Related papers: A Pair of Bayesian Network Structures has Undecida…

Constraint-based (CB) learning is a formalism for learning a causal network with a database D by performing a series of conditional-independence tests to infer structural information. This paper considers a new test of independence that…

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

Learning the structure of Bayesian networks is a difficult combinatorial optimization problem. In this paper, we consider learning of tree-augmented naive Bayes (TAN) structures for Bayesian network classifiers with discrete input features.…

We present a simple characterization of equivalent Bayesian network structures based on local transformations. The significance of the characterization is twofold. First, we are able to easily prove several new invariant properties of…

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…

Estimating conditional independence graphs from high-dimensional Gaussian data is challenging because methods must detect relevant edges while rigorously controlling statistical errors. We propose a Bayesian framework based on a prior…

It is well known that conditional independence can be used to factorize a joint probability into a multiplication of conditional probabilities. This paper proposes a constructive definition of inter-causal independence, which can be used to…

We study conditional independence relationships for random networks and their interplay with exchangeability. We show that, for finitely exchangeable network models, the empirical subgraph densities are maximum likelihood estimates of their…

The fundamental concepts underlying in Markov networks are the conditional independence and the set of rules called Markov properties that translates conditional independence constraints into graphs. In this article we introduce the concept…

Several methods have recently been developed for joint structure learning of multiple (related) graphical models or networks. These methods treat individual networks as exchangeable, such that each pair of networks are equally encouraged to…

We show that any quantum density matrix can be represented by a Bayesian network (a directed acyclic graph), and also by a Markov network (an undirected graph). We show that any Bayesian or Markov net that represents a density matrix, is…

We study the problem of learning the best Bayesian network structure with respect to a decomposable score such as BDe, BIC or AIC. This problem is known to be NP-hard, which means that solving it becomes quickly infeasible as the number of…

This work reports the most relevant technical aspects in the problem of learning the \emph{Markov network structure} from data. Such problem has become increasingly important in machine learning, and many other application fields of machine…

The graphical structure of Probabilistic Graphical Models (PGMs) encodes the conditional independence (CI) relations that hold in the modeled distribution. Graph algorithms, such as d-separation, use this structure to infer additional…

For a directed acyclic graph, there are two known criteria to decide whether any specific conditional independence statement is implied for all distributions factorized according to the given graph. Both criteria are based on special types…

Most empirical studies of complex networks do not return direct, error-free measurements of network structure. Instead, they typically rely on indirect measurements that are often error-prone and unreliable. A fundamental problem in…

We present new algorithms for inference in credal networks --- directed acyclic graphs associated with sets of probabilities. Credal networks are here interpreted as encoding strong independence relations among variables. We first present a…

Our current world is linked by a complex mesh of networks where information, people and goods flow. These networks are interdependent each other, and present structural and dynamical features different from those observed in isolated…

Though a belief network (a representation of the joint probability distribution, see [3]) and a causal network (a representation of causal relationships [14]) are intended to mean different things, they are closely related. Both assume an…

This paper analyzes irrelevance and independence relations in graphical models associated with convex sets of probability distributions (called Quasi-Bayesian networks). The basic question in Quasi-Bayesian networks is, How can…