A probabilistic powerdomain of evaluations
Proceedings of the Fourth Annual Symposium on Logic in computer science
Stochastic processes as concurrent constraint programs
Proceedings of the 26th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Stochastic lambda calculus and monads of probability distributions
POPL '02 Proceedings of the 29th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Expectation Propagation for approximate Bayesian inference
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
CSFW '02 Proceedings of the 15th IEEE workshop on Computer Security Foundations
Information Theory, Inference & Learning Algorithms
Information Theory, Inference & Learning Algorithms
Abstraction, Refinement And Proof For Probabilistic Systems (Monographs in Computer Science)
Abstraction, Refinement And Proof For Probabilistic Systems (Monographs in Computer Science)
A probabilistic language based upon sampling functions
Proceedings of the 32nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
The Journal of Machine Learning Research
FUNCTIONAL PEARLS: Probabilistic functional programming in Haskell
Journal of Functional Programming
Formal certification of code-based cryptographic proofs
Proceedings of the 36th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Probabilistic databases: diamonds in the dirt
Communications of the ACM - Barbara Liskov: ACM's A.M. Turing Award Winner
Composable probabilistic inference with b(laise)
Composable probabilistic inference with b(laise)
Privacy integrated queries: an extensible platform for privacy-preserving data analysis
Proceedings of the 2009 ACM SIGMOD International Conference on Management of data
IBAL: a probabilistic rational programming language
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Quantitative Analysis With the Probabilistic Model Checker PRISM
Electronic Notes in Theoretical Computer Science (ENTCS)
Labelled Markov Processes
Monolingual probabilistic programming using generalized coroutines
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
Probabilistic Graphical Models: Principles and Techniques - Adaptive Computation and Machine Learning
Distance makes the types grow stronger: a calculus for differential privacy
Proceedings of the 15th ACM SIGPLAN international conference on Functional programming
Effective Bayesian inference for stochastic programs
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
Factor graphs and the sum-product algorithm
IEEE Transactions on Information Theory
A type theory for probability density functions
POPL '12 Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A model-learner pattern for bayesian reasoning
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Deriving probability density functions from probabilistic functional programs
TACAS'13 Proceedings of the 19th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Bayesian inference using data flow analysis
Proceedings of the 2013 9th Joint Meeting on Foundations of Software Engineering
Probabilistic relational verification for cryptographic implementations
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
Tabular: a schema-driven probabilistic programming language
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
Uncertain: a first-order type for uncertain data
Proceedings of the 19th international conference on Architectural support for programming languages and operating systems
Dynamic enforcement of knowledge-based security policies using probabilistic abstract interpretation
Journal of Computer Security
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The Bayesian approach to machine learning amounts to inferring 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 combinators for measure transformers, based on 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 has a straightforward semantics via factor graphs, data structures that enable many efficient inference algorithms. We use an existing inference engine for efficient approximate inference of posterior marginal distributions, treating thousands of observations per second for large instances of realistic models.