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Abstract:
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Bayesian statisticians often use optimization as a computational tool for obtaining point estimates / variational inference. However, besides computation, there are many useful properties hidden in the minimizer of a loss function. In this talk, I will exploit optimization as a modeling tool in the prior construction --- in particular, I will introduce the class of proximal prior, which is formed by applying the proximal mapping on another continuous distribution. This framework gives rise to prior distributions on the space/manifold with a varying/unknown dimension, such as L1-ball surface, flow network, etc. I will demonstrate its ease-of-use for general Bayesian applications, such as the trend filtering of time series and modeling traffic flows during a hurricane evacuation.
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