William Krinsman | Searcharxiv

arXiv2022

Tensor Algebra and its Applications to Data Science and Statistics

This survey provides an overview of common applications, both implicit and explicit, of "tensors" and "tensor products" in the fields of data science and statistics. One goal is to reconcile seemingly distinct usages of the term "tensor" in the literature, and to explain how these usages are manifestations of a common concept. Not all relevant topics are discussed in detail, but the attempt is made to briefly describe and give references for some of the most important topics not included in the main survey. Particular attention is given to tensor decompositions.

stat.AP↗

arXiv2022

Statistics of High-Throughput Characterization of Microbial Interactions

An active area of research interest is the inference of ecological models of complex microbial communities. Inferring such ecological models entails understanding the interactions between microbes and how they affect each other's growth. This dissertation employs a statistical perspective to contribute further to the knowledge currently addressing this problem. Part I explains how high-throughput droplet-based microfluidics technology can be used to screen for microbial interactions. An explicit, statistical framework is motivated and developed that can guide the analysis of data from such experiments. Part II explains how it might be possible to predict, based on the experimental setup, how much data will be produced to infer given microbial interactions. Running the experiment once without incubating the droplets turns out to be necessary to make such predictions. Part III demonstrates the feasibility of inferring microbial interactions from the data produced by these experiments. Relevant ideas from the microbiological and ecological literature are recast into an explicit, statistical framework.

stat.AP↗