A probabilistic powerdomain of evaluations
Proceedings of the Fourth Annual Symposium on Logic in computer science
Hierarchical mixtures of experts and the EM algorithm
Neural Computation
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
POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
On the Representation of Probabilities over Structured Domains
CAV '99 Proceedings of the 11th International Conference on Computer Aided Verification
A family of algorithms for approximate bayesian inference
A family of algorithms for approximate bayesian inference
The Journal of Machine Learning Research
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
FUNCTIONAL PEARLS: Probabilistic functional programming in Haskell
Journal of Functional Programming
Proceedings of the 2006 workshop on ML
Report on the probabilistic language scheme
Proceedings of the 2007 symposium on Dynamic languages
Adaptive mixtures of local experts
Neural Computation
Modeling and Reasoning with Bayesian Networks
Modeling and Reasoning with Bayesian Networks
Compiling Bayesian networks using variable elimination
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
IBAL: a probabilistic rational programming language
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Quantitative Analysis With the Probabilistic Model Checker PRISM
Electronic Notes in Theoretical Computer Science (ENTCS)
Probabilistic inductive logic programming
Monolingual probabilistic programming using generalized coroutines
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
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
Measure transformer semantics for Bayesian machine learning
ESOP'11/ETAPS'11 Proceedings of the 20th European conference on Programming languages and systems: part of the joint European conferences on theory and practice of software
Practical probabilistic programming
ILP'10 Proceedings of the 20th international conference on Inductive logic programming
Dynamic Enforcement of Knowledge-Based Security Policies
CSF '11 Proceedings of the 2011 IEEE 24th Computer Security Foundations Symposium
Bayesian hierarchical mixtures of experts
UAI'03 Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence
Probabilistic relational reasoning for differential privacy
POPL '12 Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A type theory for probability density functions
POPL '12 Proceedings of the 39th 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
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
Tabular: a schema-driven probabilistic programming language
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
On coinductive equivalences for higher-order probabilistic functional programs
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
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A Bayesian model is based on a pair of probability distributions, known as the prior and sampling distributions. A wide range of fundamental machine learning tasks, including regression, classification, clustering, and many others, can all be seen as Bayesian models. We propose a new probabilistic programming abstraction, a typed Bayesian model, which is based on a pair of probabilistic expressions for the prior and sampling distributions. A sampler for a model is an algorithm to compute synthetic data from its sampling distribution, while a learner for a model is an algorithm for probabilistic inference on the model. Models, samplers, and learners form a generic programming pattern for model-based inference. They support the uniform expression of common tasks including model testing, and generic compositions such as mixture models, evidence-based model averaging, and mixtures of experts. A formal semantics supports reasoning about model equivalence and implementation correctness. By developing a series of examples and three learner implementations based on exact inference, factor graphs, and Markov chain Monte Carlo, we demonstrate the broad applicability of this new programming pattern.