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Principal component analysis (PCA) is a widespread technique for data analysis that relies on the covariance-correlation matrix of the analyzed data. However to properly work with high-dimensional data, PCA poses severe mathematical…
This paper considers identifying and estimating causal effect parameters in a staggered treatment adoption setting -- that is, where a researcher has access to panel data and treatment timing varies across units. We consider the case where…
Principal Component Analysis (PCA) is a widely used technique in exploratory data analysis, visualization, and data preprocessing, leveraging the concept of variance to identify key dimensions in datasets. In this study, we focus on the…
Turing patterns play a fundamental role in morphogenesis and population dynamics, encoding key information about the underlying biological mechanisms. Yet, traditional inverse problems have largely relied on non-biological data such as…
In biophysics, the search for analytical solutions of stochastic models of cellular processes is often a challenging task. In recent work on models of gene expression, it was shown that a mapping based on partitioning of Poisson arrivals…
A core component of precision medicine research involves optimizing individualized treatment rules (ITRs) based on patient characteristics. Many studies used to estimate ITRs are longitudinal in nature, collecting outcomes over time. Yet,…
Piecewise Aggregate Approximation (PAA) is a competitive basic dimension reduction method for high-dimensional time series mining. When deployed, however, the limitations are obvious that some important information will be missed,…
Test-time adaptation (TTA) has emerged as a promising paradigm to handle the domain shifts at test time for medical images from different institutions without using extra training data. However, existing TTA solutions for segmentation tasks…
This paper develops a nonparametric model that represents how sequences of outcomes and treatment choices influence one another in a dynamic manner. In this setting, we are interested in identifying the average outcome for individuals in…
In comparative studies of progressive diseases, such as randomized controlled trials (RCTs), the mean Change From Baseline (CFB) of a continuous outcome at a pre-specified follow-up time across subjects in the target population is a…
Parkinson's disease (PD) is a common neurodegenerative disease with a high degree of heterogeneity in its clinical features, rate of progression, and change of variables over time. In this work, we present a novel data-driven, network-based…
Over the years, Principal Component Analysis (PCA) has served as the baseline approach for dimensionality reduction in gene expression data analysis. It primary objective is to identify a subset of disease-causing genes from a vast pool of…
Advancements in cytometry technologies have led to a remarkable increase in the number of markers that can be analyzed simultaneously, presenting significant challenges in data analysis. Traditional approaches, such as dimensional reduction…
Joint models for longitudinal and time-to-event data are commonly used in longitudinal studies to forecast disease trajectories over time. While there are many advantages to joint modeling, the standard forms suffer from limitations that…
Time series data is one of the most popular data modalities in critical domains such as industry and medicine. The demand for algorithms that not only exhibit high accuracy but also offer interpretability is crucial in such fields, as…
Test-time adaptation (TTA) is an emerging paradigm that addresses distributional shifts between training and testing phases without additional data acquisition or labeling cost; only unlabeled test data streams are used for continual model…
Principal component analysis (PCA) is recognised as a quintessential data analysis technique when it comes to describing linear relationships between the features of a dataset. However, the well-known sensitivity of PCA to non-Gaussian…
We propose a new data-driven method to select the optimal number of relevant components in Principal Component Analysis (PCA). This new method applies to correlation matrices whose time autocorrelation function decays more slowly than an…
An improved mixture of probabilistic principal component analysis (PPCA) has been introduced for nonlinear data-driven process monitoring in this paper. To realize this purpose, the technique of a mixture of probabilistic principal…
Analyzing data in non-Euclidean spaces, such as bioinformatics, biology, and geology, where variables represent directions or angles, poses unique challenges. This type of data is known as circular data in univariate cases and can be termed…