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A graphical model is a statistical model that is associated to a graph whose nodes correspond to variables of interest. The edges of the graph reflect allowed conditional dependencies among the variables. Graphical models admit…

We develop a Bayesian "sum-of-trees" model where each tree is constrained by a regularization prior to be a weak learner, and fitting and inference are accomplished via an iterative Bayesian backfitting MCMC algorithm that generates samples…

Tree-based networks are a class of phylogenetic networks that attempt to formally capture what is meant by "tree-like" evolution. A given non-tree-based phylogenetic network, however, might appear to be very close to being tree-based, or…

Recent efforts to learn reward functions from human feedback have tended to use deep neural networks, whose lack of transparency hampers our ability to explain agent behaviour or verify alignment. We explore the merits of learning…

Dependency networks (Heckerman et al., 2000) are potential probabilistic graphical models for systems comprising a large number of variables. Like Bayesian networks, the structure of a dependency network is represented by a directed graph,…

Staged tree models are a discrete generalization of Bayesian networks. We show that these form curved exponential families and derive their natural parameters, sufficient statistic, and cumulant-generating function as functions of their…

Testing the validity of probabilistic models containing unmeasured (hidden) variables is shown to be a hard task. We show that the task of testing whether models are structurally incompatible with the data at hand, requires an exponential…

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…

Bayesian networks are basic graphical models, used widely both in statistics and artificial intelligence. These statistical models of conditional independence structure are described by acyclic directed graphs whose nodes correspond to…

Using ensemble methods for regression has been a large success in obtaining high-accuracy prediction. Examples are Bagging, Random forest, Boosting, BART (Bayesian additive regression tree), and their variants. In this paper, we propose a…

In order to speed-up classification models when facing a large number of categories, one usual approach consists in organizing the categories in a particular structure, this structure being then used as a way to speed-up the prediction…

We address the problem of Bayesian structure learning for domains with hundreds of variables by employing non-parametric bootstrap, recursively. We propose a method that covers both model averaging and model selection in the same framework.…

Owing to their inherently interpretable structure, decision trees are commonly used in applications where interpretability is essential. Recent work has focused on improving various aspects of decision trees, including their predictive…

The best-performing models in ML are not interpretable. If we can explain why they outperform, we may be able to replicate these mechanisms and obtain both interpretability and performance. One example are decision trees and their…

Gaussian graphical models provide a powerful framework to reveal the conditional dependency structure between multivariate variables. The process of uncovering the conditional dependency network is known as structure learning. Bayesian…

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…

Bayesian additive regression trees (BART) (Chipman et. al., 2010) is a powerful predictive model that often outperforms alternative models at out-of-sample prediction. BART is especially well-suited to settings with unstructured predictor…

Segmenting tree structures is common in several image processing applications. In medical image analysis, reliable segmentations of airways, vessels, neurons and other tree structures can enable important clinical applications. We present a…

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…

The adoption of the distributed paradigm has allowed applications to increase their scalability, robustness and fault tolerance, but it has also complicated their structure, leading to an exponential growth of the applications'…