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DTSTART:20070311T020000
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DTSTAMP:20260403T135851
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SUMMARY:Lecture / Discussion:Transport-Based Methods for Inference and Generation with Graphical Structure
DESCRIPTION:Statistical learning posits a structured relationship between observed data and unobserved quantities — latent components underlying a mixture\, counterfactual outcomes unobserved under the realized treatment assignment\, or low-dimensional representations encoding complex generative factors — and makes inference over the parameters that govern this relationship. In each case\, a graphical model encodes the structural assumptions through conditional independence and factorization\, but inference over the resulting distributional objects demands tools that are stable under the geometric irregularities — limited overlap\, high dimensionality\, unknown model complexity — that arise in practice. This thesis develops a distributional framework that pairs graphical model structure with optimal transport geometry to address this need. We apply the framework to causal inference under limited overlap\, replacing density-ratio reweighting with geometrically stable transport maps and developing Wasserstein-based sensitivity analysis for partial identification\; to structured generative modeling\, introducing Structured Flow Autoencoders that combine conditional normalizing flows with latent graphical models via a novel flow matching objective\; and to mixture model estimation\, where Bayes fixed-point iteration and entropy-regularized semi-discrete optimal transport yield a geometry-driven approach to component recovery and model selection. Across all settings\, the thesis demonstrates that replacing pointwise inference procedures with distributional\, geometry-aware ones — anchored by graphical model structure — yields methods that are simultaneously more principled and more practically reliable.
UID:147391-21900960@events.umich.edu
URL:https://events.umich.edu/event/147391
CLASS:PUBLIC
STATUS:CONFIRMED
CATEGORIES:Dissertation
LOCATION:West Hall - 438
CONTACT:
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