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Tensor Density Estimator by Convolution-Deconvolution

Numerical Analysis 2025-10-29 v4 Numerical Analysis

Abstract

We propose a linear algebraic framework for performing density estimation. It consists of three simple steps: convolving the empirical distribution with certain smoothing kernels to remove the exponentially large variance; compressing the empirical distribution after convolution as a tensor train, with efficient tensor decomposition algorithms; and finally, applying a deconvolution step to recover the estimated density from such tensor-train representation. Numerical results demonstrate the high accuracy and efficiency of the proposed methods.

Keywords

Cite

@article{arxiv.2412.18964,
  title  = {Tensor Density Estimator by Convolution-Deconvolution},
  author = {Yifan Peng and Siyao Yang and Yuehaw Khoo and Daren Wang},
  journal= {arXiv preprint arXiv:2412.18964},
  year   = {2025}
}