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

arXiv: https://arxiv.org/abs/2309.15366 · HTML: https://mlsanity.com/paper/2309.15366/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 51 references that are in the map.
- First posted on arXiv 27 Sep 2023.

## Builds on (most cited first, 11 of 11)

- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Coupling techniques for nonlinear ensemble filtering](https://mlsanity.com/paper/1907.00389/) (2019)
- [Inference via low-dimensional couplings](https://mlsanity.com/paper/1703.06131/) (2017)
- [On the representation and learning of monotone triangular transport maps](https://mlsanity.com/paper/2009.10303/) (2020)
- [Beyond normality: Learning sparse probabilistic graphical models in the non-Gaussian setting](https://mlsanity.com/paper/1711.00950/) (2017)
- [Scalable Bayesian transport maps for high-dimensional non-Gaussian spatial fields](https://mlsanity.com/paper/2108.04211/) (2021)
- [Comparative Performance Evaluation of Large Language Models for Extracting Molecular Interactions and Pathway Knowledge](https://mlsanity.com/paper/2307.08813/) (2023)
- [Conditional Density Estimation, Latent Variable Discovery and Optimal Transport](https://mlsanity.com/paper/1910.14090/) (2019)
- [Comprehensive analysis of gene expression profiles to radiation exposure reveals molecular signatures of low-dose radiation response](https://mlsanity.com/paper/2301.01769/) (2023)

## Built on by (most cited first, 2 of 2)

- [A friendly introduction to triangular transport](https://mlsanity.com/paper/2503.21673/) (2025)
- [Multifidelity Formulations for Triangular Transport](https://mlsanity.com/paper/2610.00698/) (2026)

## Abstract (arXiv)

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.