4 papers
Accelerating Power Method with Fast Sketching for Stronger Low-Rank Approximation
Shabarish Chenakkod, MichaÅ DereziÅski
The power method is one of the most fundamental tools for extracting top principal components from data through low-rank matrix approximation. Yet, when the target rank is large, t…
Well-Conditioned Oblivious Perturbations in Linear Space
Shabarish Chenakkod, MichaÅ DereziÅski, Xiaoyu Dong +1
Perturbing a deterministic -dimensional matrix with small Gaussian noise is a cornerstone of smoothed analysis of algorithms [Spielman and Teng, JACM 2004], as it reduces the co…
Optimal Subspace Embeddings: Resolving Nelson-Nguyen Conjecture Up to Sub-Polylogarithmic Factors
Shabarish Chenakkod, MichaÅ DereziÅski, Xiaoyu Dong
We give a proof of the conjecture of Nelson and Nguyen [FOCS 2013] on the optimal dimension and sparsity of oblivious subspace embeddings, up to sub-polylogarithmic factors: For an…
Optimal Oblivious Subspace Embeddings with Near-optimal Sparsity
Shabarish Chenakkod, MichaÅ DereziÅski, Xiaoyu Dong
An oblivious subspace embedding is a random matrix such that, for any -dimensional subspace, with high probability preserves the norms of all vectors in th…