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Being cautious is crucial for enhancing the trustworthiness of machine learning systems integrated into decision-making pipelines. Although calibrated probabilities help in optimal decision-making, perfect calibration remains unattainable,…
A new tree model is introduced based on ordered trees, by distinguishing exactly one child of each node that \emph{has} children. The basic enumeration leads to a cubic equation of the generating function. The extraction of its coefficients…
We define a new balance index for rooted phylogenetic trees based on the symmetry of the evolutive history of every set of 4 leaves. This index makes sense for multifurcating trees and it can be computed in time linear in the number of…
Bayesian calibration of black-box computer models offers an established framework to obtain a posterior distribution over model parameters. Traditional Bayesian calibration involves the emulation of the computer model and an additive model…
A novel multiphysics-decision tree learning algorithm is presented for (1) estimating transport properties in the variably saturated subsurface governed by explicitly coupled equations for water, heat, and solute transport; and (2)…
In this paper we introduce and study three new measures for efficient discriminative comparison of phylogenetic trees. The NNI navigation dissimilarity $d_{nav}$ counts the steps along a "combing" of the Nearest Neighbor Interchange (NNI)…
Several classification methods assume that the underlying distributions follow tree-structured graphical models. Indeed, trees capture statistical dependencies between pairs of variables, which may be crucial to attain low classification…
Most supervised machine learning tasks are subject to irreducible prediction errors. Probabilistic predictive models address this limitation by providing probability distributions that represent a belief over plausible targets, rather than…
In the density estimation model, the question of adaptive inference using P\'olya tree-type prior distributions is considered. A class of prior densities having a tree structure, called spike-and-slab P\'olya trees, is introduced. For this…
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…
Classifier calibration does not always go hand in hand with the classifier's ability to separate the classes. There are applications where good classifier calibration, i.e. the ability to produce accurate probability estimates, is more…
Binary trees are fundamental objects in models of evolutionary biology and population genetics. Here, we discuss some of their combinatorial and structural properties as they depend on the tree class considered. Furthermore, the process by…
Tree shape statistics quantify some aspect of the shape of a phylogenetic tree. They are commonly used to compare reconstructed trees to evolutionary models and to find evidence of tree reconstruction bias. Historically, to find a useful…
Approximate Bayesian Computation (ABC) is a popular inference method when likelihoods are hard to come by. Practical bottlenecks of ABC applications include selecting statistics that summarize the data without losing too much information or…
Bayesian simulation-based inference (SBI) methods are used in statistical models where simulation is feasible but the likelihood is intractable. Standard SBI methods can perform poorly in cases of model misspecification, and there has been…
Many classification applications require accurate probability estimates in addition to good class separation but often classifiers are designed focusing only on the latter. Calibration is the process of improving probability estimates by…
Accurate identification of synergistic treatment combinations and their underlying biological mechanisms is critical across many disease domains, especially cancer. In translational oncology research, preclinical systems such as…
We study learning-augmented binary search trees (BSTs) via Treaps with carefully designed priorities. The result is a simple search tree in which the depth of each item $x$ is determined by its predicted weight $w_x$. Specifically, each…
Bayesian averaging over classification models allows the uncertainty of classification outcomes to be evaluated, which is of crucial importance for making reliable decisions in applications such as financial in which risks have to be…
Bayesian model selection is premised on the assumption that the data are generated from one of the postulated models. However, in many applications, all of these models are incorrect (that is, there is misspecification). When the models are…