Wed 18 Jan 2023 16:45 - 17:10 at Grand Ballroom A - Probabilistic Inference Chair(s): Steven Holtzen

We show that streams and lazy data structures are a natural idiom for programming with infinite-dimensional Bayesian methods such as Poisson processes, Gaussian processes, jump processes, Dirichlet processes, and Beta processes. The crucial semantic idea, inspired by developments in synthetic probability theory, is to work with two separate monads: an affine monad of probability, which supports laziness, and a commutative, non-affine monad of measures, which does not. (Affine means that $T(1)\cong 1$.) We show that the separation is important from a decidability perspective, and that the recent model of quasi-Borel spaces supports these two monads.

To perform Bayesian inference with these examples, we introduce new inference methods that are specially adapted to laziness; they are proven correct by reference to the Metropolis-Hastings-Green method. Our theoretical development is implemented as a Haskell library, LazyPPL.

Wed 18 Jan

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16:45 - 18:00
Probabilistic InferencePOPL at Grand Ballroom A
Chair(s): Steven Holtzen Northeastern University
16:45
25m
Talk
Affine Monads and Lazy Structures for Bayesian Programming
POPL
Swaraj Dash University of Oxford, Younesse Kaddar University of Oxford, Hugo Paquet University of Oxford, Sam Staton University of Oxford
DOI
17:10
25m
Talk
Type-Preserving, Dependence-Aware Guide Generation for Sound, Effective Amortized Probabilistic InferenceVirtual
POPL
Jianlin Li University of Waterloo, Leni Ven University of Waterloo, Pengyuan Shi University of Waterloo, Yizhou Zhang University of Waterloo
DOI
17:35
25m
Talk
Smoothness Analysis for Probabilistic Programs with Application to Optimised Variational Inference
POPL
Wonyeol Lee Stanford University, Xavier Rival Inria; ENS; CNRS; PSL University, Hongseok Yang KAIST; IBS
DOI