Related papers: Adaptive Reference-Guided Estimation of Principal …
This paper addresses the challenge of efficient principal component analysis (PCA) in high-dimensional spaces by analyzing a compressively sampled variant of Oja's algorithm with adaptive sensing. Traditional PCA methods incur substantial…
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…
In this paper, we investigate the impact of high-dimensional Principal Component (PC) adjustments on inferring the effects of variables on outcomes, with a focus on applications in genetic association studies where PC adjustment is commonly…
A number of settings arise in which it is of interest to predict Principal Component (PC) scores for new observations using data from an initial sample. In this paper, we demonstrate that naive approaches to PC score prediction can be…
Principal component analysis is an important pattern recognition and dimensionality reduction tool in many applications. Principal components are computed as eigenvectors of a maximum likelihood covariance $\widehat{\Sigma}$ that…
In modern statistics, interests shift from pursuing the uniformly minimum variance unbiased estimator to reducing mean squared error (MSE) or residual squared error. Shrinkage based estimation and regression methods offer better prediction…
In this paper, we present a sharp analysis for a class of alternating projected gradient descent algorithms which are used to solve the covariate adjusted precision matrix estimation problem in the high-dimensional setting. We demonstrate…
Retrieval-Augmented Generation (RAG) helps LLMs stay accurate, but feeding long documents into a prompt makes the model slow and expensive. This has motivated context compression, ranging from token pruning and summarization to…
A high-dimensional $r$-factor model for an $n$-dimensional vector time series is characterised by the presence of a large eigengap (increasing with $n$) between the $r$-th and the $(r+1)$-th largest eigenvalues of the covariance matrix.…
Dimensionality reduction is a fundamental task in modern data science. Several projection methods specifically tailored to take into account the non-linearity of the data via local embeddings have been proposed. Such methods are often based…
Stacking regressions is an ensemble technique that forms linear combinations of different regression estimators to enhance predictive accuracy. The conventional approach uses cross-validation data to generate predictions from the…
Principal component regression (PCR) is a two-stage procedure that selects some principal components and then constructs a regression model regarding them as new explanatory variables. Note that the principal components are obtained from…
The high-dimensional feature space of the hyperspectral imagery poses major challenges to the processing and analysis of the hyperspectral data sets. In such a case, dimensionality reduction is necessary to decrease the computational…
Retrieval-Augmented Generation (RAG), by integrating non-parametric knowledge from external knowledge bases into models, has emerged as a promising approach to enhancing response accuracy while mitigating factual errors and hallucinations.…
This paper explores and analyzes two randomized designs for robust Principal Component Analysis (PCA) employing low-dimensional data sketching. In one design, a data sketch is constructed using random column sampling followed by low…
The first order behavior of multivariate heavy-tailed random vectors above large radial thresholds is ruled by a limit measure in a regular variation framework. For a high dimensional vector, a reasonable assumption is that the support of…
The effectiveness of Retrieval-Augmented Generation (RAG) is highly dependent on how documents are chunked, that is, segmented into smaller units for indexing and retrieval. Yet, commonly used "one-size-fits-all" approaches often fail to…
Computer experiments with quantitative and qualitative inputs are widely used to study many scientific and engineering processes. Much of the existing work has focused on design and modeling or process optimization for such experiments.…
Vector autoregression (VAR) is a fundamental tool for modeling multivariate time series. However, as the number of component series is increased, the VAR model becomes overparameterized. Several authors have addressed this issue by…
Many applications involve estimation of a signal matrix from a noisy data matrix. In such cases, it has been observed that estimators that shrink or truncate the singular values of the data matrix perform well when the signal matrix has…