{
"event_id": "268567",
"eventinstance_id": "960831",
"calendar": {
"id": 1684,
"title": "Mathematics Department Calendar",
"slug": "mathematics-department-calendar",
"url": "https://events.ucf.edu/calendar/1684/mathematics-department-calendar/"
},
"id": "960831",
"title": "Colloquium",
"subtitle": null,
"description": "\u003Cp\u003E\u003Cstrong\u003ELearning of low\u002Ddimensional geometric structure in high\u002Ddimensional data\u003C/strong\u003E\u003C/p\u003E\u000A\u003Cp\u003E\u003Cstrong\u003EProfessor David Dunson\u003C/strong\u003E\u003C/p\u003E\u000A\u003Cp\u003E\u003Cstrong\u003EArts and Sciences Distinguished Professor of Statistical Science, \u003C/strong\u003E\u003C/p\u003E\u000A\u003Cp\u003E\u003Cstrong\u003EMathematics and Electrical \u0026amp\u003B Computer Engineering\u003C/strong\u003E\u003C/p\u003E\u000A\u003Cp\u003E\u003Cstrong\u003EDuke University\u003C/strong\u003E\u003C/p\u003E\u000A\u003Cp\u003E\u003Cstrong\u003E \u003C/strong\u003E\u003Cstrong\u003EABSTRACT:\u003C/strong\u003E High\u002Ddimensional data are collected in an amazing variety of application areas. As the sample size is often modest relative to the dimension of the data, dimensionality reduction is needed. For example, PCA reduces p\u002Ddimensional data to coordinates on a d\u002Ddimensional subspace, with d\u0026lt\u003B\u0026lt\u003Bp. There is a literature on non\u002Dlinear extensions of PCA\u003B such approaches are commonly referred to as “manifold learning”. Manifold learning usually relies on local linearity, necessitating a large number of pieces to obtain accurate approximations of highly curved subspaces. We propose a broad new dictionary for approximating manifolds based on pieces of spheres or spherelets. We provide theory showing dramatic reductions in covering numbers needed to produce a particular small MSE relative to locally linear methods. We develop a simple spherical PCA algorithm for implementation, and show very substantial gains in performance on toy and non\u002Dtoy examples. A novel supervised nearest neighbor algorithm exploiting spherelets obtains state\u002Dof\u002Dthe\u002Dart classification performance including relative to deep learning. We additionally develop a Bayesian model that characterizes uncertainty in subspace learning, along with an MCMC algorithm for implementation. \u003C/p\u003E",
"location": "Mathematical Sciences Building: 318",
"location_url": "http://map.ucf.edu/locations/12/mathematical\u002Dsciences\u002Dbuilding\u002Dmsb/",
"starts": "Fri, 12 Oct 2018 12:00:00 -0400",
"ends": "Fri, 12 Oct 2018 13:00:00 -0400",
"ongoing": "False",
"category": "Speaker/Lecture/Seminar",
"tags": null,
"contact_name": "Marianna Pensky",
"contact_phone": null,
"contact_email": "marianna.pensky@ucf.edu",
"url": "https://events.ucf.edu/event/960831/colloquium/"
}