Bayesian inference and learning in Probabilistic Type Theory with Records

• Event: Seminar
• Lecturer: Staffan Larsson
• Date: 12 May 2021
• Duration: 2 hours
• Venue: Gothenburg

We propose a probabilistic account of semantic inference, classification and learning formulated in terms of probabilistic type theory with records (ProbTTR), building on Cooper et al. (2014, 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 and learning. We also show how two alternative accounts of learning in this context can be cast in ProbTTR. (This is work that has been presented in earlier stages to CLASP but it is still in progress, in collaboration with Robin Cooper and Jean-Philippe Bernardy).