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We study the problem of learning a Bayesian network (BN) of a set of variables when structural side information about the system is available. It is well known that learning the structure of a general BN is both computationally and…

Bayesian Neural Networks (BNNs) offer a principled and natural framework for proper uncertainty quantification in the context of deep learning. They address the typical challenges associated with conventional deep learning methods, such as…

Directed acyclic graphs (DAGs) are commonly used to represent causal relationships among random variables in graphical models. Applications of these models arise in the study of physical, as well as biological systems, where directed edges…

Motivation: Several different threads of research have been proposed for modeling and mining temporal data. On the one hand, approaches such as dynamic Bayesian networks (DBNs) provide a formal probabilistic basis to model relationships…

Approximate Bayesian Computation is widely used in systems biology for inferring parameters in stochastic gene regulatory network models. Its performance hinges critically on the ability to summarize high-dimensional system responses such…

In Bayesian Networks (BNs), the direction of edges is crucial for causal reasoning and inference. However, Markov equivalence class considerations mean it is not always possible to establish edge orientations, which is why many BN structure…

Score-based methods for learning Bayesain networks(BN) aim to maximizing the global score functions. However, if local variables have direct and indirect dependence simultaneously, the global optimization on score functions misses edges…

We give methods for Bayesian inference of directed acyclic graphs, DAGs, and the induced causal effects from passively observed complete data. Our methods build on a recent Markov chain Monte Carlo scheme for learning Bayesian networks,…

Due to its causal semantics, Bayesian networks (BN) have been widely employed to discover the underlying data relationship in exploratory studies, such as brain research. Despite its success in modeling the probability distribution of…

Recovering the underlying Directed Acyclic Graph (DAG) structures from observational data presents a formidable challenge, partly due to the combinatorial nature of the DAG-constrained optimization problem. Recently, researchers have…

We study active structure learning of Bayesian networks in an observational setting, in which there are external limitations on the number of variable values that can be observed from the same sample. Random samples are drawn from the joint…

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 problem of learning a directed acyclic graph (DAG) up to Markov equivalence is equivalent to the problem of finding a permutation of the variables that induces the sparsest graph. Without additional assumptions, this task is known to be…

Within the framework of complex system design, it is often necessary to solve mixed variable optimization problems, in which the objective and constraint functions can depend simultaneously on continuous and discrete variables.…

Capturing the underlying structural causal relations represented by Directed Acyclic Graphs (DAGs) has been a fundamental task in various AI disciplines. Causal DAG learning via the continuous optimization framework has recently achieved…

Bayesian networks have been used as a mechanism to represent the joint distribution of multiple random variables in a flexible yet interpretable manner. One major challenge in learning the structure of a Bayesian network is how to model…

We consider the problem of inferring the values of an arbitrary set of variables (e.g., risk of diseases) given other observed variables (e.g., symptoms and diagnosed diseases) and high-dimensional signals (e.g., MRI images or EEG). This is…

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…

A well-studied challenge that arises in the structure learning problem of causal directed acyclic graphs (DAG) is that using observational data, one can only learn the graph up to a "Markov equivalence class" (MEC). The remaining undirected…

To learn (statistical) dependencies among random variables requires exponentially large sample size in the number of observed random variables if any arbitrary joint probability distribution can occur. We consider the case that sparse data…