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Program synthesis is the task of automatically generating a program consistent with a given specification. A natural way to specify programs is to provide examples of desired input-output behavior, and many current program synthesis…

Higher-order probabilistic programming languages allow programmers to write sophisticated models in machine learning and statistics in a succinct and structured way, but step outside the standard measure-theoretic formalization of…

Functional dependencies -- traditional, approximate and conditional are of critical importance in relational databases, as they inform us about the relationships between attributes. They are useful in schema normalization, data…

A random set is a generalisation of a random variable, i.e. a set-valued random variable. The random set theory allows a unification of other uncertainty descriptions such as interval variable, mass belief function in Dempster-Shafer theory…

We consider the problem of Bayesian inference in the family of probabilistic models implicitly defined by stochastic generative models of data. In scientific fields ranging from population biology to cosmology, low-level mechanistic…

Gaussian Processes (GPs) are widely used tools in statistics, machine learning, robotics, computer vision, and scientific computation. However, despite their popularity, they can be difficult to apply; all but the simplest classification or…

We propose and analyze an algorithm to approximate distribution functions and densities of perpetuities. Our algorithm refines an earlier approach based on iterating discretized versions of the fixed point equation that defines the…

The likelihood function plays a pivotal role in statistical inference; it is adaptable to a wide range of models and the resultant estimators are known to have good properties. However, these results hinge on correct specification of the…

This paper addresses a fundamental problem in random variate generation: given access to a random source that emits a stream of independent fair bits, what is the most accurate and entropy-efficient algorithm for sampling from a discrete…

The problem addressed concerns the determination of the average number of successive attempts of guessing a word of a certain length consisting of letters with given probabilities of occurrence. Both first- and second-order approximations…

We consider reusing established non-probabilistic output analyses (either forward or backwards) that yield over-approximations of a program's pre-image or image relation, e.g., interval analyses. We assume a probability measure over the…

We tackle the problem of conditioning probabilistic programs on distributions of observable variables. Probabilistic programs are usually conditioned on samples from the joint data distribution, which we refer to as deterministic…

Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…

In this work, we consider the fundamental problem of deriving quantitative bounds on the probability that a given assertion is violated in a probabilistic program. We provide automated algorithms that obtain both lower and upper bounds on…

This work offers a broad perspective on probabilistic modeling and inference in light of recent advances in probabilistic programming, in which models are formally expressed in Turing-complete programming languages. We consider a typical…

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…

Here several perfect simulation algorithms are brought under a single framework, and shown to derive from the same probabilistic result, called here the Fundamental Theorem of Perfect Simulation (FTPS). An exact simulation algorithm has…

Naive approaches to amortized inference in probabilistic programs with unbounded loops can produce estimators with infinite variance. This is particularly true of importance sampling inference in programs that explicitly include rejection…

Probabilistic logic programs are logic programs in which some of the facts are annotated with probabilities. Several classical probabilistic inference tasks (such as MAP and computing marginals) have not yet received a lot of attention for…

Models of complex systems are often formalized as sequential software simulators: computationally intensive programs that iteratively build up probable system configurations given parameters and initial conditions. These simulators enable…