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Motivation: Although principal component analysis (PCA) is widely used for the dimensional reduction of biomedical data, interpretation of PCA results remains daunting. Most existing methods attempt to explain each principal component (PC)…
Sparse principal component analysis (SPCA) is a popular tool for dimensionality reduction in high-dimensional data. However, there is still a lack of theoretically justified Bayesian SPCA methods that can scale well computationally. One of…
Sparse principal component analysis (sPCA) has become one of the most widely used techniques for dimensionality reduction in high-dimensional datasets. The main challenge underlying sPCA is to estimate the first vector of loadings of the…
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…
Tensor Robust Principal Component Analysis (TRPCA) holds a crucial position in machine learning and computer vision. It aims to recover underlying low-rank structures and to characterize the sparse structures of noise. Current approaches…
Sparse and outlier-robust Principal Component Analysis (PCA) has been a very active field of research recently. Yet, most existing methods apply PCA to a single dataset whereas multi-source data-i.e. multiple related datasets requiring…
The ability to manipulate complex systems, such as the brain, to modify specific outcomes has far-reaching implications, particularly in the treatment of psychiatric disorders. One approach to designing appropriate manipulations is to…
Principal component analysis (PCA) is a tool to capture factors that explain variation in data. Across domains, data are now collected across multiple contexts (for example, individuals with different diseases, cells of different types, or…
Standard Gaussian Process (GP) regression, a powerful machine learning tool, is computationally expensive when it is applied to large datasets, and potentially inaccurate when data points are sparsely distributed in a high-dimensional…
In clinical and biomedical research, multiple high-dimensional datasets are nowadays routinely collected from omics and imaging devices. Multivariate methods, such as Canonical Correlation Analysis (CCA), integrate two (or more) datasets to…
Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…
Sparse compiler is a promising solution for sparse tensor algebra optimization. In compiler implementation, reduction in sparse-dense hybrid algebra plays a key role in performance. Though GPU provides various reduction semantics that can…
We consider a method to jointly estimate sparse precision matrices and their underlying graph structures using dependent high-dimensional datasets. We present a penalized maximum likelihood estimator which encourages both sparsity and…
In this paper, we propose a new method to perform Sparse Kernel Principal Component Analysis (SKPCA) and also mathematically analyze the validity of SKPCA. We formulate SKPCA as a constrained optimization problem with elastic net…
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…
Sparse Canonical Correlation Analysis (SCCA) is a fundamental statistical tool for identifying linear relationships in high-dimensional, multi-view data. While minimax theory establishes an optimal sample complexity scaling additively with…
The robust principal component analysis (RPCA) decomposes a data matrix into a low-rank part and a sparse part. There are mainly two types of algorithms for RPCA. The first type of algorithm applies regularization terms on the singular…
Principal component analysis (PCA) is a widely employed statistical tool used primarily for dimensionality reduction. However, it is known to be adversely affected by the presence of outlying observations in the sample, which is quite…
Sparse Principal Component Analysis (PCA) is a dimensionality reduction technique wherein one seeks a low-rank representation of a data matrix with additional sparsity constraints on the obtained representation. We consider two…
We propose an algorithmic framework for computing sparse components from rotated principal components. This methodology, called SIMPCA, is useful to replace the unreliable practice of ignoring small coefficients of rotated components when…