# Kernel approximation on algebraic varieties

@article{Altschuler2021KernelAO, title={Kernel approximation on algebraic varieties}, author={Jason M. Altschuler and Pablo A. Parrilo}, journal={ArXiv}, year={2021}, volume={abs/2106.02755} }

Low-rank approximation of kernels is a fundamental mathematical problem with widespread algorithmic applications. Often the kernel is restricted to an algebraic variety, e.g., in problems involving sparse or low-rank data. We show that significantly better approximations are obtainable in this setting: the rank required to achieve a given error depends on the variety’s dimension rather than the ambient dimension, which is typically much larger. This is true in both high-precision and high…

## One Citation

### Flows, Scaling, and Entropy Revisited: a Unified Perspective via Optimizing Joint Distributions

- Computer ScienceArXiv
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A unified algorithmic perspective on several classical problems which have traditionally been studied in different communities is described, which leads to a simple and unified framework spanning problem formulation, algorithm development, and runtime analysis.

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