Math Modeling Seminar: Bayesian Occupancy Estimation in Heterogenous and Uncertain Data Environments

Bayesian Occupancy Estimation in Heterogenous and Uncertain Data Environments

Dr. Robert Stewart
Senior Scientist, GeoAI Group
Oak Ridge National Laboratory
Joint Faculty, Geography, University of Tennessee

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Abstract:
High-throughput, high-dimensional data has become ubiquitous in the biomedical, health and social sciences as a result of breakthroughs in measurement technologies and data collection. While these large datasets containing millions of observations of cells, peoples, or brain voxels  hold great potential for understanding generative state space of the data, as well as drivers of differentiation, disease and progression, they also pose new challenges in terms of noise, missing data, measurement artifacts, and the so-called “curse of dimensionality.” In this talk, I will cover data geometric and topological approaches to understanding the shape and structure of the data.  First, we show how diffusion geometry and deep learning can be  used to obtain useful representations of the data that enable denoising (MAGIC), dimensionality reduction (PHATE), and factor analysis (Archetypal Analysis Network) of the data.  Next we will show how to learn dynamics from static snapshot data by using a manifold-regularized neural ODE-based optimal transport (TrajectoryNet). Finally, we cover a novel approach to combine diffusion geometry with topology to extract multi-granular features from the data (Diffusion Condensation and Multiscale PHATE) to assist in differential and predictive analysis. On the flip side, we also create a manifold geometry from topological descriptors, and show its applications to neuroscience. Together, we will show a complete framework for exploratory and unsupervised analysis of big biomedical data.

Speaker Bio:
Dr. Robert Stewart is a senior scientist in the GeoAI group at the Oak Ridge National Laboratory (ORNL) and adjunct associate professor of Geography at the University of Tennessee. He leads projects engaged in a wide array of R&D including machine learning, spatio-temporal analytics, data mining, big data workflows, simulation, visualization, and tool development. His work is informed by and applied to a wide range of use cases emerging from population dynamics, maritime safety, geomatics, urban dynamics, security, energy-water nexus, health, environmental risk and many others. His own research is focused on applied mathematical, statistical, and computational methods in the areas of spatio-temporal analytics, probability modeling, and uncertainty quantification with an emphasis on risk and decision support. As a faculty member at UT, Dr. Stewart engages graduate students in geography, mathematics, and the Bredesen Center Data Science Ph.D. program. He regularly serves on thesis committees, advises students, and facilitates internships at ORNL.

Intended Audience:
Undergraduates, graduates, and experts. Those with interest in the topic.
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The Math Modeling Seminar will recur each week throughout the semester on the same day and time. Find out more about upcoming speakers on the Mathematical Modeling Seminar Series webpage.