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DTSTART;TZID=America/New_York:20230119T133000
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SUMMARY:AMS Weekly Seminar | PhD Candidate Joshua Agterberg
DESCRIPTION:Location: Gilman 132 \nWhen: January 19th at 1:30 p.m. \nTitle: Estimating Higher-Order Mixed Memberships via the Two to Infinity Tensor Perturbation Bound \nAbstract: Higher-order multiway data is ubiquitous in machine learning and statistics and often exhibits community-like structures\, where each component (node) along each different mode has a community membership associated with it. In this talk we propose the tensor mixed-membership blockmodel\, a generalization of the tensor blockmodel positing that memberships need not be discrete\, but instead are convex combinations of latent communities. We establish the identifiability of our model and propose a computationally efficient estimation procedure based on the higher-order orthogonal iteration algorithm (HOOI) for tensor SVD composed with a simplex corner-finding algorithm. We then demonstrate the consistency of our estimation procedure by providing a per-node error bound\, which showcases the effect of higher-order structures on estimation accuracy. To prove our consistency result\, we develop the $\ell_{2\,\infty}$ tensor perturbation bound for HOOI under independent\, possibly heteroskedastic\, subgaussian noise that may be of independent interest. Our analysis uses a novel leave-one-out construction for the iterates\, and our bounds depend only on spectral properties of the underlying low-rank tensor under nearly optimal signal-to-noise ratio conditions such that tensor SVD is computationally feasible. Whereas other leave-one-out analyses typically focus on sequences constructed by analyzing the output of a given algorithm with a small part of the noise removed\, our leave-one-out analysis constructions use both the previous iterates and the additional tensor structure to eliminate a potential additional source of error. Finally\, we apply our methodology to US flight data\, showcasing the effect of COVID-19 on flights. This talk is based on the preprint https://arxiv.org/abs/2212.08642. \nJoin via zoom: https://wse.zoom.us/j/95738965246 \n
URL:https://engineering.jhu.edu/ams/event/ams-weekly-seminar-phd-candidate-joshua-agterberg/
CATEGORIES:Seminars and Lectures
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