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This paper exploits extended Bayesian networks for uncertainty reasoning on Petri nets, where firing of transitions is probabilistic. In particular, Bayesian networks are used as symbolic representations of probability distributions,…

Spoken communication occurs in a "noisy channel" characterized by high levels of environmental noise, variability within and between speakers, and lexical and syntactic ambiguity. Given these properties of the received linguistic input,…

We survey recent developments in the study of probabilistic complexity classes. While the evidence seems to support the conjecture that probabilism can be deterministically simulated with relatively low overhead, i.e., that $P=BPP$, it also…

The asymptotic study of the conjugacy classes of a random element of the finite affine group leads one to define a probability measure on the set of all partitions of all positive integers. Four different probabilistic understandings of…

ProbNetKAT is a probabilistic extension of NetKAT with a denotational semantics based on Markov kernels. The language is expressive enough to generate continuous distributions, which raises the question of how to compute effectively in the…

Probability trees are one of the simplest models of causal generative processes. They possess clean semantics and -- unlike causal Bayesian networks -- they can represent context-specific causal dependencies, which are necessary for e.g.…

In this paper, we advocate the use of stratified logical theories for representing probabilistic models. We argue that such encodings can be more interpretable than those obtained in existing frameworks such as Markov logic networks. Among…

In a series of recent works, an interesting quantum generative model based on parameterized instantaneous polynomial quantum (IQP) circuits has emerged as they can be trained efficiently classically using any loss function that depends only…

The use of operational methods of different nature is shown to be a fairly powerful tool to study different problems regarding the theory of Legendre and Legendre-like polynomials. We show how the use of the well known integral…

We introduce symmetric arithmetic circuits, i.e. arithmetic circuits with a natural symmetry restriction. In the context of circuits computing polynomials defined on a matrix of variables, such as the determinant or the permanent, the…

Possibilistic logic bases and possibilistic graphs are two different frameworks of interest for representing knowledge. The former stratifies the pieces of knowledge (expressed by logical formulas) according to their level of certainty,…

Moralisation and Triangulation are transformations allowing to switch between different ways of factoring a probability distribution into a graphical model. Moralisation allows to view a Bayesian network (a directed model) as a Markov…

Finding human-understandable circuits in language models is a central goal of the field of mechanistic interpretability. We train models to have more understandable circuits by constraining most of their weights to be zeros, so that each…

Recently, there has been considerable progress on designing algorithms with provable guarantees -- typically using linear algebraic methods -- for parameter learning in latent variable models. But designing provable algorithms for inference…

While probability theory is normally applied to external environments, there has been some recent interest in probabilistic modeling of the outputs of computations that are too expensive to run. Since mathematical logic is a powerful tool…

The implicit graph conjecture states that every sufficiently small, hereditary graph class has a labeling scheme with a polynomial-time computable label decoder. We approach this conjecture by investigating classes of label decoders defined…

This study investigates the frame potential and expressiveness of commutative quantum circuits. Based on the Fourier series representation of these circuits, we express quantum expectation and pairwise fidelity as characteristic functions…

We show that probabilistic computable functions, i.e., those functions outputting distributions and computed by probabilistic Turing machines, can be characterized by a natural generalization of Church and Kleene's partial recursive…

Probabilistic logic programming is a major part of statistical relational artificial intelligence, where approaches from logic and probability are brought together to reason about and learn from relational domains in a setting of…

We develop a technique for generalising from data in which models are samplers represented as program text. We establish encouraging empirical results that suggest that Markov chain Monte Carlo probabilistic programming inference techniques…