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arXiv · 2204.07879

Polynomial-time Sparse Measure Recovery: From Mean Field Theory to Algorithm Design

Hadi Daneshmand·Francis Bach
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Abstract

Mean field theory has provided theoretical insights into various algorithms by letting the problem size tend to infinity. We argue that the applications of mean-field theory go beyond theoretical insights as it can inspire the design of practical algorithms. Leveraging mean-field analyses in physics, we propose a novel algorithm for sparse measure recovery. For sparse measures over $\mathbb{R}$, we propose a polynomial-time recovery method from Fourier moments that improves upon convex relaxation methods in a specific parameter regime; then, we demonstrate the application of our results for the optimization of particular two-dimensional, single-layer neural networks in realizable settings.

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Hadi Daneshmand, Francis Bach. 2022-04-16. Polynomial-time Sparse Measure Recovery: From Mean Field Theory to Algorithm Design. https://arxiv.org/abs/2204.07879

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