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DTSTART;TZID=America/Los_Angeles:20260803T160000
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SUMMARY:Le\, A. (STAT) -  Bayesian Nonparametric Analysis of Densities for Replicated Point Patterns
DESCRIPTION:Many scientific applications produce repeated point pattern realizations across subjects\, regions\, or time. While such point patterns exhibit individual variation\, we assume they arise from related point processes that share a common distributional structure. This dissertation develops a Bayesian nonparametric modeling framework built around an interpretable baseline. We work with Poisson processes\, such that the point process stochastic mechanism is characterized by the total intensity and a density with compact support. Flexible\, parsimonious weighted combinations of beta densities represent both the baseline and the replicate-specific densities. The weights corresponding to each replicate encode the features that characterize its density and are pooled hierarchically across replicates to estimate the shared baseline. Throughout\, we illustrate the framework using bike-share demand at a Chicago Divvy station\, where weekly demand shares a common daily pattern while its features evolve across weeks. \nWe lay the foundation with a conditionally independent model\, relating the replicates through a Dirichlet process prior centered on the shared baseline. The model admits a Pólya urn representation that yields fully conjugate posterior updates and partially parallel computation across replicates. Inference proceeds at both the shared and replicate-specific levels\, and predictive inference on the density of demand for a new week follows readily through the baseline. \nMoving to a dynamic extension\, we use the representation of the replicate-specific discrete random distributions to express structured dependence separately through the atoms and the weights. Stochastic processes on these components relate the locations of density features and their relative importance. The weights follow a geometric construction that keeps the model parsimonious. For the atoms\, we develop a novel stochastic process with the baseline as its marginal distribution\, so its interpretation is unchanged under temporal dependence. Across the Divvy weeks\, the contributions of these two forms of dependence are visible in the forecast uncertainty\, and both forecast the weekly densities more precisely than the conditionally independent model. \nFinally\, we model the full intensity of the underlying nonhomogeneous Poisson process by exploiting its factorization into a total intensity and a density. The factorization keeps the likelihood tractable and separates the volume of demand from its shape across the day. The dynamic density model carries directly over\, while the total intensity follows a stationary autoregressive process centered hierarchically on a baseline total intensity. This gives a baseline intensity\, extending the idea from densities to intensities. In the Divvy application\, the model yields smoother intensity estimates and sharper forecasts of the weekly intensities. \nThe common thread throughout the framework is the preservation of the baseline\, which retains the same interpretation as dependence and intensity modeling are introduced. Together\, the models give a unified characterization of the shared\, replicate-specific\, and dynamic structure of replicated point patterns. \nEvent Host: Andrew Le\, Ph.D. Candidate\, Statistical Science \nAdvisor: Athanasios Kottas \nZoom: https://ucsc.zoom.us/j/94954212320?pwd=lmcDG6LvDQTb73BOE2NqabU9M2Uzms.1 \nPasscode: 772566 \n 
URL:https://live-events-ucsc.pantheonsite.io/event/le-a-stat-bayesian-nonparametric-analysis-of-densities-for-replicated-point-patterns/
CATEGORIES:Ph.D. Presentations
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DTSTART;TZID=America/Los_Angeles:20260810T103000
DTEND;TZID=America/Los_Angeles:20260810T123000
DTSTAMP:20260721T182603Z
CREATED:20260721T182603Z
LAST-MODIFIED:20260721T182603Z
UID:10015110-1786357800-1786365000@live-events-ucsc.pantheonsite.io
SUMMARY:Zhao\, Z. (CSE) - TOWARD VERIFIABLE REASONING IN LLMS
DESCRIPTION:Chain-of-thought (CoT) prompting can improve final-answer performance\, but it does not guarantee that intermediate reasoning steps are faithful\, valid\, or checkable. This proposal studies how formal methods can make natural-language reasoning more reliable by translating CoT rationales into Lean artifacts\, checking the resulting theorem statements and proofs\, and using compiler feedback to diagnose and repair failures. The completed work evaluates direct zero-shot and few-shot auto-formalization pipelines for quantity- and logic-focused reasoning problems\, measuring proof type-check rate\, theorem-statement validity\, assumption faithfulness\, and repair behavior. The ongoing work extends this pipeline with AMR-guided semantic representations and altered-rationale stress tests. The planned work proposes methods of modeling LLM Agent thinking in Lean. Together\, these components separate two questions that are often conflated: whether a model translated the reasoning into the right formal goal\, and whether that goal can be proved once translated. The research goal is to develop an evaluation framework and a tool-supported workflow to improve the reliability\, auditability\, and semantic faithfulness of LLM reasoning. \nEvent Host: Zekun Zhao\, Ph.D. Student\, Computer Science & Engineering \nAdvisor: Jeffrey Flanigan \nZoom: https://ucsc.zoom.us/j/96068207641?pwd=anTpLhBXhIdaIhXKDTB32HlDMA6uIO.1 \nPasscode: 656037
URL:https://live-events-ucsc.pantheonsite.io/event/zhao-z-cse-toward-verifiable-reasoning-in-llms/
LOCATION:Silicon Valley Campus\, 3175 Bowers Avenue\, Santa Clara\, CA\, 95054\, United States
CATEGORIES:Ph.D. Presentations
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