A type theory for probability density functions

Conference Record of the Annual ACM Symposium on Principles of Programming Languages

Volumn , Issue , 2012, Pages 545-556

  Bhat, Sooraj ^a   Agarwal, Ashish ^b   Vuduc, Richard ^a   Gray, Alexander ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b NEW YORK UNIVERSITY   (United States)

Author keywords

Continuous probability; Probability density functions

Indexed keywords

AC DISTRIBUTIONS; CALCULATION PROCEDURE; CONTINUOUS PROBABILITY DISTRIBUTION; PROBABILISTIC LANGUAGE; PROBABILISTIC MODELS; PROBABILISTIC PROGRAMMING LANGUAGE; STATISTICAL TECHNIQUES; TYPE SYSTEMS; TYPE THEORY;

COMPUTER PROGRAMMING LANGUAGES; FORMAL LANGUAGES; PROBABILITY DISTRIBUTIONS;

PROBABILITY DENSITY FUNCTION;

EID: 84857881505     PISSN: 07308566     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/2103656.2103721     Document Type: Conference Paper

References (26)

1. A. Agarwal, S. Bhat, A. Gray, and I. E. Grossmann. Automating Mathematical Program Transformations. In Practical Aspects of Declarative Languages, 2010.
2. P. Audebaud and C. Paulin-Mohring. Proofs of Randomized Algorithms in Coq. In Mathematics of Program Construction, pages 49-68. Springer, 2006. (Pubitemid 44072011)
3. C. Bishop. Pattern Recognition and Machine Learning. Springer, 2006.
4. J. Borgstram, A. D. Gordon, M. Greenberg, J. Margetson, and J. V. Gael. Measure Transformer Semantics for Bayesian Machine Learning. In European Symposium on Programming, pages 77-96, 2011.
5. H. Daumé III. HBC: Hierarchical Bayes Compiler, 2007. URL http://hal3.name/HBC.
6. L. Devroye. Non-Uniform Random Variate Generation, 1986.
7. M. Erwig and S. Kollmansberger. Functional Pearls: Probabilistic Functional Programming in Haskell. Journal of Functional Programming, 16(01):21-34, 2005.
8. M. Giry. A Categorical Approach to Probability Theory. Categorical Aspects of Topology and Analysis, 915:68-85, 1981.
9. N. Goodman, V. Mansinghka, D. Roy, K. Bonawitz, and J. Tenenbaum. Church: A Language for Generative Models. In Uncertainty in Artificial Intelligence, 2008.
10. A. G. Gray, B. Fischer, J. Schumann, and W. Buntine. Automatic Derivation of Statistical Algorithms: The EM Family and Beyond. In Advances in Neural Information Processing Systems, 2003.
11. M. Hoyrup, C. Rojas, and K. Weihrauch. The Radon-Nikodym operator is not computable. In Computability & Complexity in Analysis, 2011.
12. K. Kersting and L. De Raedt. Bayesian Logic Programming: Theory and Tool. In Introduction to Statistical Relational Learning. 2007.
13. O. Kiselyov and C. Shan. Embedded Probabilistic Programming. In Working Conference on Domain Specific Languages. Springer, 2009.
14. D. Kozen. Semantics of Probabilistic Programs. Journal of Computer and System Sciences, 22(3):328-350, 1981.
15. T. Mhamdi, O. Hasan, and S. Tahar. On the Formalization of the Lebesgue Integration Theory in HOL. Interactive Theorem Proving, pages 387-402, 2010.
16. B. Milch, B. Marthi, S. Russell, D. Sontag, D. Ong, and A. Kolobov. BLOG: Probabilistic Models with Unknown Objects. In International Joint Conference on Artificial Intelligence, volume 19, 2005.
17. O. Nielsen. An Introduction to Integration and Measure Theory. Wiley-Interscience, 1997.
18. S. Park, F. Pfenning, and S. Thrun. A Probabilistic Language based upon Sampling Functions. In Principles of Programming Languages, pages 171-182. ACM New York, NY, USA, 2005.
19. A. Pfeffer. IBAL: A Probabilistic Rational Programming Language. In International Joint Conference on Artificial Intelligence, 2001.
20. N. Ramsey and A. Pfeffer. Stochastic Lambda Calculus and Monads of Probability Distributions. volume 37, pages 154-165. ACM, 2002.
21. M. Richardson and P. Domingos. Markov Logic Networks. Machine Learning, 62(1):107-136, 2006. (Pubitemid 43202307)
22. T. Sato and Y. Kameya. PRISM: A Symbolic-Statistical Modeling Language. In International Joint Conference on Artificial Intelligence, pages 1330-1339, 1997.
23. D. Scott. Parametric Statistical Modeling by Minimum Integrated Square Error. Technometrics, 43(3):274-285, 2001. (Pubitemid 32813524)
24. B. Silverman. Density Estimation for Statistics and Data Analysis. Chapman & Hall/CRC, 1986.
25. R. Solovay. A Model of Set-Theory in Which Every Set of Reals is Lebesgue Measurable. Annals of Mathematics, pages 1-56, 1970.
26. L. Wasserman. All of Statistics: A Concise Course in Statistical Inference. Springer, 2004.