Related papers: Information-theoretic limits of Bayesian network s…
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…
Probabilistic graphical models (PGMs) provide a compact and flexible framework to model very complex real-life phenomena. They combine the probability theory which deals with uncertainty and logical structure represented by a graph which…
The problem of learning the structure of Bayesian networks from complete discrete data with a limit on parent set size is considered. Learning is cast explicitly as an optimisation problem where the goal is to find a BN structure which…
In this paper, we analyze the information theoretic lower bound on the necessary number of samples needed for recovering a sparse signal under different compressed sensing settings. We focus on the weighted graph model, a model-based…
The problem of recovering the sparsity pattern of a fixed but unknown vector $\beta^* \in \real^p based on a set of $n$ noisy observations arises in a variety of settings, including subset selection in regression, graphical model selection,…
Learning the structure of Bayesian networks (BNs) from data is challenging, especially for datasets involving a large number of variables. The recently proposed divide-and-conquer (D\&D) strategies present a promising approach for learning…
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…
Successful machine learning methods require a trade-off between memorization and generalization. Too much memorization and the model cannot generalize to unobserved examples. Too much over-generalization and we risk under-fitting the data.…
Many algorithms for score-based Bayesian network structure learning (BNSL), in particular exact ones, take as input a collection of potentially optimal parent sets for each variable in the data. Constructing such collections naively is…
We study the information-theoretic limits of exactly recovering the support of a sparse signal using noisy projections defined by various classes of measurement matrices. Our analysis is high-dimensional in nature, in which the number of…
Bayesian networks are a powerful framework for studying the dependency structure of variables in a complex system. The problem of learning Bayesian networks is tightly associated with the given data type. Ordinal data, such as stages of…
Three classes of algorithms to learn the structure of Bayesian networks from data are common in the literature: constraint-based algorithms, which use conditional independence tests to learn the dependence structure of the data; score-based…
Bayesian structure learning is the NP-hard problem of discovering a Bayesian network that optimally represents a given set of training data. In this paper we study the computational worst-case complexity of exact Bayesian structure learning…
In recent years there has been an increasing interest in learning Bayesian networks from data. One of the most effective methods for learning such networks is based on the minimum description length (MDL) principle. Previous work has shown…
Learning the structure of Bayesian networks from data is known to be a computationally challenging, NP-hard problem. The literature has long investigated how to perform structure learning from data containing large numbers of variables,…
We study the information-theoretic lower bound of the sample complexity of the correct recovery of diffusion network structures. We introduce a discrete-time diffusion model based on the Independent Cascade model for which we obtain a lower…
Bayesian network (BN) structure learning from complete data has been extensively studied in the literature. However, fewer theoretical results are available for incomplete data, and most are related to the Expectation-Maximisation (EM)…
Learning joint probability distributions on n random variables requires exponential sample size in the generic case. Here we consider the case that a temporal (or causal) order of the variables is known and that the (unknown) graph of…
Bayesian Networks (BNs) represent conditional probability relations among a set of random variables (nodes) in the form of a directed acyclic graph (DAG), and have found diverse applications in knowledge discovery. We study the problem of…
Searching the complete space of possible Bayesian networks is intractable for problems of interesting size, so Bayesian network structure learning algorithms, such as the commonly used Sparse Candidate algorithm, employ heuristics. However,…