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We propose a novel score-based approach to learning a directed acyclic graph (DAG) from observational data. We adapt a recently proposed continuous constrained optimization formulation to allow for nonlinear relationships between variables…

We consider jointly estimating the coefficient matrix and the error precision matrix in high-dimensional multivariate linear regression models. Bayesian methods in this context often face computational challenges, leading to previous…

Bayesian networks are widely used to learn and reason about the dependence structure of discrete variables. However, they are only capable of formally encoding symmetric conditional independence, which in practice is often too strict to…

This paper addresses a gap in the current state of the art by providing a solution for modeling causal relationships that evolve over time and occur at different time scales. Specifically, we introduce the multiscale non-stationary directed…

Although many algorithms have been designed to construct Bayesian network structures using different approaches and principles, they all employ only two methods: those based on independence criteria, and those based on a scoring function…

The graph of a Bayesian Network (BN) can be machine learned, determined by causal knowledge, or a combination of both. In disciplines like bioinformatics, applying BN structure learning algorithms can reveal new insights that would…

When working with multimodal Bayesian posterior distributions, Markov chain Monte Carlo (MCMC) algorithms have difficulty moving between modes, and default variational or mode-based approximate inferences will understate posterior…

Learning directed acyclic graph (DAG) that describes the causality of observed data is a very challenging but important task. Due to the limited quantity and quality of observed data, and non-identifiability of causal graph, it is almost…

Classical parameter-space Bayesian inference for Bayesian neural networks (BNNs) suffers from several unresolved prior issues, such as knowledge encoding intractability and pathological behaviours in deep networks, which can lead to…

Despite several advances in recent years, learning causal structures represented by directed acyclic graphs (DAGs) remains a challenging task in high dimensional settings when the graphs to be learned are not sparse. In this paper, we…

Bayesian network is a frequently-used method for fault detection and diagnosis in industrial processes. The basis of Bayesian network is structure learning which learns a directed acyclic graph (DAG) from data. However, the search space…

As data size and computing power increase, the architectures of deep neural networks (DNNs) have been getting more complex and huge, and thus there is a growing need to simplify such complex and huge DNNs. In this paper, we propose a novel…

Deriving Bayesian inference for exponential random graph models (ERGMs) is a challenging "doubly intractable" problem as the normalizing constants of the likelihood and posterior density are both intractable. Markov chain Monte Carlo (MCMC)…

We consider the problem of learning causal Directed Acyclic Graphs (DAGs) using combinations of observational and interventional experimental data. Current methods tailored to this setting assume that interventions either destroy…

Recently continuous relaxations have been proposed in order to learn Directed Acyclic Graphs (DAGs) from data by backpropagation, instead of using combinatorial optimization. However, a number of techniques for fully discrete…

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…

We propose a novel approach to perform approximate Bayesian inference in complex models such as Bayesian neural networks. The approach is more scalable to large data than Markov Chain Monte Carlo, it embraces more expressive models than…

Dealing with uncertainty in Bayesian Network structures using maximum a posteriori (MAP) estimation or Bayesian Model Averaging (BMA) is often intractable due to the superexponential number of possible directed, acyclic graphs. When the…

Bayesian Networks (BN) provide robust probabilistic methods of reasoning under uncertainty, but despite their formal grounds are strictly based on the notion of conditional dependence, not much attention has been paid so far to their use in…

Bayesian Neural Networks (BNNs) offer robust uncertainty quantification in model predictions, but training them presents a significant computational challenge. This is mainly due to the problem of sampling multimodal posterior distributions…