Related papers: Accelerating Bayesian Structure Learning in Sparse…
One of the fundamental tasks of science is to find explainable relationships between observed phenomena. One approach to this task that has received attention in recent years is based on probabilistic graphical modelling with sparsity…
Structure learning of Gaussian graphical models is an extensively studied problem in the classical multivariate setting where the sample size n is larger than the number of random variables p, as well as in the more challenging setting when…
We consider the problem of learning a conditional Gaussian graphical model in the presence of latent variables. Building on recent advances in this field, we suggest a method that decomposes the parameters of a conditional Markov random…
As data sets grow in size, the ability of learning methods to find structure in them is increasingly hampered by the time needed to search the large spaces of possibilities and generate a score for each that takes all of the observed data…
Dynamic Bayesian networks have been well explored in the literature as discrete-time models: however, their continuous-time extensions have seen comparatively little attention. In this paper, we propose the first constraint-based algorithm…
Sparsity-constrained optimization is an important and challenging problem that has wide applicability in data mining, machine learning, and statistics. In this paper, we focus on sparsity-constrained optimization in cases where the cost…
It is well known in the literature that the problem of learning the structure of Bayesian networks is very hard to tackle: its computational complexity is super-exponential in the number of nodes in the worst case and polynomial in most…
Marginal likelihood, also known as model evidence, is a fundamental quantity in Bayesian statistics. It is used for model selection using Bayes factors or for empirical Bayes tuning of prior hyper-parameters. Yet, the calculation of…
Graphical models provide a powerful methodology for learning the conditional independence structure in multivariate data. Inference is often focused on estimating individual edges in the latent graph. Nonetheless, there is increasing…
The Gaussian Graphical Model (GGM) is a popular tool for incorporating sparsity into joint multivariate distributions. The G-Wishart distribution, a conjugate prior for precision matrices satisfying general GGM constraints, has now been in…
We describe algorithms for learning Bayesian networks from a combination of user knowledge and statistical data. The algorithms have two components: a scoring metric and a search procedure. The scoring metric takes a network structure,…
Graphical models are widely used in scienti fic and engineering research to represent conditional independence structures between random variables. In many controlled experiments, environmental changes or external stimuli can often alter…
Gaussian graphical model selection is usually studied under independent sampling, but in many applications observations arise from dependent dynamics. We study structure learning when the data consist of a single trajectory of Gaussian…
Precision matrices are crucial in many fields such as social networks, neuroscience, and economics, representing the edge structure of Gaussian graphical models (GGMs), where a zero in an off-diagonal position of the precision matrix…
We consider a graphical model where a multivariate normal vector is associated with each node of the underlying graph and estimate the graphical structure. We minimize a loss function obtained by regressing the vector at each node on those…
Bayesian optimization (BO) is a powerful framework for optimizing expensive black-box objectives, yet extending it to graph-structured domains remains challenging due to the discrete and combinatorial nature of graphs. Existing approaches…
Our concern is selecting the concentration matrix's nonzero coefficients for a sparse Gaussian graphical model in a high-dimensional setting. This corresponds to estimating the graph of conditional dependencies between the variables. We…
We study the conjugacy approximation method in the context of Bayesian ranking and selection with unknown correlations. Under the assumption of normal-inverse-Wishart prior distribution, the posterior distribution remains a…
The focus in this paper is Bayesian system identification based on noisy incomplete modal data where we can impose spatially-sparse stiffness changes when updating a structural model. To this end, based on a similar hierarchical sparse…
Graphical Gaussian models with edge and vertex symmetries were introduced by \citet{HojLaur:2008} who also gave an algorithm to compute the maximum likelihood estimate of the precision matrix for such models. In this paper, we take a…