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We extend Probability Bracket Notation (PBN), inspired by the Dirac notation in quantum mechanics, to multivariable probability systems and static Bayesian networks (BNs). By defining probability distributions and conditional expectations…

We provide a survey on relational models. Relational models describe complete networked {domains by taking into account global dependencies in the data}. Relational models can lead to more accurate predictions if compared to non-relational…

The validation of any database mining methodology goes through an evaluation process where benchmarks availability is essential. In this paper, we aim to randomly generate relational database benchmarks that allow to check probabilistic…

Learning the parameters of complex probabilistic-relational models from labeled training data is a standard technique in machine learning, which has been intensively studied in the subfield of Statistical Relational Learning (SRL), but---so…

Probabilistic context-free grammars (PCFGs) and dynamic Bayesian networks (DBNs) are widely used sequence models with complementary strengths and limitations. While PCFGs allow for nested hierarchical dependencies (tree structures), their…

A generative probabilistic model for relational data consists of a family of probability distributions for relational structures over domains of different sizes. In most existing statistical relational learning (SRL) frameworks, these…

Stochastic processes that involve the creation of objects and relations over time are widespread, but relatively poorly studied. For example, accurate fault diagnosis in factory assembly processes requires inferring the probabilities of…

The stochastic block model (SBM) is a probabilistic model for community structure in networks. Typically, only the adjacency matrix is used to perform SBM parameter inference. In this paper, we consider circumstances in which nodes have an…

Recurrent neural networks (RNNs) are nonlinear dynamical models commonly used in the machine learning and dynamical systems literature to represent complex dynamical or sequential relationships between variables. More recently, as deep…

Many databases store data in relational format, with different types of entities and information about links between the entities. The field of statistical-relational learning (SRL) has developed a number of new statistical models for such…

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…

The membership inference problem for publicly released statistics from a private dataset is well-studied. When developing and formally analyzing attack strategies, however, the focus has been on attacks that model the population using only…

Graph neural networks (GNNs) excel at predictive tasks on graph-structured data but often lack the ability to incorporate symbolic domain knowledge and perform general reasoning. Relational Bayesian Networks (RBNs), in contrast, enable…

In cognitive radio (CR) technology, the trend of sensing is no longer to only detect the presence of active primary users. A large number of applications demand for more comprehensive knowledge on primary user behaviors in spatial,…

Statistical node clustering in discrete time dynamic networks is an emerging field that raises many challenges. Here, we explore statistical properties and frequentist inference in a model that combines a stochastic block model (SBM) for…

In this paper, the relationship between probabilistic graphical models, in particular Bayesian networks, and causal diagrams, also called structural causal models, is studied. Structural causal models are deterministic models, based on…

Dependencies on the relative frequency of a state in the domain are common when modelling probabilistic dependencies on relational data. For instance, the likelihood of a school closure during an epidemic might depend on the proportion of…

In many supervised learning tasks, the entities to be labeled are related to each other in complex ways and their labels are not independent. For example, in hypertext classification, the labels of linked pages are highly correlated. A…

Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using a…

Various NLP problems -- such as the prediction of sentence similarity, entailment, and discourse relations -- are all instances of the same general task: the modeling of semantic relations between a pair of textual elements. A popular model…