Media Summary: 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.
Algorithms For Big Data Compsci 229r Lecture 10 - Detailed Analysis & Overview
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. Low-rank approximation, column-based matrix reconstruction, k-means, compressed sensing. Necessity of randomized/approximate guarantees, linear sketching, AMS sketch, p-stable sketch for p less than 2. Communication complexity (indexing, gap hamming) + application to median and F0 lower bounds.
MapReduce: TeraSort, minimum spanning tree, triangle counting. Logistics, course topics, basic tail bounds (Markov, Chebyshev, Chernoff, Bernstein), Morris' Amnesic dynamic programming (approximate distance to monotonicity). Online primal/dual: e/(e-1) ski rental, set cover; approximation Alon's JL lower bound, beyond worst case analysis: suprema of gaussian processes, Gordon's theorem. ORS theorem (distributional JL implies Gordon's theorem), sparse JL.
Oblivious subspace embeddings, faster iterative regression, sketch-and-solve regression. ℓ1/ℓ1 recovery, RIP1, unbalanced expanders, Sequential Sparse Matching Pursuit. RIP and connection to incoherence, basis pursuit, Krahmer-Ward theorem.
