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Leslie P. Kaelbling. Roy, Daniel Murphy Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science 2011-10-17T21:28:58Z 2011-10-17T21:28:58Z 2011 2011 http://hdl.handle.net/1721.1/66463 756045048 Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2011. Cataloged from PDF version of thesis. Includes bibliographical references (p. 135-144). We investigate the class of computable probability distributions and explore the fundamental limitations of using this class to describe and compute conditional distributions. In addition to proving the existence of noncomputable conditional distributions, and thus ruling out the possibility of generic probabilistic inference algorithms (even inefficient ones), we highlight some positive results showing that posterior inference is possible in the presence of additional structure like exchangeability and noise, both of which are common in Bayesian hierarchical modeling. This theoretical work bears on the development of probabilistic programming languages (which enable the specification of complex probabilistic models) and their implementations (which can be used to perform Bayesian reasoning). The probabilistic programming approach is particularly well suited for defining infinite-dimensional, recursively-defined stochastic processes of the sort used in nonparametric Bayesian statistics. We present a new construction of the Mondrian process as a partition-valued Markov process in continuous time, which can be viewed as placing a distribution on an infinite kd-tree data structure. by Daniel M. Roy. Ph.D. 144 p. eng Massachusetts Institute of Technology M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 Electrical Engineering and Computer Science. Computability, inference and modeling in probabilistic programming Thesis application/pdf Publication unknown unknown <Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="9e494732-b46e-47dc-a9b2-e923ff993b6b"> <Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type> <Language>eng</Language> <Title>Computability, inference and modeling in probabilistic programming</Title> <PublishedIn> <Publication> </Publication> </PublishedIn> <PublicationDate>2011</PublicationDate> <Authors> <Author> <DisplayName>Roy, Daniel Murphy</DisplayName> <Affiliation> <OrgUnit> </OrgUnit> </Affiliation> </Author> </Authors> <Editors> </Editors> <Publishers> <Publisher> <DisplayName>Massachusetts Institute of Technology</DisplayName> <OrgUnit /> </Publisher> </Publishers> <License>http://dspace.mit.edu/handle/1721.1/7582</License> <Keyword>Electrical Engineering and Computer Science.</Keyword> <Abstract>We investigate the class of computable probability distributions and explore the fundamental limitations of using this class to describe and compute conditional distributions. In addition to proving the existence of noncomputable conditional distributions, and thus ruling out the possibility of generic probabilistic inference algorithms (even inefficient ones), we highlight some positive results showing that posterior inference is possible in the presence of additional structure like exchangeability and noise, both of which are common in Bayesian hierarchical modeling. This theoretical work bears on the development of probabilistic programming languages (which enable the specification of complex probabilistic models) and their implementations (which can be used to perform Bayesian reasoning). The probabilistic programming approach is particularly well suited for defining infinite-dimensional, recursively-defined stochastic processes of the sort used in nonparametric Bayesian statistics. We present a new construction of the Mondrian process as a partition-valued Markov process in continuous time, which can be viewed as placing a distribution on an infinite kd-tree data structure.</Abstract> <Access xmlns="http://purl.org/coar/access_right" > </Access> </Publication>