Understanding Algorithms For Big Data Compsci 229r Lecture 16

Exploring Algorithms For Big Data Compsci 229r Lecture 16 reveals several interesting facts. Linear least squares via subspace embeddings, leverage score sampling, non-commutative Khintchine, oblivious subspace ...

Key Takeaways about Algorithms For Big Data Compsci 229r Lecture 16

  • Randomized and approximate F0 lower bounds, disjointness, Fp lower bound, dimensionality reduction (JL lemma).
  • Low-rank approximation, column-based matrix reconstruction, k-means, compressed sensing.
  • Khintchine, decoupling, Hanson-Wright, proof of distributional JL lemma.
  • Sparse JL proof wrap-up, Fast JL Transform, approximate nearest neighbor.
  • Matrix completion.

Detailed Analysis of Algorithms For Big Data Compsci 229r Lecture 16

Oblivious subspace embeddings, faster iterative regression, sketch-and-solve regression. Logistics, course topics, basic tail bounds (Markov, Chebyshev, Chernoff, Bernstein), Morris' Approximate matrix multiplication with Frobenius error via sampling / JL, matrix median trick, subspace embeddings.

Alon's JL lower bound, beyond worst case analysis: suprema of gaussian processes, Gordon's theorem.

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