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We introduce a novel statistical framework for the analysis of replicated point processes that allows for the study of point pattern variability at a population level. By treating point process realizations as random measures, we adopt a…
Principal Component Analysis (PCA) and its nonlinear extension Kernel PCA (KPCA) are widely used across science and industry for data analysis and dimensionality reduction. Modern deep learning tools have achieved great empirical success,…
A reduced-rank mixed effects model is developed for robust modeling of sparsely observed paired functional data. In this model, the curves for each functional variable are summarized using a few functional principal components, and the…
We consider Fair Principal Component Analysis (FPCA) and search for a low dimensional subspace that spans multiple target vectors in a fair manner. FPCA is defined as a non-concave maximization of the worst projected target norm within a…
Dimensionality reduction is critical across various domains of science including neuroscience. Probabilistic Principal Component Analysis (PPCA) is a prominent dimensionality reduction method that provides a probabilistic approach unlike…
In many longitudinal microarray studies, the gene expression levels in a random sample are observed repeatedly over time under two or more conditions. The resulting time courses are generally very short, high-dimensional, and may have…
Many studies of neural activity in behaving animals aim to discover interpretable low-dimensional structure in large-scale neural population recordings. One approach to this problem is demixed principal component analysis (dPCA), a…
In this paper we review existing methods for robust functional principal component analysis (FPCA) and propose a new method for FPCA that can be applied to longitudinal data where only a few observations per trajectory are available. This…
Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA…
Principal component analysis (PCA) is a well-known linear dimension-reduction method that has been widely used in data analysis and modeling. It is an unsupervised learning technique that identifies a suitable linear subspace for the input…
Principal component analysis (PCA) has well-documented merits for data extraction and dimensionality reduction. PCA deals with a single dataset at a time, and it is challenged when it comes to analyzing multiple datasets. Yet in certain…
Multivariate binary data is becoming abundant in current biological research. Logistic principal component analysis (PCA) is one of the commonly used tools to explore the relationships inside a multivariate binary data set by exploiting the…
Microbiome researchers often need to model the temporal dynamics of multiple complex, nonlinear outcome trajectories simultaneously. This motivates our development of multivariate Sparse Functional Principal Components Analysis (mSFPCA),…
Recovering intrinsic low dimensional subspaces from data distributed on them is a key preprocessing step to many applications. In recent years, there has been a lot of work that models subspace recovery as low rank minimization problems. We…
We generalize the low-rank decomposition problem, such as principal and independent component analysis (PCA, ICA) for continuous-time vector-valued signals and provide a model-agnostic implicit neural signal representation framework to…
Machine Learning models are prone to fail when test data are different from training data, a situation often encountered in real applications known as distribution shift. While still valid, the training-time knowledge becomes less…
Sequential or online dimensional reduction is of interests due to the explosion of streaming data based applications and the requirement of adaptive statistical modeling, in many emerging fields, such as the modeling of energy end-use…
Principal Component Analysis (PCA) is a workhorse of modern data science. While PCA assumes the data conforms to Euclidean geometry, for specific data types, such as hierarchical and cyclic data structures, other spaces are more…
Principal Component Analysis (PCA) is a popular tool for dimensionality reduction and feature extraction in data analysis. There is a probabilistic version of PCA, known as Probabilistic PCA (PPCA). However, standard PCA and PPCA are not…
In recent decades, the main focus of computer modeling has been on supporting the design and development of engineering prototyes, but it is now ubiquitous in non-traditional areas such as medical rehabilitation. Conventional modeling…