Bayesian Classification and Inference in a Probabilistic Type Theory with Records

Staffan Larsson, Robin Cooper


Abstract
We propose a probabilistic account of semantic inference and classification formulated in terms of probabilistic type theory with records, building on Cooper et. al. (2014) and Cooper et. al. (2015). We suggest probabilistic type theoretic formulations of Naive Bayes Classifiers and Bayesian Networks. A central element of these constructions is a type-theoretic version of a random variable. We illustrate this account with a simple language game combining probabilistic classification of perceptual input with probabilistic (semantic) inference.
Anthology ID:
2021.naloma-1.7
Volume:
Proceedings of the 1st and 2nd Workshops on Natural Logic Meets Machine Learning (NALOMA)
Month:
June
Year:
2021
Address:
Groningen, the Netherlands (online)
Venues:
IWCS | NALOMA
SIG:
SIGSEM
Publisher:
Association for Computational Linguistics
Note:
Pages:
51–59
Language:
URL:
https://aclanthology.org/2021.naloma-1.7
DOI:
Bibkey:
Cite (ACL):
Staffan Larsson and Robin Cooper. 2021. Bayesian Classification and Inference in a Probabilistic Type Theory with Records. In Proceedings of the 1st and 2nd Workshops on Natural Logic Meets Machine Learning (NALOMA), pages 51–59, Groningen, the Netherlands (online). Association for Computational Linguistics.
Cite (Informal):
Bayesian Classification and Inference in a Probabilistic Type Theory with Records (Larsson & Cooper, NALOMA 2021)
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PDF:
https://aclanthology.org/2021.naloma-1.7.pdf