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Many Bayesian Network structure learning algorithms are unstable, with the learned graph sensitive to arbitrary dataset artifacts, such as the ordering of columns (i.e., variable order). PC-Stable attempts to address this issue for the…

Learning-based methods for inverse problems, adapting to the data's inherent structure, have become ubiquitous in the last decade. Besides empirical investigations of their often remarkable performance, an increasing number of works…

Bayesian networks are probabilistic graphical models with a wide range of application areas including gene regulatory networks inference, risk analysis and image processing. Learning the structure of a Bayesian network (BNSL) from discrete…

In this paper we address the problem of discretization in the context of learning Bayesian networks (BNs) from data containing both continuous and discrete variables. We describe a new technique for <EM>multivariate</EM> discretization,…

Bayesian networks (BNs) are a widely used graphical model in machine learning for representing knowledge with uncertainty. The mainstream BN structure learning methods require performing a large number of conditional independence (CI)…

Estimating dependence relationships between variables is a crucial issue in many applied domains, such as medicine, social sciences and psychology. When several variables are entertained, these can be organized into a network which encodes…

Presence of bias (in datasets or tasks) is inarguably one of the most critical challenges in machine learning applications that has alluded to pivotal debates in recent years. Such challenges range from spurious associations between…

This paper investigates a new learning formulation called structured sparsity, which is a natural extension of the standard sparsity concept in statistical learning and compressive sensing. By allowing arbitrary structures on the feature…

One of the basic tasks for Bayesian networks (BNs) is that of learning a network structure from data. The BN-learning problem is NP-hard, so the standard solution is heuristic search. Many approaches have been proposed for this task, but…

A Bayesian network is a directed acyclic graph that represents statistical dependencies between variables of a joint probability distribution. A fundamental task in data science is to learn a Bayesian network from observed data.…

In this paper, we derive optimality results for greedy Bayesian-network search algorithms that perform single-edge modifications at each step and use asymptotically consistent scoring criteria. Our results extend those of Meek (1997) and…

In this paper, we focus on the unsupervised setting for structure learning of deep neural networks and propose to adopt the efficient coding principle, rooted in information theory and developed in computational neuroscience, to guide the…

We commonly assume that data are a homogeneous set of observations when learning the structure of Bayesian networks. However, they often comprise different data sets that are related but not homogeneous because they have been collected in…

Spline basis exploration via Bayesian model selection is a widely employed strategy for determining the optimal set of basis terms in nonparametric regression. However, despite its widespread use, this approach often encounters performance…

Structured sparsity has recently emerged in statistics, machine learning and signal processing as a promising paradigm for learning in high-dimensional settings. All existing methods for learning under the assumption of structured sparsity…

Methods for learning Bayesian network structure can discover dependency structure between observed variables, and have been shown to be useful in many applications. However, in domains that involve a large number of variables, the space of…

In this paper, we present a guide to the foundations of learning Dynamic Bayesian Networks (DBNs) from data in the form of multiple samples of trajectories for some length of time. We present the formalism for a generic as well as a set of…

We study the theoretical behavior of denoising score matching--the learning task associated to diffusion models--when the data distribution is supported on a low-dimensional manifold and the score is parameterized using a random feature…

In this work, dynamic Bayesian multinets are introduced where a Markov chain state at time t determines conditional independence patterns between random variables lying within a local time window surrounding t. It is shown how…

Structural missingness breaks 'just impute and train': values can be undefined by causal or logical constraints, and the mask may depend on observed variables, unobserved variables (MNAR), and other missingness indicators. It simultaneously…