11:00 am Monday, November 12, 2012
Statistics: Capturing Heteroscedasticity and Long-Range Dependencies with Gaussian Processes by
Emily FOX (UW) in CBA 6.420, 11:00AM–12:00 noon
We first focus on developing a class of nonparametric covariance regression models, which allow an unknown p x p covariance matrix to change flexibly with predictors (e.g., time, space, categories, etc.). To cope with the dimensionality of the data, the framework harnesses a latent factor model representation with predictor-dependent factor loadings modeled as a sparse combination of Gaussian process random functions. Our prior specification leads to a highly-flexible, but computationally tractable formulation with simple conjugate posterior updates that can readily handle missing data and unequally spaced observations. We then turn to the problem of modeling long-range dependencies and abrupt changes in the mean regression. We propose a multiresolution GP that hierarchically couples a collection of smooth GPs, each defined over an element of a random nested partition. Long-range dependencies are captured by the top-level GP while the partition points define the abrupt changes in the time series. The inherent conjugacy of the GPs allows for efficient inference of the hierarchical partition, for which we employ graph-theoretic techniques. Submitted by
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