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We study various types of consistency of honest decision trees and random forests in the regression setting. In contrast to related literature, our proofs are elementary and follow the classical arguments used for smoothing methods. Under…
This paper studies the decentralized learning of tree-structured Gaussian graphical models (GGMs) from noisy data. In decentralized learning, data set is distributed across different machines (sensors), and GGMs are widely used to model…
Incomplete lineage sorting (ILS) is a common source of gene tree incongruence in multilocus analyses. A large number of methods have been developed to infer species trees in the presence of ILS. Here we provide a mathematical analysis of…
A new synthesis scheme is proposed to effectively generate a random vector with prescribed joint density that induces a (latent) Gaussian tree structure. The quality of synthesis is measured by total variation distance between the…
The objective function of a matrix factorization model usually aims to minimize the average of a regression error contributed by each element. However, given the existence of stochastic noises, the implicit deviations of sample data from…
When hybridization or other forms of lateral gene transfer have occurred, evolutionary relationships of species are better represented by phylogenetic networks than by trees. While inference of such networks remains challenging, several…
Most biological systems are formed by component parts that to some degree are inter-related. Groups of parts that are more associated among themselves and are relatively autonomous from others are called modules. One of the consequences of…
In this paper we present a new way to understand the timing of branching events in phylogenetic trees. Our method explicitly considers the relative timing of diversification events between sister clades; as such it is complimentary to…
The iterative and stochastic nature of diffusion models enables test-time scaling, whereby spending additional compute during denoising generates higher-fidelity samples. Increasing the number of denoising steps is the primary scaling axis,…
There have been many studies to examine whether one trait is correlated with another trait across a group of present-day species (for example, do species with larger brains tend to have longer gestation times. Since the introduction of the…
Continued demand for accurate and computationally efficient transport methods to solve optically thick, fixed-source transport problems has inspired research on variance-reduction (VR) techniques for Monte Carlo (MC). Methods that use…
How do phylogenetic reconstruction algorithms go astray when they return incorrect trees? This simple question has not been answered in detail, even for maximum parsimony (MP), the simplest phylogenetic criterion. Understanding MP has…
Stochastic evolution equations with compensated Poisson noise are considered in the variational approach with monotone and coercive coefficients. Here the Poisson noise is assumed to be time-homogeneous with $\sigma$-finite intensity…
Motivation: The abundance of gene flow in the Tree of Life challenges the notion that evolution can be represented with a fully bifurcating process, as this process cannot capture important biological realities like hybridization,…
Clustering analysis is one of the most widely used statistical tools in many emerging areas such as microarray data analysis. For microarray and other high-dimensional data, the presence of many noise variables may mask underlying…
Background: In clinical research, the Bland-Altman analysis is commonly used to assess agreement of metric measurements made by two or more techniques, devices or methods. The approach can also deal with repeated measurements per subject or…
Machine learning methods for estimating treatment effect heterogeneity promise greater flexibility than existing methods that test a few pre-specified hypotheses. However, one problem these methods can have is that it can be challenging to…
Self-consistency boosts inference-time performance by sampling multiple reasoning traces in parallel and voting. However, in constrained domains like math and code, this strategy is compute-inefficient because it samples with replacement,…
Uncertainty estimation in large deep-learning models is a computationally challenging task, where it is difficult to form even a Gaussian approximation to the posterior distribution. In such situations, existing methods usually resort to a…
Recent years have witnessed significant progress in developing effective training and fast sampling techniques for diffusion models. A remarkable advancement is the use of stochastic differential equations (SDEs) and their…