Related papers: Enhancing Sufficient Dimension Reduction via Helli…
Unsupervised learning aims to capture the underlying structure of potentially large and high-dimensional datasets. Traditionally, this involves using dimensionality reduction (DR) methods to project data onto lower-dimensional spaces or…
Selecting the optimal resolution for discretizing high-dimensional data is a central problem in physics and data analysis, particularly in unsupervised settings where the underlying distribution is unknown. The Relevance-Resolution…
Data are not only ubiquitous in society, but are increasingly complex both in size and dimensionality. Dimension reduction offers researchers and scholars the ability to make such complex, high dimensional data spaces simpler and more…
We introduce a novel and scalable Bayesian framework for multivariate-density-density regression (DDR), designed to model relationships between multivariate distributions. Our approach addresses the critical issue of distributions residing…
We consider the problem of sufficient dimension reduction (SDR) for multi-index models. The estimators of the central mean subspace in prior works either have slow (non-parametric) convergence rates, or rely on stringent distributional…
We consider forecasting a single time series when there is a large number of predictors and a possible nonlinear effect. The dimensionality was first reduced via a high-dimensional (approximate) factor model implemented by the principal…
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,…
We provide here a framework to analyze the phase transition phenomenon of slice inverse regression (SIR), a supervised dimension reduction technique introduced by \cite{Li:1991}. Under mild conditions, the asymptotic ratio $\rho= \lim p/n$…
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…
The multiple-input multiple-output (MIMO) detection problem, a fundamental problem in modern digital communications, is to detect a vector of transmitted symbols from the noisy outputs of a fading MIMO channel. The maximum likelihood…
Dimension reduction is an important tool for analyzing high-dimensional data. The predictor envelope is a method of dimension reduction for regression that assumes certain linear combinations of the predictors are immaterial to the…
Weakly-supervised semantic segmentation (WSS) ensures high-quality segmentation with limited data and excels when employed as input seed masks for large-scale vision models such as Segment Anything. However, WSS faces challenges related to…
Data visualization and dimension reduction for regression between a general metric space-valued response and Euclidean predictors is proposed. Current Fr\'ech\'et dimension reduction methods require that the response metric space be…
The issue of data sparsity poses a significant challenge to recommender systems. In response to this, algorithms that leverage side information such as review texts have been proposed. Furthermore, Cross-Domain Recommendation (CDR), which…
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.…
The theoretical basis of the phenomenon of effective and exact dimensional reduction, or holographic correspondence, is investigated in a wide variety of physical systems. We first derive general inequalities linking quantum systems of…
Evaluating the accuracy of dimensionality reduction (DR) projections in preserving the structure of high-dimensional data is crucial for reliable visual analytics. Diverse evaluation metrics targeting different structural characteristics…
Representations learned via self-supervised learning (SSL) can be susceptible to dimensional collapse, where the learned representation subspace is of extremely low dimensionality and thus fails to represent the full data distribution and…
Spatial autocorrelation coefficients such as Moran's index proved to be an eigenvalue of the spatial correlation matrixes. An eigenvalue represents a kind of characteristic length for quantitative analysis. However, if a spatial correlation…
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…