Density Estimation via Measure Transport: Outlook for Applications in the Biological Sciences

TL;DR

This paper explores the use of measure transport methods, especially adaptive triangular transport maps, for density estimation in biological data with limited samples, demonstrating their potential to uncover hidden information and generate hypotheses.

Contribution

It introduces adaptive transport maps as a novel approach for density estimation in biological sciences, particularly effective with limited data samples.

Findings

Adaptive transport maps outperform traditional methods with limited data.

Series of transport maps reveal hidden data structures.

Application to radiation biology aids hypothesis generation.

Abstract

One among several advantages of measure transport methods is that they allow for a unified framework for processing and analysis of data distributed according to a wide class of probability measures. Within this context, we present results from computational studies aimed at assessing the potential of measure transport techniques, specifically, the use of triangular transport maps, as part of a workflow intended to support research in the biological sciences. Scenarios characterized by the availability of limited amount of sample data, which are common in domains such as radiation biology, are of particular interest. We find that when estimating a distribution density function given limited amount of sample data, adaptive transport maps are advantageous. In particular, statistics gathered from computing series of adaptive transport maps, trained on a series of randomly chosen subsets of the set of available data samples, leads to uncovering information hidden in the data. As a result, in the radiation biology application considered here, this approach provides a tool for generating hypotheses about gene relationships and their dynamics under radiation exposure.