David Dunson
Department of Statistical Science
Duke University
Bayesian nonparametric learning from high-dimensional data
In modern applications, it has become routine to collect high-dimensional
and highly-structured data, with the number of "subjects", n, often substantially less
than the number of variables, p, under study. In such settings, dimensionality
reduction is crucial and one common strategy relies on "learning" of a lower dimensional
subspace the data are concentrated near. After such learning, the effective number of
parameters is hopefully substantially less than the sample size, so that one has a hope
of obtaining reliable statistical inferences and predictions. In this talk, I will
provide an overview and illustration of recent approaches for nonparametric Bayes learning
of lower-dimensional structure in complex massive dimensional data. The common emphasis
will be on defining a prior that fully accounts for uncertainty in the lower dimensional
structure in a flexible manner, with tensor products providing a useful paradigm. The
concepts will be illustrated through application to nonparametric regression in many continuous
predictors, analysis of large contingency tables, functional data analysis and shape analysis.
Theoretical properties will be mentioned briefly, but the emphasis will be on biomedical
applications.
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