{"43290":{"#nid":"43290","#data":{"type":"event","title":"Penalized regularization for functional linear models","body":[{"value":"\u003Cp\u003E\u003Cstrong\u003ETITLE:\u003C\/strong\u003E  Penalized regularization for functional linear models\n\u003C\/p\u003E\n\u003Cp\u003E\u003Cstrong\u003ESPEAKER:\u003C\/strong\u003E  Dr. Tim Randolph\n\u003C\/p\u003E\n\u003Cp\u003E\u003Cstrong\u003EABSTRACT:\u003C\/strong\u003E\n\u003C\/p\u003E\n\u003Cp\u003EIn a \u0027functional linear model\u0027 the aim is to estimate the linear relationship between a scaler response, y, and a random L2 function, x. This formally fits into the classical regression model, y = X*b + e, but the estimation of b is inherently ill-posed. A common method used to address this problem regularizes the solution by penalizing L*b, where L is a linear operator. This constrains b (which is nominally any L2 function) by bounding the norm of L*b.  Special cases include Marquardt\u0027s generalized regression, Hoerl\u0027s ridge regression (L=I) and\n\u003C\/p\u003E\n\u003Cp\u003ETikhonov-Philips\u0027 regularization (L=D, a differential operator). This talk considers (linear) penalized estimates in general and their expression via generalized singular vectors of the pair (X,L).  This provides perspective on the functional structure of an estimate and on criteria for choosing the penalty operator.  Corresponding explicit expressions for bias and variance provide insight regarding the trade-off between the properties of L versus X. \u003C\/p\u003E","summary":null,"format":"limited_html"}],"field_subtitle":"","field_summary":[{"value":"Penalized regularization for functional linear models","format":"limited_html"}],"field_summary_sentence":[{"value":"Penalized regularization for functional linear models"}],"uid":"27187","created_gmt":"2009-10-12 20:37:41","changed_gmt":"2016-10-08 01:47:34","author":"Anita Race","boilerplate_text":"","field_publication":"","field_article_url":"","field_event_time":{"event_time_start":"2008-11-06T10:00:00-05:00","event_time_end":"2008-11-06T11:00:00-05:00","event_time_end_last":"2008-11-06T11:00:00-05:00","gmt_time_start":"2008-11-06 15:00:00","gmt_time_end":"2008-11-06 16:00:00","gmt_time_end_last":"2008-11-06 16:00:00","rrule":null,"timezone":"America\/New_York"},"extras":[],"groups":[{"id":"1242","name":"School of Industrial and Systems Engineering (ISYE)"}],"categories":[],"keywords":[{"id":"5424","name":"Linear"}],"core_research_areas":[],"news_room_topics":[],"event_categories":[{"id":"1795","name":"Seminar\/Lecture\/Colloquium"}],"invited_audience":[],"affiliations":[],"classification":[],"areas_of_expertise":[],"news_and_recent_appearances":[],"phone":[],"contact":[{"value":"\u003Cstrong\u003EAnita  Race\u003C\/strong\u003E\u003Cbr \/\u003EH. Milton Stewart School of Industrial and Systems Engineering\u003Cbr \/\u003E\u003Ca href=\u0022http:\/\/www.gatech.edu\/contact\/index.html?id=ar9\u0022\u003EContact Anita  Race\u003C\/a\u003E","format":"limited_html"}],"email":[],"slides":[],"orientation":[],"userdata":""}}}