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Found 4 papers, 0 papers with code
Matrix Completion in Almost-Verification Time
In the well-studied setting where $\mathbf{M}$ has incoherent row and column spans, our algorithms complete $\mathbf{M}$ to high precision from $mr^{2+o(1)}$ observations in $mr^{3 + o(1)}$ time (omitting logarithmic factors in problem parameters), improving upon the prior state-of-the-art [JN15] which used $\approx mr^5$ samples and $\approx mr^7$ time.
Semi-Random Sparse Recovery in Nearly-Linear Time
We design a new iterative method tailored to the geometry of sparse recovery which is provably robust to our semi-random model.
Distributional Hardness Against Preconditioned Lasso via Erasure-Robust Designs
Surprisingly, at the heart of our lower bound is a new positive result in compressed sensing.
Dictionary Learning and Tensor Decomposition via the Sum-of-Squares Method
We give a new approach to the dictionary learning (also known as "sparse coding") problem of recovering an unknown $n\times m$ matrix $A$ (for $m \geq n$) from examples of the form \[ y = Ax + e, \] where $x$ is a random vector in $\mathbb R^m$ with at most $\tau m$ nonzero coordinates, and $e$ is a random noise vector in $\mathbb R^n$ with bounded magnitude.
