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09/18/2023
A model of stochastic memoization and name generation in probabilistic programming: categorical semantics via monads on presheaf categories
Stochastic memoization is a higher-order construct of probabilistic prog...
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02/21/2023
ωPAP Spaces: Reasoning Denotationally About Higher-Order, Recursive Probabilistic and Differentiable Programs
We introduce a new setting, the category of ωPAP spaces, for reasoning d...
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12/14/2022
Affine Monads and Lazy Structures for Bayesian Programming
We show that streams and lazy data structures are a natural idiom for pr...
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12/13/2022
ADEV: Sound Automatic Differentiation of Expected Values of Probabilistic Programs
Optimizing the expected values of probabilistic processes is a central p...
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07/12/2022
Quantum de Finetti Theorems as Categorical Limits, and Limits of State Spaces of C*-algebras
De Finetti theorems tell us that if we expect the likelihood of outcomes...
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05/31/2022
Concrete categories and higher-order recursion (With applications including probability, differentiability, and full abstraction)
We study concrete sheaf models for a call-by-value higher-order language...
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12/28/2021
Monads for Measurable Queries in Probabilistic Databases
We consider a bag (multiset) monad on the category of standard Borel spa...
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05/05/2021
Recursion and Sequentiality in Categories of Sheaves
We present a fully abstract model of a call-by-value language with highe...
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01/27/2021
Compositional Semantics for Probabilistic Programs with Exact Conditioning
We define a probabilistic programming language for Gaussian random varia...
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01/26/2021
A Monad for Probabilistic Point Processes
A point process on a space is a random bag of elements of that space. In...
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01/17/2021
Higher Order Automatic Differentiation of Higher Order Functions
We present semantic correctness proofs of automatic differentiation (AD)...
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07/16/2020
Probabilistic Programming Semantics for Name Generation
We make a formal analogy between random sampling and fresh name generati...
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01/07/2020
Correctness of Automatic Differentiation via Diffeologies and Categorical Gluing
We present semantic correctness proofs of Automatic Differentiation (AD)...
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04/21/2019
Quantum channels as a categorical completion
We propose a categorical foundation for the connection between pure and ...
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01/29/2019
Universal Properties in Quantum Theory
We argue that notions in quantum theory should have universal properties...
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12/15/2018
A Generalization of Hierarchical Exchangeability on Trees to Directed Acyclic Graphs
Motivated by problems in Bayesian nonparametrics and probabilistic progr...
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11/10/2018
A Domain Theory for Statistical Probabilistic Programming
We give an adequate denotational semantics for languages with recursive ...
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02/26/2018
The Beta-Bernoulli process and algebraic effects
In this paper we analyze the Beta-Bernoulli process from Bayesian nonpar...
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11/14/2017
Classical Control, Quantum Circuits and Linear Logic in Enriched Category Theory
We describe categorical models of a circuit-based (quantum) functional p...
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11/09/2017
Denotational validation of higher-order Bayesian inference
We present a modular semantic account of Bayesian inference algorithms f...
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01/10/2017
A Convenient Category for Higher-Order Probability Theory
Higher-order probabilistic programming languages allow programmers to wr...
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01/19/2016