Media Summary: Logistics, course topics, basic tail bounds (Markov, Chebyshev, Chernoff, Bernstein), Morris' Khintchine, decoupling, Hanson-Wright, proof of distributional JL lemma. Oblivious subspace embeddings, faster iterative regression, sketch-and-solve regression.
Algorithms For Big Data Compsci - Detailed Analysis & Overview
Logistics, course topics, basic tail bounds (Markov, Chebyshev, Chernoff, Bernstein), Morris' Khintchine, decoupling, Hanson-Wright, proof of distributional JL lemma. Oblivious subspace embeddings, faster iterative regression, sketch-and-solve regression. Low-rank approximation, column-based matrix reconstruction, k-means, compressed sensing. Amnesic dynamic programming (approximate distance to monotonicity). External memory model: linked list, matrix multiplication, B-tree, buffered repository tree, sorting.
Linear least squares via subspace embeddings, leverage score sampling, non-commutative Khintchine, oblivious subspace ... Communication complexity (indexing, gap hamming) + application to median and F0 lower bounds. Approximate matrix multiplication with Frobenius error via sampling / JL, matrix median trick, subspace embeddings. Sparse JL proof wrap-up, Fast JL Transform, approximate nearest neighbor. Alon's JL lower bound, beyond worst case analysis: suprema of gaussian processes, Gordon's theorem. RIP and connection to incoherence, basis pursuit, Krahmer-Ward theorem.
ORS theorem (distributional JL implies Gordon's theorem), sparse JL. ℓ1/ℓ1 recovery, RIP1, unbalanced expanders, Sequential Sparse Matching Pursuit. MapReduce: TeraSort, minimum spanning tree, triangle counting. Krahmer-Ward proof, Iterative Hard Thresholding.
