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Penalized regression methods, such as lasso and elastic net, are used in many biomedical applications when simultaneous regression coefficient estimation and variable selection is desired. However, missing data complicates the…

Inverse problem for the identification of the parameters for large-scale systems of nonlinear ordinary differential equations (ODEs) arising in systems biology is analyzed. In a recent paper in \textit{Mathematical Biosciences, 305(2018),…

Probabilistic extensions of logic programming languages, such as ProbLog, integrate logical reasoning with probabilistic inference to evaluate probabilities of output relations; however, prior work does not account for potential statistical…

In machine learning, the process of feature selection involves finding a reduced subset of features that captures most of the information required to train an accurate and efficient model. This work presents FeatureCuts, a novel feature…

We revisit the problem of feature selection in linear discriminant analysis (LDA), that is, when features are correlated. First, we introduce a pooled centroids formulation of the multiclass LDA predictor function, in which the relative…

Displacement plays a crucial role in structural health monitoring (SHM) and damage detection of structural systems subjected to dynamic loads. However, due to the inconvenience associated with the direct measurement of displacement during…

We develop Structured-Knowledge-Informed Neural Networks (SKINNs), a unified estimation framework that embeds theoretical, simulated, previously learned, or cross-domain insights as differentiable constraints within flexible neural function…

In this paper, a novel learning paradigm is presented to automatically identify groups of informative and correlated features from very high dimensions. Specifically, we explicitly incorporate correlation measures as constraints and then…

In the current era of vast data and transparent machine learning, it is essential for techniques to operate at a large scale while providing a clear mathematical comprehension of the internal workings of the method. Although there already…

Cognitive workload is a topic of increasing interest across various fields such as health, psychology, and defense applications. In this research, we focus on classifying cognitive workload using the COLET dataset, employing a window-based…

In many data science applications, the objective is to extract appropriately-ordered smooth low-dimensional data patterns from high-dimensional data sets. This is challenging since common sorting algorithms are primarily aiming at finding…

In this work, we introduce MOLA: a Multi-block Orthogonal Long short-term memory Autoencoder paradigm, to conduct accurate, reliable fault detection of industrial processes. To achieve this, MOLA effectively extracts dynamic orthogonal…

Design patterns are elegant and well-tested solutions to recurrent software development problems. They are the result of software developers dealing with problems that frequently occur, solving them in the same or a slightly adapted way. A…

We used a collocation method in refinable spline space to solve a linear dynamical system having fractional derivative in time. The method takes advantage of an explicit derivation rule for the B-spline basis that allows us to efficiently…

Standard deep learning models that employ the categorical cross-entropy loss are known to perform well at image classification tasks. However, many standard models thus obtained often exhibit issues like feature redundancy, low…

Linear discriminant analysis (LDA) is an important classification tool in statistics and machine learning. This paper investigates the varying coefficient LDA model for dynamic data, with Bayes' discriminant direction being a function of…

While machine learning (ML) includes a valuable array of tools for analyzing biomedical data, significant time and expertise is required to assemble effective, rigorous, and unbiased pipelines. Automated ML (AutoML) tools seek to facilitate…

The analysis of complex nonlinear systems is often carried out using simpler piecewise linear representations of them. A principled and practical technique is proposed to linearize and evaluate arbitrary continuous nonlinear functions using…

We consider estimation and inference in a single index regression model with an unknown but smooth link function. In contrast to the standard approach of using kernels or regression splines, we use smoothing splines to estimate the smooth…

We consider the detection of multivariate spatial clusters in the Bernoulli model with $N$ locations, where the design distribution has weakly dependent marginals. The locations are scanned with a rectangular window with sides parallel to…