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INDEPENDENT COMPONENT ANALYSIS VIA NONPARAMETRIC MAXIMUM LIKELIHOOD ESTIMATION
If you have a question about this talk, please contact Dr Ramji Venkataramanan.
Abstract: Independent Component Analysis (ICA) models are very popular semi-parametric models in which we observe independent copies of a random vector X = AS, where A is a non-singular matrix and S has independent components. We propose a new way of estimating the unmixing matrix W = A^-1 and the marginal distributions of the components of S using nonparametric maximum likelihood. Specifically, we study the projection of the emipirical distribution onto the subset of ICA distributions having log-concave marginals. We show that, from the point of view of estimating the unmixing matrix, it makes no difference whether or not the log-concavity is correctly specified. The approach is further justified by both theoretical results and a simulation study.
Bio: Richard Samworth obtained his PhD in Statistics from the University of Cambridge in 2004. Following a research fellowship at St John’s College, Cambridge, he was appointed to a lectureship in Statistics at the Statistical Laboratory in Cambridge in 2005. He was promoted to a readership in 2010 and to a full professorship from October 2013. Richard remains a fellow of St John’s College, and currently holds an EPSRC Early Career Fellowship (worth GBP 1 .2M) for five years from December 2012.
His main research interests are in nonparametric and high-dimensional statistics. Particular topics include shape-constrained density and other nonparametric function estimation problems, nonparametric classification, clustering and regression, Independent Component Analysis, the bootstrap and high-dimensional variable selection problems. He was awarded the Royal Statistical Society Research prize (2008), a Leverhulme Research Fellowship (2011) and the Royal Statistical Society Guy Medal in Bronze (2012). He currently serves as an Associate Editor for the Annals of Statistics, the Journal of the Royal Statistical Society Series B, Biometrika and Statistica Sinica.
This talk is part of the Signal Processing and Communications Lab Seminars series.
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