Tensor Density Estimator by Convolution-Deconvolution

TL;DR

This paper introduces a novel tensor-based density estimation framework that combines convolution, tensor train compression, and deconvolution to achieve high accuracy and efficiency.

Contribution

It presents a new linear algebraic approach for density estimation using tensor trains, integrating convolution and deconvolution steps.

Findings

High accuracy demonstrated in numerical experiments

Efficient tensor decomposition algorithms used

Effective variance reduction through smoothing kernels

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.