Related papers: Geometry-driven Bayesian Inference for Ultrametric…

We introduce a new method for learning Bayesian neural networks, treating them as a stack of multivariate Bayesian linear regression models. The main idea is to infer the layerwise posterior exactly if we know the target outputs of each…

Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…

This paper investigates the integration of gradient boosted decision trees and varying coefficient models. We introduce the tree boosted varying coefficient framework which justifies the implementation of decision tree boosting as the…

Gene and protein networks are very important to model complex large-scale systems in molecular biology. Inferring or reverseengineering such networks can be defined as the process of identifying gene/protein interactions from experimental…

Bayesian latent space models offer a principled approach to network representation, but rely on correct specification of both geometry and link function. Real-world networks often violate these assumptions, exhibiting geometric mismatch and…

Decision trees are commonly used predictive models due to their flexibility and interpretability. This paper is directed at quantifying the uncertainty of decision tree predictions by employing a Bayesian inference approach. This is…

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 develop a new Bayesian modelling framework for the class of higher-order, variable-memory Markov chains, and introduce an associated collection of methodological tools for exact inference with discrete time series. We show that a version…

Evolutionary relationships between species are represented by phylogenetic trees, but these relationships are subject to uncertainty due to the random nature of evolution. A geometry for the space of phylogenetic trees is necessary in order…

In Bayesian learning of Gaussian graphical model structure, it is common to restrict attention to certain classes of graphs and approximate the posterior distribution by repeatedly moving from one graph to another, using MCMC or methods…

Undirected graphical models are applied in genomics, protein structure prediction, and neuroscience to identify sparse interactions that underlie discrete data. Although Bayesian methods for inference would be favorable in these contexts,…

The ongoing explosion of genome sequence data is transforming how we reconstruct and understand the histories of biological systems. Across biological scales, from individual cells to populations and species, trees-based models provide a…

We study infinite tree and ultrametric matrices, and their action on the boundary of the tree. For each tree matrix we show the existence of a symmetric random walk associated to it and we study its Green potential. We provide a…

Learning informative representations of phylogenetic tree structures is essential for analyzing evolutionary relationships. Classical distance-based methods have been widely used to project phylogenetic trees into Euclidean space, but they…

We propose to use a simulation driven inverse inference approach to model the dynamics of tree branches under manipulation. Learning branch dynamics and gaining the ability to manipulate deformable vegetation can help with occlusion-prone…

Felsenstein's classical model for Gaussian distributions on a phylogenetic tree is shown to be a toric variety in the space of concentration matrices. We present an exact semialgebraic characterization of this model, and we demonstrate how…

Phylogenetic comparative methods correct for shared evolutionary history among a set of non-independent organisms by modeling sample traits as arising from a diffusion process along on the branches of a possibly unknown history. To…

Conditional independence models in the Gaussian case are algebraic varieties in the cone of positive definite covariance matrices. We study these varieties in the case of Bayesian networks, with a view towards generalizing the recursive…

We develop Bayesian predictive stacking for geostatistical models, where the primary inferential objective is to provide inference on the latent spatial random field and conduct spatial predictions at arbitrary locations. We exploit…

Accurate image registration is essential in many medical imaging applications, yet most deep registration networks provide little indication of when or where their predictions are unreliable. Existing uncertainty estimation approaches, such…