6 citations · 9 across the 23 of their papers we have counts for
11 papers · 1 filter
Well-Conditioned Oblivious Perturbations in Linear Space
Shabarish Chenakkod, Michał Dereziński, 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…
The matrix-vector complexity of
Michał Dereziński, Ethan N. Epperly, Raphael A. Meyer
Matrix--vector algorithms, particularly Krylov subspace methods, are widely viewed as the most effective algorithms for solving large systems of linear equations. This paper establ…
Optimal Subspace Embeddings: Resolving Nelson-Nguyen Conjecture Up to Sub-Polylogarithmic Factors
Shabarish Chenakkod, Michał Dereziński, 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…
Faster Low-Rank Approximation and Kernel Ridge Regression via the Block-Nyström Method
Sachin Garg, Michał Dereziński
The Nyström method is a popular low-rank approximation technique for large matrices that arise in kernel methods and convex optimization. Yet, when the data exhibits heavy-tailed s…
Approaching Optimality for Solving Dense Linear Systems with Low-Rank Structure
Michał Dereziński, Aaron Sidford
We provide new high-accuracy randomized algorithms for solving linear systems and regression problems that are well-conditioned except for large singular values. For solving su…
Optimal Oblivious Subspace Embeddings with Near-optimal Sparsity
Shabarish Chenakkod, Michał Dereziński, 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 that…
Distributed Least Squares in Small Space via Sketching and Bias Reduction
Sachin Garg, Kevin Tan, Michał Dereziński
Matrix sketching is a powerful tool for reducing the size of large data matrices. Yet there are fundamental limitations to this size reduction when we want to recover an accurate e…
Faster Linear Systems and Matrix Norm Approximation via Multi-level Sketched Preconditioning
Michał Dereziński, Christopher Musco, Jiaming Yang
We present a new class of preconditioned iterative methods for solving linear systems of the form . Our methods are based on constructing a low-rank Nyström approximation t…
Fine-grained Analysis and Faster Algorithms for Iteratively Solving Linear Systems
Michał Dereziński, Daniel LeJeune, Deanna Needell +1
Despite being a key bottleneck in many machine learning tasks, the cost of solving large linear systems has proven challenging to quantify due to problem-dependent quantities such…
Solving Dense Linear Systems Faster Than via Preconditioning
Michał Dereziński, Jiaming Yang
We give a stochastic optimization algorithm that solves a dense real-valued linear system , returning such that in time: $…
Optimal Embedding Dimension for Sparse Subspace Embeddings
Shabarish Chenakkod, Michał Dereziński, Xiaoyu Dong +1
A random matrix is an oblivious subspace embedding (OSE) with parameters , and , if for any -dimensional subspace $W\subseteq R…