{"id":44460,"date":"2023-01-17T14:27:30","date_gmt":"2023-01-17T19:27:30","guid":{"rendered":"https:\/\/engineering.jhu.edu\/ams\/?post_type=tribe_events&p=44460"},"modified":"2023-01-17T15:06:21","modified_gmt":"2023-01-17T20:06:21","slug":"ams-weekly-seminar-phd-candidate-joshua-agterberg","status":"publish","type":"tribe_events","link":"https:\/\/engineering.jhu.edu\/ams\/event\/ams-weekly-seminar-phd-candidate-joshua-agterberg\/","title":{"rendered":"AMS Weekly Seminar | PhD Candidate Joshua Agterberg"},"content":{"rendered":"

Location:<\/strong> Gilman 132<\/span><\/p>\n

When:<\/strong> January 19th at 1:30 p.m.<\/p>\n

Title:<\/strong> Estimating Higher-Order Mixed Memberships via the Two to Infinity Tensor Perturbation Bound<\/span><\/p>\n

Abstract:<\/strong> 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.\u00a0 This talk is based on the preprint <\/span>https:\/\/arxiv.org\/abs\/2212.08642<\/a>.<\/span><\/p>\n

Join via zoom:<\/strong> https:\/\/wse.zoom.us\/j\/95738965246<\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

Location: Gilman 132 When: January 19th at 1:30 p.m. Title: Estimating Higher-Order Mixed Memberships via the Two to Infinity Tensor Perturbation Bound Abstract: Higher-order multiway data is ubiquitous in 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