Media Summary: Alon's JL lower bound, beyond worst case analysis: suprema of gaussian processes, Gordon's theorem. Khintchine, decoupling, Hanson-Wright, proof of distributional JL lemma. Necessity of randomized/approximate guarantees, linear sketching, AMS sketch, p-stable sketch for p less than 2.
Algorithms For Big Data Compsci 229r Lecture 12 - Detailed Analysis & Overview
Alon's JL lower bound, beyond worst case analysis: suprema of gaussian processes, Gordon's theorem. Khintchine, decoupling, Hanson-Wright, proof of distributional JL lemma. Necessity of randomized/approximate guarantees, linear sketching, AMS sketch, p-stable sketch for p less than 2. ORS theorem (distributional JL implies Gordon's theorem), sparse JL. External memory model: linked list, matrix multiplication, B-tree, buffered repository tree, sorting. Approximate matrix multiplication with Frobenius error via sampling / JL, matrix median trick, subspace embeddings.
ℓ1/ℓ1 recovery, RIP1, unbalanced expanders, Sequential Sparse Matching Pursuit. Logistics, course topics, basic tail bounds (Markov, Chebyshev, Chernoff, Bernstein), Morris' Linear least squares via subspace embeddings, leverage score sampling, non-commutative Khintchine, oblivious subspace ... Stay Connected! Get the latest insights on Artificial Intelligence (AI) , Natural Language Processing (NLP) , and Low-rank approximation, column-based matrix reconstruction, k-means, compressed sensing. MapReduce: TeraSort, minimum spanning tree, triangle counting.
Distinct elements, k-wise independence, geometric subsampling of streams. Amnesic dynamic programming (approximate distance to monotonicity). FPTAS (knapsack), FPRAS (DNF counting), semidefinite programming, Goemans-Williamson MAXCUT
