Related papers: On dimension folding of matrix- or array-valued st…
High-dimensional compositional data, such as those from human microbiome studies, pose unique statistical challenges due to the simplex constraint and excess zeros. While dimension reduction is indispensable for analyzing such data,…
The real-life data have a complex and non-linear structure due to their nature. These non-linearities and the large number of features can usually cause problems such as the empty-space phenomenon and the well-known curse of dimensionality.…
A dimension reduction-based adaptive-to-model test is proposed for significance of a subset of covariates in the context of a nonparametric regression model. Unlike existing local smoothing significance tests, the new test behaves like a…
This paper models categorical data with two or multiple responses, focusing on the interactions between responses. We propose an efficient iterative procedure based on sufficient dimension reduction. We study the theoretical guarantees of…
Unsupervised machine learning lacks ground truth by definition. This poses a major difficulty when designing metrics to evaluate the performance of such algorithms. In sharp contrast with supervised learning, for which plenty of quality…
Data dimensionality reduction in radio interferometry can provide savings of computational resources for image reconstruction through reduced memory footprints and lighter computations per iteration, which is important for the scalability…
Matrix-covariate is now frequently encountered in many biomedical researches. It is common to fit conventional statistical models by vectorizing matrix-covariate. This strategy, however, results in a large number of parameters, while the…
In this paper, we propose a dimension reduction model for spatially dependent variables. Namely, we investigate an extension of the \emph{inverse regression} method under strong mixing condition. This method is based on estimation of the…
Over the years data has become increasingly higher dimensional, which has prompted an increased need for dimension reduction techniques. This is perhaps especially true for clustering (unsupervised classification) as well as semi-supervised…
Our research proposes a novel method for reducing the dimensionality of functional data, specifically for the case where the response is a scalar and the predictor is a random function. Our method utilizes distance covariance, and has…
Anomaly detection using dimensionality reduction has been an essential technique for monitoring multidimensional data. Although deep learning-based methods have been well studied for their remarkable detection performance, their…
Unsupervised dimension selection is an important problem that seeks to reduce dimensionality of data, while preserving the most useful characteristics. While dimensionality reduction is commonly utilized to construct low-dimensional…
Large-scale numerical simulations often produce high-dimensional gridded data that is challenging to process for downstream applications. A prime example is numerical weather prediction, where atmospheric processes are modeled using…
Low-dimensional embeddings are widely used as visual summaries of high-dimensional data and to enable downstream scientific discoveries. Yet, popular nonlinear dimension reduction methods, such as t-SNE and UMAP, are often selected based on…
Nonlinear dimensionality reduction methods are a popular tool for data scientists and researchers to visualize complex, high dimensional data. However, while these methods continue to improve and grow in number, it is often difficult to…
Sufficient dimension reduction [J. Amer. Statist. Assoc. 86 (1991) 316-342] has long been a prominent issue in multivariate nonparametric regression analysis. To uncover the central dimension reduction space, we propose in this paper an…
Dimension reduction (DR) is inherently non-unique: multiple embeddings can preserve the structure of high-dimensional data equally well while differing in layout or geometry. In this paper, we formally define the Rashomon set for DR -- the…
The global dimensionality of a neural representation manifold provides rich insight into the computational process underlying both artificial and biological neural networks. However, all existing measures of global dimensionality are…
Despite many applications, dimensionality reduction in the $\ell_1$-norm is much less understood than in the Euclidean norm. We give two new oblivious dimensionality reduction techniques for the $\ell_1$-norm which improve exponentially…
We propose a constrained maximum partial likelihood estimator for dimension reduction in integrative (e.g., pan-cancer) survival analysis with high-dimensional covariates. We assume that for each population in the study, the hazard function…