Related papers: A New Characterization of Probabilities in Bayesia…
Bayesian networks (BNs) are a widely used class of probabilistic graphical models employed in numerous application domains. However, inferring the network's graphical structure from data remains challenging. Bayesian structure learners…
A Bayesian network is a widely used probabilistic graphical model with applications in knowledge discovery and prediction. Learning a Bayesian network (BN) from data can be cast as an optimization problem using the well-known…
Neural networks (NN) have achieved state-of-the-art performance in various applications. Unfortunately in applications where training data is insufficient, they are often prone to overfitting. One effective way to alleviate this problem is…
The true posterior distribution of a Bayesian neural network is massively multimodal. Whilst most of these modes are functionally equivalent, we demonstrate that there remains a level of real multimodality that manifests in even the…
This paper explores semi-qualitative probabilistic networks (SQPNs) that combine numeric and qualitative information. We first show that exact inferences with SQPNs are NPPP-Complete. We then show that existing qualitative relations in…
Mechanistic models can provide an intuitive and interpretable explanation of network growth by specifying a set of generative rules. These rules can be defined by domain knowledge about real-world mechanisms governing network growth or may…
This paper investigates a representation language with flexibility inspired by probabilistic logic and compactness inspired by relational Bayesian networks. The goal is to handle propositional and first-order constructs together with…
Four decades after their invention, quasi-Newton methods are still state of the art in unconstrained numerical optimization. Although not usually interpreted thus, these are learning algorithms that fit a local quadratic approximation to…
Understanding the uncertainty of a neural network's (NN) predictions is essential for many purposes. The Bayesian framework provides a principled approach to this, however applying it to NNs is challenging due to large numbers of parameters…
Bayes' rule plays a crucial piece of logical inference in information and physical sciences alike. Its extension into the quantum regime has been the object of several recent works. These quantum versions of Bayes' rule have been expressed…
The analytic inference, e.g. predictive distribution being in closed form, may be an appealing benefit for machine learning practitioners when they treat wide neural networks as Gaussian process in Bayesian setting. The realistic widths,…
We uncover a strong correspondence between Bayesian Networks and (Multiplicative) Linear Logic Proof-Nets, relating the two as a representation of a joint probability distribution and at the level of computation, so yielding a…
Separable Bayesian Networks, or the Influence Model, are dynamic Bayesian Networks in which the conditional probability distribution can be separated into a function of only the marginal distribution of a node's neighbors, instead of the…
We present a new approach for inference in Bayesian networks, which is mainly based on partial differentiation. According to this approach, one compiles a Bayesian network into a multivariate polynomial and then computes the partial…
We present and implement two algorithms for analytic asymptotic evaluation of the marginal likelihood of data given a Bayesian network with hidden nodes. As shown by previous work, this evaluation is particularly hard for latent Bayesian…
Latent Euclidean embedding models a given network by representing each node in a Euclidean space, where the probability of two nodes sharing an edge is a function of the distances between the nodes. This implies that for two nodes to share…
Bayesian networks are a canonical formalism for representing probabilistic dependencies, yet their integration within logic programming frameworks remains a nontrivial challenge, mainly due to the complex structure of these networks. In…
For many real-life Bayesian networks, common knowledge dictates that the output established for the main variable of interest increases with higher values for the observable variables. We define two concepts of monotonicity to capture this…
We revisit and generalize the concept of composite likelihood as a method to make a probabilistic inference by aggregation of multiple Bayesian agents, thereby defining a class of predictive models which we call composite Bayesian. This…
Relational data are usually highly incomplete in practice, which inspires us to leverage side information to improve the performance of community detection and link prediction. This paper presents a Bayesian probabilistic approach that…