Media Summary: MapReduce: TeraSort, minimum spanning tree, triangle counting. Zeta transform, Möbius inversion, streaming External memory model: linked list, matrix multiplication, B-tree, buffered repository tree, sorting.
Algorithms For Big Data Compsci 229r Lecture 25 - Detailed Analysis & Overview
MapReduce: TeraSort, minimum spanning tree, triangle counting. Zeta transform, Möbius inversion, streaming External memory model: linked list, matrix multiplication, B-tree, buffered repository tree, sorting. Oblivious subspace embeddings, faster iterative regression, sketch-and-solve regression. P-stable sketch analysis, Nisan's PRG, ℓp estimation for p Linear least squares via subspace embeddings, leverage score sampling, non-commutative Khintchine, oblivious subspace ...
Logistics, course topics, basic tail bounds (Markov, Chebyshev, Chernoff, Bernstein), Morris' Low-rank approximation, column-based matrix reconstruction, k-means, compressed sensing. Power of random signs: ℓ2 norm estimation, subspace embeddings (regression), Johnson-Lindenstrauss, deterministic point ... Path-following interior point, first order methods (gradient descent). ℓ1/ℓ1 recovery, RIP1, unbalanced expanders, Sequential Sparse Matching Pursuit. second order methods (Newton's method), path-following interior point wrap-up.
Necessity of randomized/approximate guarantees, linear sketching, AMS sketch, p-stable sketch for p less than 2. Khintchine, decoupling, Hanson-Wright, proof of distributional JL lemma. RIP and connection to incoherence, basis pursuit, Krahmer-Ward theorem.
