Media Summary: Communication complexity (indexing, gap hamming) + application to median and F0 lower bounds. Amnesic dynamic programming (approximate distance to monotonicity). Randomized and approximate F0 lower bounds, disjointness, Fp lower bound, dimensionality reduction (JL lemma).
Algorithms For Big Data Compsci 229r Lecture 9 - Detailed Analysis & Overview
Communication complexity (indexing, gap hamming) + application to median and F0 lower bounds. Amnesic dynamic programming (approximate distance to monotonicity). Randomized and approximate F0 lower bounds, disjointness, Fp lower bound, dimensionality reduction (JL lemma). Khintchine, decoupling, Hanson-Wright, proof of distributional JL lemma. External memory model: linked list, matrix multiplication, B-tree, buffered repository tree, sorting. P-stable sketch analysis, Nisan's PRG, ℓp estimation for p larger than 2 via max-stability.
Low-rank approximation, column-based matrix reconstruction, k-means, compressed sensing. Oblivious subspace embeddings, faster iterative regression, sketch-and-solve regression. Logistics, course topics, basic tail bounds (Markov, Chebyshev, Chernoff, Bernstein), Morris' RIP and connection to incoherence, basis pursuit, Krahmer-Ward theorem.
