Lipschitz-regularized gradient flows and generative particle algorithms for high-dimensional scarce data

TL;DR

This paper introduces a novel class of particle-based generative algorithms that leverage Lipschitz-regularized divergence gradient flows to efficiently learn and generate from high-dimensional, scarce data, demonstrated on gene expression datasets.

Contribution

The paper presents a new particle-based generative method using Lipschitz-regularized divergence flows, capable of handling high-dimensional and scarce data effectively.

Findings

Successfully transported gene expression data with over 54,000 dimensions.

Efficiently learned target distributions from limited high-dimensional data.

Demonstrated stability and accuracy in data transport tasks.

Abstract

We build a new class of generative algorithms capable of efficiently learning an arbitrary target distribution from possibly scarce, high-dimensional data and subsequently generate new samples. These generative algorithms are particle-based and are constructed as gradient flows of Lipschitz-regularized Kullback-Leibler or other $f$-divergences, where data from a source distribution can be stably transported as particles, towards the vicinity of the target distribution. As a highlighted result in data integration, we demonstrate that the proposed algorithms correctly transport gene expression data points with dimension exceeding 54K, while the sample size is typically only in the hundreds.