Computability, inference and modeling in probabilistic programming
Name
756045048-MIT.pdf
Description
Full printable version
Size
10.11 MB
Format
Adobe PDF
Checksum (MD5)
29198ec04c796162972ed54fa913c576
Author(s)
Roy, Daniel Murphy
Advisor(s)
Leslie P. Kaelbling.
Date Issued
2011
Publisher
Massachusetts Institute of Technology
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.
Description
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).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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reproduction or distribution in any format is prohibited without written
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