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Inference in nonlinear continuous stochastic processes on trees is challenging, particularly when observations are sparse and the topology is complex. Exact smoothing via Doob's $h$-transform is intractable for general nonlinear dynamics.…

Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…

Decision trees are a popular machine learning method, known for their inherent explainability. In Explainable AI, decision trees can be used as surrogate models for complex black box AI models or as approximations of parts of such models. A…

Decision trees are important both as interpretable models amenable to high-stakes decision-making, and as building blocks of ensemble methods such as random forests and gradient boosting. Their statistical properties, however, are not well…

Vector autoregression has been widely used for modeling and analysis of multivariate time series data. In high-dimensional settings, model parameter regularization schemes inducing sparsity yield interpretable models and achieved good…

The perspective of developing trustworthy AI for critical applications in science and engineering requires machine learning techniques that are capable of estimating their own uncertainty. In the context of regression, instead of estimating…

Deep Gaussian processes (DGP) have appealing Bayesian properties, can handle variable-sized data, and learn deep features. Their limitation is that they do not scale well with the size of the data. Existing approaches address this using a…

The advent of Scientific Machine Learning has heralded a transformative era in scientific discovery, driving progress across diverse domains. Central to this progress is uncovering scientific laws from experimental data through symbolic…

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…

Decision trees and random forest remain highly competitive for classification on medium-sized, standard datasets due to their robustness, minimal preprocessing requirements, and interpretability. However, a single tree suffers from high…

Credible intervals and credible sets, such as highest posterior density (HPD) intervals, form an integral statistical tool in Bayesian phylogenetics, both for phylogenetic analyses and for development. Readily available for continuous…

Computer models, aiming at simulating a complex real system, are often calibrated in the light of data to improve performance. Standard calibration methods assume that the optimal values of calibration parameters are invariant to the model…

We tackle the problem of building explainable recommendation systems that are based on a per-user decision tree, with decision rules that are based on single attribute values. We build the trees by applying learned regression functions to…

Variable selection is an important statistical problem. This problem becomes more challenging when the candidate predictors are of mixed type (e.g. continuous and binary) and impact the response variable in nonlinear and/or non-additive…

Model selection consists in comparing several candidate models according to a metric to be optimized. The process often involves a grid search, or such, and cross-validation, which can be time consuming, as well as not providing much…

Contextual bandits are a core technology for personalized mobile health interventions, where decision-making requires adapting to complex, non-linear user behaviors. While Thompson Sampling (TS) is a preferred strategy for these problems,…

We present an algorithm for building probabilistic rule lists that is two orders of magnitude faster than previous work. Rule list algorithms are competitors for decision tree algorithms. They are associative classifiers, in that they are…

Bayesian Additive Regression Trees (BART) is a statistical sum of trees model. It can be considered a Bayesian version of machine learning tree ensemble methods where the individual trees are the base learners. However for data sets where…

Bayesian networks are popular probabilistic models that capture the conditional dependencies among a set of variables. Inference in Bayesian networks is a fundamental task for answering probabilistic queries over a subset of variables in…

We give methods for Bayesian inference of directed acyclic graphs, DAGs, and the induced causal effects from passively observed complete data. Our methods build on a recent Markov chain Monte Carlo scheme for learning Bayesian networks,…