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Activity Number:
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57
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Type:
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Topic Contributed
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Date/Time:
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Sunday, July 29, 2007 : 4:00 PM to 5:50 PM
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Sponsor:
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IMS
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| Abstract - #309488 |
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Title:
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Characterizing the Function Space for Bayesian Kernel Models
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Author(s):
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Natesh Pillai*+
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Companies:
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Duke University
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Address:
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1022 Sedgefield Street, Durham, NC, 27705,
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Keywords:
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RKHS ; non-parametric Bayes ; Levy processes ; Integral operators
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Abstract:
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Kernel methods have been very popular in the machine learning literature in the last ten years, often in the context of Tikhonov regularization algorithms. In this paper we study a coherent Bayesian kernel model based on an integral operator whose domain is a space of signed measures. Priors on the signed measures induce prior distributions on their image functions under the integral operator. We study several classes of signed measures and their images, and identify general classes of measures whose images are dense in the reproducing kernel Hilbert space (RKHS) induced by the kernel. This gives a function-theoretic foundation for some nonparametric prior specifications commonly-used in Bayesian modeling, including Gaussian processes and Dirichlet processes, and suggests generalizations. We outline a general framework for the construction of priors on measures using Lévy processes.
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- The address information is for the authors that have a + after their name.
- Authors who are presenting talks have a * after their name.
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