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Due to their power and ease of use, tree-based machine learning models, such as random forests and gradient-boosted tree ensembles, have become very popular. To interpret them, local feature attributions based on marginal expectations, e.g.…
The problem of reconstructing evolutionary trees or phylogenies is of great interest in computational biology. A popular model for this problem assumes that we are given the set of leaves (current species) of an unknown binary tree and the…
How can one analyze detailed 3D biological objects, such as neurons and botanical trees, that exhibit complex geometrical and topological variation? In this paper, we develop a novel mathematical framework for representing, comparing, and…
Undirected graphical models are powerful tools for uncovering complex relationships among high-dimensional variables. This paper aims to fully recover the structure of an undirected graphical model when the data naturally take matrix form,…
Variational Bayes (VB) has become a widely-used tool for Bayesian inference in statistics and machine learning. Nonetheless, the development of the existing VB algorithms is so far generally restricted to the case where the variational…
In this paper, we study a newly developed shearlet system on bounded domains which yields frames for $H^s(\Omega)$ for some $s\in \mathbb{N}$, $\Omega \subset \mathbb{R}^2$. We will derive approximation rates with respect to $H^s(\Omega)$…
Many machine learning tools for regression are based on recursive partitioning of the covariate space into smaller regions, where the regression function can be estimated locally. Among these, regression trees and their ensembles have…
A framework for coherent pattern extraction and prediction of observables of measure-preserving, ergodic dynamical systems with both atomic and continuous spectral components is developed. It is based on an approximation of the generator of…
Learning high-quality oblique decision trees remains a significant challenge due to the discrete and non-convex nature of split optimization. We present the Hinge Regression Tree (HRT) framework, which reframes each oblique split as a…
Advancements in modern science have led to the increasing availability of non-Euclidean data in metric spaces. This paper addresses the challenge of modeling relationships between non-Euclidean responses and multivariate Euclidean…
In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an…
Survival random forest is a popular machine learning tool for modeling censored survival data. However, there is currently no statistically valid and computationally feasible approach for estimating its confidence band. This paper proposes…
Ensembles are popular methods for solving practical supervised learning problems. They reduce the risk of having underperforming models in production-grade software. Although critical, methods for learning heterogeneous regression ensembles…
The real-world data of power networks is often inaccessible due to privacy and security concerns, highlighting the need for tools to generate realistic synthetic network data. Existing methods leverage geographic tools like OpenStreetMap…
Tree ensembles are flexible predictive models that can capture relevant variables and to some extent their interactions in a compact and interpretable manner. Most algorithms for obtaining tree ensembles are based on versions of boosting or…
Previous algorithms for constructing regression tree models for longitudinal and multiresponse data have mostly followed the CART approach. Consequently, they inherit the same selection biases and computational difficulties as CART. We…
Clustered data, which arise when observations are nested within groups, are incredibly common in clinical, education, and social science research. Traditionally, a linear mixed model, which includes random effects to account for…
Robust machine learning models with accurately calibrated uncertainties are crucial for safety-critical applications. Probabilistic machine learning and especially the Bayesian formalism provide a systematic framework to incorporate…
In the setting of clinical imaging, differences in between vendors, hospitals and sequences can yield highly inhomogeneous imaging data. In MRI in particular, voxel dimension, slice spacing and acquisition plane can vary substantially. For…
The recently developed variational autoencoders (VAEs) have proved to be an effective confluence of the rich representational power of neural networks with Bayesian methods. However, most work on VAEs use a rather simple prior over the…