Related papers: Unifying Inference for Bayesian and Petri Nets

We define a new method for taking advantage of net reductions in combination with a SMT-based model checker. Our approach consists in transforming a reachability problem about some Petri net, into the verification of an updated reachability…

General results from statistical learning theory suggest to understand not only brain computations, but also brain plasticity as probabilistic inference. But a model for that has been missing. We propose that inherently stochastic features…

Network metrics form a fundamental part of the network analysis toolbox. Used to quantitatively measure different aspects of the network, these metrics can give insights into the underlying network structure and function. In this work, we…

Probabilistic representations, such as Bayesian and Markov networks, are fundamental to much of statistical machine learning. Thus, learning probabilistic representations directly from data is a deep challenge, the main computational…

Decomposable models and Bayesian networks can be defined as sequences of oligo-dimensional probability measures connected with operators of composition. The preliminary results suggest that the probabilistic models allowing for effective…

Bayesian neural networks (BNNs) allow rigorous uncertainty quantification in deep learning, but often come at a prohibitive computational cost. We propose three different innovative architectures of partial trace-class Bayesian neural…

We introduce factorize sum split product networks (FSPNs), a new class of probabilistic graphical models (PGMs). FSPNs are designed to overcome the drawbacks of existing PGMs in terms of estimation accuracy and inference efficiency.…

We classify all additive invariants of open Petri nets: these are $\mathbb{N}$-valued invariants which are additive with respect to sequential and parallel composition of open Petri nets. In particular, we prove two classification theorems:…

The interdependence between nodes in graphs is key to improve class predictions on nodes and utilized in approaches like Label Propagation (LP) or in Graph Neural Networks (GNN). Nonetheless, uncertainty estimation for non-independent…

The natural habitat of most Bayesian methods is data represented by exchangeable sequences of observations, for which de Finetti's theorem provides the theoretical foundation. Dirichlet process clustering, Gaussian process regression, and…

A reliable modeling of uncertain evidence in Bayesian networks based on a set-valued quantification is proposed. Both soft and virtual evidences are considered. We show that evidence propagation in this setup can be reduced to standard…

Bayesian networks provide a probabilistic semantics for qualitative assertions about likelihood. A qualitative reasoner based on an algebra over these assertions can derive further conclusions about the influence of actions. While the…

We apply the principle of maximum entropy to select a unique joint probability distribution from the set of all joint probability distributions specified by a credal network. In detail, we start by showing that the unique joint distribution…

Probabilistic graphical models are a central tool in AI; however, they are generally not as expressive as deep neural models, and inference is notoriously hard and slow. In contrast, deep probabilistic models such as sum-product networks…

Bayesian neural networks (BNNs) augment deep networks with uncertainty quantification by Bayesian treatment of the network weights. However, such models face the challenge of Bayesian inference in a high-dimensional and usually…

Improved computational power has enabled different disciplines to predict causal relationships among modeled variables using Bayesian network inference. While many alternative algorithms have been proposed to improve the efficiency and…

Many biological networks include cyclic structures. In such cases, Bayesian networks (BNs), which must be acyclic, are not sound models for structure learning. Dynamic BNs can be used but require relatively large time series data. We…

Bayes belief networks and influence diagrams are tools for constructing coherent probabilistic representations of uncertain knowledge. The process of constructing such a network to represent an expert's knowledge is used to illustrate a…

Network models provide a powerful framework for analysing single-cell count data, facilitating the characterisation of cellular identities, disease mechanisms, and developmental trajectories. However, uncertainty modeling in unsupervised…

Supervised classification is one of the most ubiquitous tasks in machine learning. Generative classifiers based on Bayesian networks are often used because of their interpretability and competitive accuracy. The widely used naive and TAN…