Related papers: Does a Program Yield the Right Distribution? Verif…

We study probability distributions of convergent random series of a special structure, called perpetuities. By giving a new argument, we prove that such distributions are of pure type: degenerate, absolutely continuous, or continuously…

In multiple classification, one aims to determine whether a testing sequence is generated from the same distribution as one of the M training sequences or not. Unlike most of existing studies that focus on discrete-valued sequences with…

We consider distributions on $\mathbb{R}$ that can be written as the sum of a non-zero discrete distribution and an absolutely continuous distribution. We show that such a distribution is quasi-infinitely divisible if and only if its…

Generative models at times produce "invalid" outputs, such as images with generation artifacts and unnatural sounds. Validity-constrained distribution learning attempts to address this problem by requiring that the learned distribution have…

Prediction, where observed data is used to quantify uncertainty about a future observation, is a fundamental problem in statistics. Prediction sets with coverage probability guarantees are a common solution, but these do not provide…

We describe techniques for synthesis and verification of recursive functional programs over unbounded domains. Our techniques build on top of an algorithm for satisfiability modulo recursive functions, a framework for deductive synthesis,…

Diffusion models have had a profound impact on many application areas, including those where data are intrinsically infinite-dimensional, such as images or time series. The standard approach is first to discretize and then to apply…

In contrast to the usual understanding of probabilistic systems as stochastic processes, recently these systems have also been regarded as transformers of probabilities. In this paper, we give a natural definition of strong bisimulation for…

Probabilistic programming is becoming increasingly popular thanks to its ability to specify problems with a certain degree of uncertainty. In this work, we focus on term rewriting, a well-known computational formalism. In particular, we…

We develop an approach to estimate the probability that a program sampled from a large language model is correct. Given a natural language description of a programming problem, our method samples both candidate programs as well as candidate…

LLMs are widely used for code generation and mathematical reasoning tasks where they are required to generate structured output. They either need to reason about code, generate code for a given specification, or reason using programs of…

We present a new proof rule for verifying lower bounds on quantities of probabilistic programs. Our proof rule is not confined to almost-surely terminating programs -- as is the case for existing rules -- and can be used to establish…

Probabilistic programs are a powerful and convenient approach to formalise distributions over system executions. A classical verification problem for probabilistic programs is temporal inference: to compute the likelihood that the execution…

For a variant of the algorithm in [Pit19] (arXiv:1903.10816) to compute the approximate density or distribution function of a linear mixture of independent random variables known by a finite sample, it is presented a proof of the functional…

Most of the methods that produce space weather forecasts are based on deterministic models. In order to generate a probabilistic forecast, a model needs to be run several times sampling the input parameter space, in order to generate an…

We consider the problems of statically refuting equivalence and similarity of output distributions defined by a pair of probabilistic programs. Equivalence and similarity are two fundamental relational properties of probabilistic programs…

Several interesting generative learning algorithms involve a complex probability distribution over many random variables, involving intractable normalization constants or latent variable normalization. Some of them may even not have an…

We study the problem of completely automatically verifying uninterpreted programs---programs that work over arbitrary data models that provide an interpretation for the constants, functions and relations the program uses. The verification…

Probabilistic programs provide an expressive representation language for generative models. Given a probabilistic program, we are interested in the task of posterior inference: estimating a latent variable given a set of observed variables.…

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,…