CIF:Small:Minimum Mean Square Error Estimation and Control of Partially-Observed Boolean Dynamical Systems with Applications in Metagenomics
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This research concerns the development and application of innovative signal processing techniques to dynamical systems associated with the complex interactions among microbes, human cells, and their metabolic products. This project investigates innovative methods for estimation and control of processes that consist of the complex interactions of many switching elements, such as "presence" and "absence" of a particular microbial species in the human gut, enabling the characterization of microbial communities and their interactions with host cells. This project provides life scientists with computational tools for biochemical pathway discovery as well as rational intervention design, as in optimal drug scheduling and diet modifications to treat human disease.This project develops computational methods for systems identification and optimal control of Boolean dynamical systems partially observable through noisy time series data, with application in the modeling of metabolic interactions in the gut microbiome and their evolution. This project facilitates the integrative analysis of multimodal microbiota data, including transcriptomic, metatranscriptomic, metagenomic, and metabolomic data, enabling the characterization of environmental exposures, microbial communities, and their interactions with host gut epithelial cells. While previous work on Boolean dynamical systems has been based on ad-hoc binarization of measurement data and ignore the presence of unobservable variables, the methodology developed here allows the state process to be hidden and relies directly on indirect or incomplete noisy time series measurements of the states. A novel aspect of this work is that it is based on a minimum mean-square error criterion for optimal estimation and control, as opposed to maximum-a-posteriori methods typically used in Boolean and other discrete spaces. This project includes the construction of likelihood functions for various modalities of metagenomic data for use with exact and approximate optimal estimation and systems identification methods using the noisy measurement data. The methodology developed in this research is validated using novel time series metagenomic data provided by the project''s life science collaborators.