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Exact approximations of Markov chain Monte Carlo (MCMC) algorithms are a general emerging class of sampling algorithms. One of the main ideas behind exact approximations consists of replacing intractable quantities required to run standard…
Causal discovery algorithms aim at untangling complex causal relationships from data. Here, we study causal discovery and inference methods based on staged tree models, which can represent complex and asymmetric causal relationships between…
Parametric Markov chains have been introduced as a model for families of stochastic systems that rely on the same graph structure, but differ in the concrete transition probabilities. The latter are specified by polynomial constraints for…
We study rooted planar random trees with a probability distribution which is proportional to a product of weight factors $w_n$ associated to the vertices of the tree and depending only on their individual degrees $n$. We focus on the case…
Penalized transformation models (PTMs) are a semiparametric location-scale regression family that estimate a response's conditional distribution directly from the data, and model the location and scale through structured additive…
A weighted recursive tree is an evolving tree in which vertices are assigned random vertex-weights and new vertices connect to a predecessor with a probability proportional to its weight. Here, we study the maximum degree and near-maximum…
Binary trait data record the presence or absence of distinguishing traits in individuals. We treat the problem of estimating ancestral trees with time depth from binary trait data. Simple analysis of such data is problematic. Each homology…
Bayesian Decision Trees are known for their probabilistic interpretability. However, their construction can sometimes be costly. In this article we present a general Bayesian Decision Tree algorithm applicable to both regression and…
Advances in neural variational inference have facilitated the learning of powerful directed graphical models with continuous latent variables, such as variational autoencoders. The hope is that such models will learn to represent rich,…
It is becoming increasingly important for machine learning methods to make predictions that are interpretable as well as accurate. In many practical applications, it is of interest which features and feature interactions are relevant to the…
We present a new method to propagate lower bounds on conditional probability distributions in conventional Bayesian networks. Our method guarantees to provide outer approximations of the exact lower bounds. A key advantage is that we can…
A new shrinkage-based construction is developed for a compressible vector $\boldsymbol{x}\in\mathbb{R}^n$, for cases in which the components of $\xv$ are naturally associated with a tree structure. Important examples are when $\xv$…
Word embeddings predict a word from its neighbours by learning small, dense embedding vectors. In practice, this prediction corresponds to a semantic score given to the predicted word (or term weight). We present a novel model that, given a…
Understanding the relative contributions of environmental, spatial, and temporal processes in shaping species distribution is a central objective in ecology. Bayesian species distribution models (SDMs) offer a flexible framework for this…
We investigate the use of normalizing flow (NF) models as flexible priors in Bayesian inference via Markov Chain Monte Carlo (MCMC) sampling for iterative Bayesian calibration. Trained on posteriors from previous analyses, these models can…
The Bayesian elastic net regression model is characterized by the regression coefficient prior distribution, the negative log density of which corresponds to the elastic net penalty function. While Markov chain Monte Carlo (MCMC) methods…
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…
The idea of "stratified medicine" is an important driver of methodological research on the identification of predictive biomarkers. Most methods proposed so far for this purpose have been developed for the use on randomized data only.…
We show that if a strictly positive joint probability distribution for a set of binary random variables factors according to a tree, then vertex separation represents all and only the independence relations enclosed in the distribution. The…
A symbolic-computational algorithm, fully implemented in Maple, is described, that computes explicit expressions for generating functions that enable the efficient computations of the expectation, variance, and higher moments, of the random…