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