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A Bayesian network is a probabilistic graphical model that consists of a directed acyclic graph (DAG), where each node is a random variable and attached to each node is a conditional probability distribution (CPD). A Bayesian network can be…
Theory of graphical models has matured over more than three decades to provide the backbone for several classes of models that are used in a myriad of applications such as genetic mapping of diseases, credit risk evaluation, reliability and…
Directed acyclic graphs (DAGs) constitute a central modeling tool to enable principled reasoning about cause-effect interactions in complex systems. However, since the causal structure underlying a group of variables is often unknown and…
In the process of building (structural learning) a probabilistic graphical model from a set of observed data, the directional, cyclic dependencies between the random variables of the model are often found. Existing graphical models such as…
Generative Adversarial Networks (GANs) are modern methods to learn the underlying distribution of a data set. GANs have been widely used in sample synthesis, de-noising, domain transfer, etc. GANs, however, are designed in a model-free…
In this article, we propose a new hypothesis testing method for directed acyclic graph (DAG). While there is a rich class of DAG estimation methods, there is a relative paucity of DAG inference solutions. Moreover, the existing methods…
Bayesian networks are a versatile and powerful tool to model complex phenomena and the interplay of their components in a probabilistically principled way. Moving beyond the comparatively simple case of completely observed, static data,…
Directed acyclic graphs provide a fundamental tool for representing directed dependence structures in multivariate network data, and are widely used to model financial and economic networks. However, accurate and interpretable estimation…
Anomaly detection is a widely studied task for a broad variety of data types; among them, multiple time series appear frequently in applications, including for example, power grids and traffic networks. Detecting anomalies for multiple time…
A novel unified Bayesian framework for network detection is developed, under which a detection algorithm is derived based on random walks on graphs. The algorithm detects threat networks using partial observations of their activity, and is…
The non-convexity and intractability of distributionally robust chance constraints make them challenging to cope with. From a data-driven perspective, we propose formulating it as a robust optimization problem to ensure that the…
Hierarchical Bayesian models are increasingly used in large, inhomogeneous complex network dynamical systems by modeling parameters as draws from a hyperparameter-governed distribution. However, theoretical guarantees for these estimates as…
Mixture model-based frameworks are very popular for statistical inference in clustering. While convenient for producing probabilistic estimates of cluster assignments and uncertainty, they are prone to misspecification, which can lead to…
Dam breach models are commonly used to predict outflow hydrographs of potentially failing dams and are key ingredients for evaluating flood risk. In this paper a new dam breach modeling framework is introduced that shall improve the…
While existing mathematical descriptions can accurately account for phenomena at microscopic scales (e.g. molecular dynamics), these are often high-dimensional, stochastic and their applicability over macroscopic time scales of physical…
Causal learning from data has received much attention recently. Bayesian networks can be used to capture causal relationships. There, one recovers a weighted directed acyclic graph in which random variables are represented by vertices, and…
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…
We propose a Bayesian network model to make inferences and predictions about cardiovascular risk. Both the structure and the probability tables in the underlying model are built using a large dataset collected in Spain from annual work…
Learning the structure of dependence relations between variables is a pervasive issue in the statistical literature. A directed acyclic graph (DAG) can represent a set of conditional independences, but different DAGs may encode the same set…
Bayesian inference of Bayesian network structures is often performed by sampling directed acyclic graphs along an appropriately constructed Markov chain. We present two techniques to improve sampling. First, we give an efficient…