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Probability estimation is one of the fundamental tasks in statistics and machine learning. However, standard methods for probability estimation on discrete objects do not handle object structure in a satisfactory manner. In this paper, we…

Decision Trees are some of the most popular machine learning models today due to their out-of-the-box performance and interpretability. Often, Decision Trees models are constructed greedily in a top-down fashion via heuristic search…

There has been great interest in identifying tractable subclasses of NP complete problems and designing efficient algorithms for these tractable classes. Constraint satisfaction and Bayesian network inference are two examples of such…

Probabilistic representations, such as Bayesian and Markov networks, are fundamental to much of statistical machine learning. Thus, learning probabilistic representations directly from data is a deep challenge, the main computational…

We provide a new characterization of the Dirichlet distribution. This characterization implies that under assumptions made by several previous authors for learning belief networks, a Dirichlet prior on the parameters is inevitable.

Bayesian learning is a powerful learning framework which combines the external information of the data (background information) with the internal information (training data) in a logically consistent way in inference and prediction. By…

The recursive and hierarchical structure of full rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. In most of these cases, the full rooted tree is…

A Bayesian treatment of latent directed graph structure for non-iid data is provided where each child datum is sampled with a directed conditional dependence on a single unknown parent datum. The latent graph structure is assumed to lie in…

Daily internet communication relies heavily on tree-structured graphs, embodied by popular data formats such as XML and JSON. However, many recent generative (probabilistic) models utilize neural networks to learn a probability distribution…

Probabilistic representations, such as Bayesian and Markov networks, are fundamental to much of statistical machine learning. Thus, learning probabilistic representations directly from data is a deep challenge, the main computational…

Joint distributions over many variables are frequently modeled by decomposing them into products of simpler, lower-dimensional conditional distributions, such as in sparsely connected Bayesian networks. However, automatically learning such…

When the historical data are limited, the conditional probabilities associated with the nodes of Bayesian networks are uncertain and can be empirically estimated. Second order estimation methods provide a framework for both estimating the…

Exchangeability is a central notion in statistics and probability theory. The assumption that an infinite sequence of data points is exchangeable is at the core of Bayesian statistics. However, finite exchangeability as a statistical…

We consider the problem of change-point detection in multivariate time-series. The multivariate distribution of the observations is supposed to follow a graphical model, whose graph and parameters are affected by abrupt changes throughout…

Models with intractable likelihood functions arise in areas including network analysis and spatial statistics, especially those involving Gibbs random fields. Posterior parameter es timation in these settings is termed a doubly-intractable…

We present a method for learning treewidth-bounded Bayesian networks from data sets containing thousands of variables. Bounding the treewidth of a Bayesian greatly reduces the complexity of inferences. Yet, being a global property of the…

Bayesian inference promises a framework for principled uncertainty quantification of neural network predictions. Barriers to adoption include the difficulty of fully characterizing posterior distributions on network parameters and the…

Inference in expressive probabilistic models is generally intractable, which makes them difficult to learn and limits their applicability. Sum-product networks are a class of deep models where, surprisingly, inference remains tractable even…

Treewidth is a well-studied decompositional parameter to measure the tree-likeness of a graph. While the propositional satisfiability problem (SAT) is known to be tractable when parameterized by the treewidth of the underlying primal graph,…

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…