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

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. Scarce data scenarios, which are common in domains such as radiation biology, are of particular interest. We find that when data is scarce, sparse transport maps are advantageous. In particular, statistics gathered from computing series of (sparse) 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.