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Low-rank matrix estimation is a canonical problem that finds numerous applications in signal processing, machine learning and imaging science. A popular approach in practice is to factorize the matrix into two compact low-rank factors, and…

The accurate estimation of the noise covariance matrix (NCM) in a dynamic system is critical for state estimation and control, as it has a major influence in their optimality. Although a large number of NCM estimation methods have been…

Principal component analysis (PCA) is largely adopted for chemical process monitoring and numerous PCA-based systems have been developed to solve various fault detection and diagnosis problems. Since PCA-based methods assume that the…

Identifying key genes involved in a particular disease is a very important problem which is considered in biomedical research. GeneRank model is based on the PageRank algorithm that preserves many of its mathematical properties. The model…

The preconditioned conjugate gradient (PCG) algorithm is one of the most popular algorithms for solving large-scale linear systems Ax = b, where A is a symmetric positive definite matrix. Rather than computing residuals directly, it updates…

This research presents a machine-learning approach for tumor detection in medical images using convolutional neural networks (CNNs). The study focuses on preprocessing techniques to enhance image features relevant to tumor detection,…

In a recent paper (J. Chem. Theory. Comput., 2017, 13, 180-190) we proposed the Truncated Conjugate Gradient (TCG) approach to compute the polarization energy and forces in polarizable molecular simulations. The method consists in…

Modern scientific studies often collect data sets in the forms of tensors, which call for innovative statistical analysis methods. In particular, there is a pressing need for tensor clustering methods to understand the heterogeneity in the…

Lung cancer is a significant cause of mortality worldwide, emphasizing the importance of early detection for improved survival rates. In this study, we propose a machine learning (ML) tool trained on data from the PLCO Cancer Screening…

As computers reach exascale and beyond, the incidence of faults will increase. Solutions to this problem are an active research topic. We focus on strategies to make the preconditioned conjugate gradient (PCG) solver resilient against node…

Stochastic gradient descent algorithms for training linear and kernel predictors are gaining more and more importance, thanks to their scalability. While various methods have been proposed to speed up their convergence, the model selection…

We propose a novel linear discriminant analysis approach for the classification of high-dimensional matrix-valued data that commonly arises from imaging studies. Motivated by the equivalence of the conventional linear discriminant analysis…

In order to model risk aversion in reinforcement learning, an emerging line of research adapts familiar algorithms to optimize coherent risk functionals, a class that includes conditional value-at-risk (CVaR). Because optimizing the…

Nonlinear model predictive control (NMPC) is one of the few control methods that can handle multivariable nonlinear controlsystems with constraints. Gaussian processes (GPs) present a powerful tool to identify the required plant model and…

In this paper, we propose projected gradient descent (PGD) algorithms for signal estimation from noisy nonlinear measurements. We assume that the unknown $p$-dimensional signal lies near the range of an $L$-Lipschitz continuous generative…

The purpose of this paper is to construct confidence intervals for the regression coefficients in the Fine-Gray model for competing risks data with random censoring, where the number of covariates can be larger than the sample size. Despite…

In recent years, mixture cure models have gained increasing popularity in survival analysis as an alternative to the Cox proportional hazards model, particularly in settings where a subset of patients is considered cured. The proportional…

For Hermitian positive definite linear systems and eigenvalue problems, the eigCG algorithm is a memory efficient algorithm that solves the linear system and simultaneously computes some of its eigenvalues. The algorithm is based on the…

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…

This paper addresses patient heterogeneity associated with prediction problems in biomedical applications. We propose a systematic hypothesis testing approach to determine the existence of patient subgroup structure and the number of…