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Interpretability is crucial for machine learning in many scenarios such as quantitative finance, banking, healthcare, etc. Symbolic regression (SR) is a classic interpretable machine learning method by bridging X and Y using mathematical…

interpretable, and well understood models that are routinely employed even though, as is revealed through prior and posterior predictive checks, these can poorly characterise the spatial heterogeneity in the underlying process of interest.…

We give a new consistent scoring function for structure learning of Bayesian networks. In contrast to traditional approaches to scorebased structure learning, such as BDeu or MDL, the complexity penalty that we propose is data-dependent and…

Exponential family models, generalized linear models (GLMs), generalized linear mixed models (GLMMs) and generalized additive models (GAMs) are widely used methods in statistics. However, many scientific applications necessitate constraints…

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…

Max-linear Bayesian networks (MLBNs) are a relatively recent class of structural equation models which arise when the random variables involved have heavy-tailed distributions. Unlike most directed graphical models, MLBNs are typically not…

In recent years, there is a growing interest in learning Bayesian networks with continuous variables. Learning the structure of such networks is a computationally expensive procedure, which limits most applications to parameter learning.…

Clustering procedures typically estimate which data points are clustered together, a quantity of primary importance in many analyses. Often used as a preliminary step for dimensionality reduction or to facilitate interpretation, finding…

In recent years there has been a flurry of works on learning Bayesian networks from data. One of the hard problems in this area is how to effectively learn the structure of a belief network from incomplete data- that is, in the presence of…

Continuous time Bayesian networks (CTBNs) describe structured stochastic processes with finitely many states that evolve over continuous time. A CTBN is a directed (possibly cyclic) dependency graph over a set of variables, each of which…

Randomized algorithms are used in many state-of-the-art solvers for constraint satisfaction problems (CSP) and Boolean satisfiability (SAT) problems. For many of these problems, there is no single solver which will dominate others. Having…

Low-dimensional probability models for local distribution functions in a Bayesian network include decision trees, decision graphs, and causal independence models. We describe a new probability model for discrete Bayesian networks, which we…

Bayesian Neural Networks (BNNs) provide a probabilistic interpretation for deep learning models by imposing a prior distribution over model parameters and inferring a posterior distribution based on observed data. The model sampled from the…

We extend the decomposition approach for learning Bayesian networks (BNs) proposed by (Xie et. al.) to learning multivariate regression chain graphs (MVR CGs), which include BNs as a special case. The same advantages of this decomposition…

Deep learning models, such as convolutional neural networks, have long been applied to image and multi-media tasks, particularly those with structured data. More recently, there has been more attention to unstructured data that can be…

Bayesian networks are now being used in enormous fields, for example, diagnosis of a system, data mining, clustering and so on. In spite of their wide range of applications, the statistical properties have not yet been clarified, because…

The infinite width limit of random neural networks is known to result in Neural Networks as Gaussian Process (NNGP) (Lee et al. (2018)), characterized by task-independent kernels. It is widely accepted that larger network widths contribute…

Bayesian networks (BNs) are a probabilistic graphical model widely used for representing expert knowledge and reasoning under uncertainty. Traditionally, they are based on directed acyclic graphs that capture dependencies between random…

Solving partial differential equations (PDEs) is the canonical approach for understanding the behavior of physical systems. However, large scale solutions of PDEs using state of the art discretization techniques remains an expensive…

Score based learning (SBL) is a promising approach for learning Bayesian networks. The initial step in the majority of the SBL algorithms consists of computing the scores of all possible child and parent-set combinations for the variables.…