{"id":46180,"date":"2023-08-24T10:36:47","date_gmt":"2023-08-24T14:36:47","guid":{"rendered":"https:\/\/engineering.jhu.edu\/ams\/?post_type=tribe_events&#038;p=46180"},"modified":"2023-09-01T10:48:08","modified_gmt":"2023-09-01T14:48:08","slug":"ams-weekly-seminar-assistant-professor-mateo-diaz","status":"publish","type":"tribe_events","link":"https:\/\/engineering.jhu.edu\/ams\/event\/ams-weekly-seminar-assistant-professor-mateo-diaz\/","title":{"rendered":"AMS Weekly Seminar | Assistant Professor Mateo Diaz"},"content":{"rendered":"<div>\n<p><strong><span>Location:\u00a0<\/span><\/strong><span>Gilman 132<\/span><\/p>\n<\/div>\n<div>\n<p><strong><span>When: <\/span><\/strong>September 7th at 1:30 p.m.<span><\/span><\/p>\n<\/div>\n<div>\n<p><strong><span>Title: <\/span><\/strong>Clustering a mixture of Gaussians with unknown covariance<\/p>\n<\/div>\n<div>\n<p><strong><span>Abstract: <\/span><\/strong>Clustering\u00a0is a fundamental data scientific task with broad application. This talk investigates a simple\u00a0clustering\u00a0problem with data from a mixture of Gaussians that share a common but unknown, and potentially ill-conditioned, covariance matrix. We start by considering Gaussian mixtures with two equally-sized components and derive a Max-Cut integer program based on maximum likelihood estimation. We show its solutions achieve the optimal misclassification rate when the number of samples grows linearly in the dimension, up to a logarithmic factor. However, solving the Max-cut problem appears to be computationally intractable. To overcome this, we develop an efficient spectral algorithm that attains the optimal rate but requires a quadratic sample size. Although this sample complexity is worse than that of the Max-cut problem, we conjecture that no polynomial-time method can perform better. Furthermore, we present numerical and theoretical evidence that supports the existence of a statistical-computational gap.<\/p>\n<p><strong>Zoom link<\/strong>: https:\/\/wse.zoom.us\/j\/94601022340<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Location:\u00a0Gilman 132 When: September 7th at 1:30 p.m. Title: Clustering a mixture of Gaussians with unknown covariance Abstract: Clustering\u00a0is a fundamental data scientific task with broad application. This talk investigates&hellip;<\/p>\n","protected":false},"author":69,"featured_media":0,"template":"","meta":{"_acf_changed":false,"_relevanssi_hide_post":"","_relevanssi_hide_content":"","_relevanssi_pin_for_all":"","_relevanssi_pin_keywords":"","_relevanssi_unpin_keywords":"","_relevanssi_related_keywords":"","_relevanssi_related_include_ids":"","_relevanssi_related_exclude_ids":"","_relevanssi_related_no_append":"","_relevanssi_related_not_related":"","_relevanssi_related_posts":"","_relevanssi_noindex_reason":"","_tribe_events_status":"","_tribe_events_status_reason":"","footnotes":""},"tags":[],"tribe_events_cat":[260],"class_list":["post-46180","tribe_events","type-tribe_events","status-publish","hentry","tribe_events_cat-seminars-and-endowed-lectures","cat_seminars-and-endowed-lectures"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.8 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>AMS Weekly Seminar | Assistant Professor Mateo Diaz | Department of Applied Mathematics and Statistics<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/engineering.jhu.edu\/ams\/event\/ams-weekly-seminar-assistant-professor-mateo-diaz\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"AMS Weekly Seminar | Assistant Professor Mateo Diaz | Department of Applied Mathematics and Statistics\" \/>\n<meta property=\"og:description\" content=\"Location:\u00a0Gilman 132 When: September 7th at 1:30 p.m. Title: Clustering a mixture of Gaussians with unknown covariance Abstract: Clustering\u00a0is a fundamental data scientific task with broad application. 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