - Large Scale Matrix Computation, Optimization and Learning

Lecture slides

Lecture 1: Introduction and overview of topics

Lecture 2: Approximate Matrix Multiplication (AMM)

Lecture 3: AMM Applications, Error Analysis, Trace Estimation and Bootstrap

Lecture 4: Approximate Tensor Products, Randomized Verification and Concentration Inequalities

Lecture 5: Randomized Dimension Reduction and Johnson Lindenstrauss (JL) lemma

Lecture 6: Applications of JL Embeddings

Lecture 7: Least Squares Problems and Random Projections

Lecture 8: Randomized Least Squares Solvers, Bias and Variance, Streaming Data

Lecture 9: High-dimensional Problems, Least-norm Solutions and Randomized Methods

Lecture 10: Leverage Scores and Basic Inequality Method

Lecture 11: Spectral Approximation, Subspace Embedding and Fast JL Transforms

Lecture 12: Gradient Descent and Convex Functions

Lecture 13: Gradient Descent with Momentum, Condition Numbers and Lyapunov Analysis

Lecture 14: Second-Order Optimization Algorithms, Strong Convexity and Randomized Preconditioners

Lecture 15: Randomized Newton’s Method and Logarithmic Barrier

Lecture 16: Stochastic Gradient Methods and Randomized Kaczmarz Algorithm

Lecture 17: Randomized Singular Value Decomposition and CX Decomposition

Lecture 18: Generalized Least Squares Problems, Randomized Low Rank Approximations and Power Iteration

Lecture 19: Kernel Matrices, Effective Dimension, Nystrom Method and Random Fourier Features

Lecture 20: Determinantal Point Processes and Markov Chain Monte Carlo