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Bayesian network is a complete model for the variables and their relationships, it can be used to answer probabilistic queries about them. A Bayesian network can thus be considered a mechanism for automatically applying Bayes' theorem to…
Given a Bayesian network structure (directed acyclic graph), the celebrated d-separation algorithm efficiently determines whether the network structure implies a given conditional independence relation. We show that this changes drastically…
Mechanistic network models can capture salient characteristics of empirical networks using a small set of domain-specific, interpretable mechanisms. Yet inference remains challenging because the likelihood is often intractable. We show…
The covariance graph (aka bi-directed graph) of a probability distribution $p$ is the undirected graph $G$ where two nodes are adjacent iff their corresponding random variables are marginally dependent in $p$. In this paper, we present a…
Directed acyclic graph (DAG) models, also called Bayesian networks, impose conditional independence constraints on a multivariate probability distribution, and are widely used in probabilistic reasoning, machine learning and causal…
Recently several researchers have investigated techniques for using data to learn Bayesian networks containing compact representations for the conditional probability distributions (CPDs) stored at each node. The majority of this work has…
The dynamics of network formation are generally very complex, making the study of distributions over the space of networks often intractable. Under a condition called conservativeness, I show that the stationary distribution of a network…
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…
Probabilistic independence can dramatically simplify the task of eliciting, representing, and computing with probabilities in large domains. A key technique in achieving these benefits is the idea of graphical modeling. We survey existing…
We study the problem of learning the Markov order in categorical sequences that represent paths in a network, i.e. sequences of variable lengths where transitions between states are constrained to a known graph. Such data pose challenges…
Traditional approaches to Bayes net structure learning typically assume little regularity in graph structure other than sparseness. However, in many cases, we expect more systematicity: variables in real-world systems often group into…
Normative expert systems have not become commonplace because they have been difficult to build and use. Over the past decade, however, researchers have developed the influence diagram, a graphical representation of a decision maker's…
Traditional statistical learning theory relies on the assumption that data are identically and independently distributed (i.i.d.). However, this assumption often does not hold in many real-life applications. In this survey, we explore…
The adaptive processing of structured data is a long-standing research topic in machine learning that investigates how to automatically learn a mapping from a structured input to outputs of various nature. Recently, there has been an…
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…
General results from statistical learning theory suggest to understand not only brain computations, but also brain plasticity as probabilistic inference. But a model for that has been missing. We propose that inherently stochastic features…
Bayesian networks provide a method of representing conditional independence between random variables and computing the probability distributions associated with these random variables. In this paper, we extend Bayesian network structures to…
A dynamical network, a graph whose nodes are dynamical systems, is usually characterized by a large dimensional space which is not always accesible due to the impossibility of measuring all the variables spanning the state space. Therefore,…
Bayesian network structure learning algorithms with limited data are being used in domains such as systems biology and neuroscience to gain insight into the underlying processes that produce observed data. Learning reliable networks from…
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…