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This paper focuses on the uncertainty estimation for white matter lesions (WML) segmentation in magnetic resonance imaging (MRI). On one side, voxel-scale segmentation errors cause the erroneous delineation of the lesions; on the other…

In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…

Structural reliability methods aim at computing the probability of failure of systems with respect to some prescribed performance functions. In modern engineering such functions usually resort to running an expensive-to-evaluate…

Hybrid quantum/molecular mechanics (QM/MM) models play a pivotal role in molecular simulations. These models provide a balance between accuracy, surpassing pure MM models, and computational efficiency, offering advantages over pure QM…

Restricting randomization in the design of experiments (e.g., using blocking/stratification, pair-wise matching, or rerandomization) can improve the treatment-control balance on important covariates and therefore improve the estimation of…

Variance parameter estimation in linear mixed models is a challenge for many classical nonlinear optimization algorithms due to the positive-definiteness constraint of the random effects covariance matrix. We take a completely novel view on…

Variance components estimation and mixed model analysis are central themes in statistics with applications in numerous scientific disciplines. Despite the best efforts of generations of statisticians and numerical analysts, maximum…

Pulay's Residual Metric Minimization (RMM) method is one of the standard techniques for achieving self consistency in ab initio electronic structure calculations. We describe a reformulation of Pulay's RMM which guarantees reduction of the…

Large-scale finite element simulations of complex physical systems governed by partial differential equations (PDE) crucially depend on adaptive mesh refinement (AMR) to allocate computational budget to regions where higher resolution is…

One of the notorious issues for Reinforcement Learning (RL) is poor sample efficiency. Compared to single agent RL, the sample efficiency for Multi-Agent Reinforcement Learning (MARL) is more challenging because of its inherent partial…

Reed-Muller codes encode an $m$-variate polynomial of degree $r$ by evaluating it on all points in $\{0,1\}^m$. We denote this code by $RM(m,r)$. The minimal distance of $RM(m,r)$ is $2^{m-r}$ and so it cannot correct more than half that…

When performing supervised learning with the model selected using validation error from sample splitting and cross validation, the minimum value of the validation error can be biased downward. We propose two simple methods that use the…

We adopt and expand McDonald's (2011) regression framework for measurement precision, integrating two key perspectives: (a) reliability of observed scores and (b) optimal prediction of latent scores. Reliability arises from a measurement…

Latent variable (LV) models are widely used in psychological research to investigate relationships among unobservable constructs. When one-stage estimation of the overall LV model is challenging, two-stage factor score regression (FSR)…

Augmenting randomized controlled trials (RCTs) with external real-world data (RWD) has the potential to improve the finite sample efficiency of treatment effect estimators. We describe using adaptive targeted maximum likelihood estimation…

We study optimal variance reduction solutions for count and ratio metrics in online controlled experiments. Our methods leverage flexible machine learning tools to incorporate covariates that are independent from the treatment but have…

We propose a novel continual learning method called Residual Continual Learning (ResCL). Our method can prevent the catastrophic forgetting phenomenon in sequential learning of multiple tasks, without any source task information except the…

For many applications in signal processing and machine learning, we are tasked with minimizing a large sum of convex functions subject to a large number of convex constraints. In this paper, we devise a new random projection method (RPM) to…

Precision medicine is of considerable interest in clinical, academic and regulatory parties. The key to precision medicine is the optimal treatment regime. Recently, Zhou et al. (2017) developed residual weighted learning (RWL) to construct…

We develop a novel approach to tackle the common but challenging problem of conformal inference for missing data in machine learning, focusing on Missing at Random (MAR) data. We propose a new procedure Conformal prediction for Missing data…