A Compilation Target for Probabilistic Programming Languages

Forward inference techniques such as sequential Monte Carlo and particle Markov chain Monte Carlo for probabilistic programming can be implemented in any programming language by creative use of standardized operating system functionality including processes, forking, mutexes, and shared memory. Exploiting this we have defined, developed, and tested a probabilistic programming language intermediate representation language we call probabilistic C, which itself can be compiled to machine code by standard compilers and linked to operating system libraries yielding an efficient, scalable, portable probabilistic programming compilation target. This opens up a new hardware and systems research path for optimizing probabilistic programming systems.Comment: In Proceedings of the 31st International Conference on Machine Learning (ICML), 201

Running Probabilistic Programs Backwards

Many probabilistic programming languages allow programs to be run under constraints in order to carry out Bayesian inference. Running programs under constraints could enable other uses such as rare event simulation and probabilistic verification---except that all such probabilistic languages are necessarily limited because they are defined or implemented in terms of an impoverished theory of probability. Measure-theoretic probability provides a more general foundation, but its generality makes finding computational content difficult. We develop a measure-theoretic semantics for a first-order probabilistic language with recursion, which interprets programs as functions that compute preimages. Preimage functions are generally uncomputable, so we derive an abstract semantics. We implement the abstract semantics and use the implementation to carry out Bayesian inference, stochastic ray tracing (a rare event simulation), and probabilistic verification of floating-point error bounds.Comment: 26 pages, ESOP 2015 (to appear

Measure Transformer Semantics for Bayesian Machine Learning

The Bayesian approach to machine learning amounts to computing posterior distributions of random variables from a probabilistic model of how the variables are related (that is, a prior distribution) and a set of observations of variables. There is a trend in machine learning towards expressing Bayesian models as probabilistic programs. As a foundation for this kind of programming, we propose a core functional calculus with primitives for sampling prior distributions and observing variables. We define measure-transformer combinators inspired by theorems in measure theory, and use these to give a rigorous semantics to our core calculus. The original features of our semantics include its support for discrete, continuous, and hybrid measures, and, in particular, for observations of zero-probability events. We compile our core language to a small imperative language that is processed by an existing inference engine for factor graphs, which are data structures that enable many efficient inference algorithms. This allows efficient approximate inference of posterior marginal distributions, treating thousands of observations per second for large instances of realistic models.Comment: An abridged version of this paper appears in the proceedings of the 20th European Symposium on Programming (ESOP'11), part of ETAPS 201

Graduate Academic Catalog (1986-87)

This Graduate Catalog is provided by the Graduate Faculty of the University of Nebraska at Omaha in the hope that it will be a source of information to you on the graduate programs available through our University. We are proud of our University and of its programs. We encourage you to become acquainted with us and with the many resources available to the community through the University. We have tried to include as much information as possible, but obviously we could not include everything. If you have questions which are not answered here, please feel free to call on the Office of Graduate Studies (204 Eppley Administration Building, (402) 554-2341

Graduate Academic Catalog (1987-88)

This Graduate Catalog is provided by the Graduate Faculty of the University of Nebraska at Omaha in the hope that it will be a source of information to you on the graduate programs available through our University. We are proud of our University and of its programs. We encourage you to become acquainted with us and with the many resources available to the community through the University. We have hied to include as much information as possible, but obviously we could not include everything. If you have questions which are not answered here, please feel free to call on the Office of Graduate Studies (204 Eppley Administration Building) (402) 554-2341

Graduate Academic Catalog (1988-89)

This Graduate Catalog is provided by the Graduate Faculty of the University of Nebraska at Omaha in the hope that it will be a source of information to you on the graduate programs available through our University. We are proud of our University and of its programs. We encourage you to become acquainted with us and with the many resources available to the community through the University. We have hied to include as much information as possible, but obviously we could not include everything. If you have questions which are not answered here, please feel free to call on the Office of Graduate Studies (204 Eppley Administration Building) (402) 554-2341