Related papers: A Convenient Category for Higher-Order Probability…
We give an adequate denotational semantics for languages with recursive higher-order types, continuous probability distributions, and soft constraints. These are expressive languages for building Bayesian models of the kinds used in…
We present a modular semantic account of Bayesian inference algorithms for probabilistic programming languages, as used in data science and machine learning. Sophisticated inference algorithms are often explained in terms of composition of…
We introduce the categories of quasi-measurable spaces, which are slight generalizations of the category of quasi-Borel spaces, where we now allow for general sample spaces and less restrictive random variables, spaces and maps. We show…
Probabilistic programming provides a convenient lingua franca for writing succinct and rigorous descriptions of probabilistic models and inference tasks. Several probabilistic programming languages, including Anglican, Church or Hakaru,…
We make a formal analogy between random sampling and fresh name generation. We show that quasi-Borel spaces, a model for probabilistic programming, can soundly interpret Stark's $\nu$-calculus, a calculus for name generation. Moreover, we…
We introduce a new setting, the category of $\omega$PAP spaces, for reasoning denotationally about expressive differentiable and probabilistic programming languages. Our semantics is general enough to assign meanings to most practical…
We present a denotational semantics for higher-order probabilistic programs in terms of linear operators between Banach spaces. Our semantics is rooted in the classical theory of Banach spaces and their tensor products, but bears…
The problem of determining whether a probabilistic program terminates almost surely (i.e.~with probability one) is undecidable, and actually $\Pi^0_2$-complete. For this reason, a growing literature has explored classes of programs for…
Probabilistic programming languages allow programmers to write down conditional probability distributions that represent statistical and machine learning models as programs that use observe statements. These programs are run by accumulating…
Partiality is a natural phenomenon in computability that we cannot get around. So, the question is whether we can give the areas where partiality occurs, that is, where non-termination happens, more structure. In this paper we consider…
We study the semantic foundation of expressive probabilistic programming languages, that support higher-order functions, continuous distributions, and soft constraints (such as Anglican, Church, and Venture). We define a metalanguage (an…
Many probabilistic programming languages allow programs to be run under constraints in order to carry out Bayesian inference. Running programs under constraints could enable other uses such as rare event simulation and probabilistic…
Interpretation methods and their restrictions to polynomials have been deeply used to control the termination and complexity of first-order term rewrite systems. This paper extends interpretation methods to a pure higher order functional…
Probabilistic Logic Programming is an effective formalism for encoding problems characterized by uncertainty. Some of these problems may require the optimization of probability values subject to constraints among probability distributions…
In this note, we develop some of the basic theory of s-finite (measures and) kernels, a little-studied class that Staton has recently argued convincingly to be precisely the semantic counterpart of (first-order) probabilistic programs. We…
Deep Probabilistic Programming (DPP) allows powerful models based on recursive computation to be learned using efficient deep-learning optimization techniques. Additionally, DPP offers a unified perspective, where inference and learning…
This book is a graduate-level introduction to probabilistic programming. It not only provides a thorough background for anyone wishing to use a probabilistic programming system, but also introduces the techniques needed to design and build…
Probabilistic programs are typically normal-looking programs describing posterior probability distributions. They intrinsically code up randomized algorithms and have long been at the heart of modern machine learning and approximate…
Normalisation in probability theory turns a subdistribution into a proper distribution. It is a partial operation, since it is undefined for the zero subdistribution. This partiality makes it hard to reason equationally about normalisation.…
In this paper, a modified formulation of generalized probabilistic theories that will always give rise to the structure of Hilbert space of quantum mechanics, in any finite outcome space, is presented and the guidelines to how to extend…