Calibrating dimension reduction hyperparameters in the presence of noise.

The goal of dimension reduction tools is to construct a low-dimensional representation of high-dimensional data. These tools are employed for a variety of reasons such as noise reduction, visualization, and to lower computational costs. However, there is a fundamental issue that is discussed in other modeling problems that is often overlooked in dimension reduction-overfitting.

A convenient correspondence between k-mer-based metagenomic distances and phylogenetically-informed β-diversity measures.

k-mer-based distances are often used to describe the differences between communities in metagenome sequencing studies because of their computational convenience and history of effectiveness. Although k-mer-based distances do not use information about taxon abundances, we show that one class of k-mer distances between metagenomes (the Euclidean distance between k-mer spectra, or EKS distances) are very closely related to a class of phylogenetically-informed β-diversity measures that do explicitly use both the taxon abundances and information about the phylogenetic relationships among the taxa. Furthermore, we show that both of these distances can be interpreted as using certain features of the taxon abundances that are related to the phylogenetic tree.

Multiscale analysis of count data through topic alignment.

Topic modeling is a popular method used to describe biological count data. With topic models, the user must specify the number of topics $K$. Since there is no definitive way to choose $K$ and since a true value might not exist, we develop a method, which we call topic alignment, to study the relationships across models with different $K$.