Related papers: Calibrated Principal Component Regression
In recent years, Artificial Intelligence techniques have proved to be very successful when applied to problems in physical sciences. Here we apply an unsupervised Machine Learning (ML) algorithm called Principal Component Analysis (PCA) as…
This paper carries out a large dimensional analysis of a variation of kernel ridge regression that we call \emph{centered kernel ridge regression} (CKRR), also known in the literature as kernel ridge regression with offset. This modified…
Distributed algorithms and theories are called for in this era of big data. Under weaker local signal-to-noise ratios, we improve upon the celebrated one-round distributed principal component analysis (PCA) algorithm designed in the spirit…
Principal component analysis (PCA) is a widely used dimension reduction tool in the analysis of many kind of high-dimensional data. It is used in signal processing, mechanical engineering, psychometrics, and other fields under different…
This paper establishes bounds on the predictive performance of empirical risk minimization for principal component regression. Our analysis is nonparametric, in the sense that the relation between the prediction target and the predictors is…
This paper introduces a Projected Principal Component Analysis (Projected-PCA), which employs principal component analysis to the projected (smoothed) data matrix onto a given linear space spanned by covariates. When it applies to…
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…
When modeling multivariate data, one might have an extra parameter of contextual information that could be used to treat some observations as more similar to others. For example, images of faces can vary by age, and one would expect the…
Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a…
Principal component analysis (PCA) is widely used for dimensionality reduction, with well-documented merits in various applications involving high-dimensional data, including computer vision, preference measurement, and bioinformatics. In…
Classical methods such as Principal Component Analysis (PCA) and Canonical Correlation Analysis (CCA) are ubiquitous in statistics. However, these techniques are only able to reveal linear relationships in data. Although nonlinear variants…
Principal Component Analysis (PCA) is one of the most important methods to handle high dimensional data. However, most of the studies on PCA aim to minimize the loss after projection, which usually measures the Euclidean distance, though in…
In text classification tasks, models often rely on spurious correlations for predictions, incorrectly associating irrelevant features with the target labels. This issue limits the robustness and generalization of models, especially when…
In scientific applications, multivariate observations often come in tandem with temporal or spatial covariates, with which the underlying signals vary smoothly. The standard approaches such as principal component analysis and factor…
Accurate quantification of uncertainty is crucial for real-world applications of machine learning. However, modern deep neural networks still produce unreliable predictive uncertainty, often yielding over-confident predictions. In this…
Principal Component Analysis (PCA) has been widely used for dimensionality reduction and feature extraction. Robust PCA (RPCA), under different robust distance metrics, such as l1-norm and l2, p-norm, can deal with noise or outliers to some…
We propose a modification of linear discriminant analysis, referred to as compressive regularized discriminant analysis (CRDA), for analysis of high-dimensional datasets. CRDA is specially designed for feature elimination purpose and can be…
A first proposal of a sparse and cellwise robust PCA method is presented. Robustness to single outlying cells in the data matrix is achieved by substituting the squared loss function for the approximation error by a robust version. The…
Big data is transforming our world, revolutionizing operations and analytics everywhere, from financial engineering to biomedical sciences. The complexity of big data often makes dimension reduction techniques necessary before conducting…
Principal component analysis (PCA) frequently suffers from the disturbance of outliers and thus a spectrum of robust extensions and variations of PCA have been developed. However, existing extensions of PCA treat all samples equally even…