相关论文: Optimal Spectral Algorithms for Correlated Two-vie…
In this paper, we study high-dimensional sparse Quadratic Discriminant Analysis (QDA) and aim to establish the optimal convergence rates for the classification error. Minimax lower bounds are established to demonstrate the necessity of…
Sparse Canonical Correlation Analysis (CCA) has received considerable attention in high-dimensional data analysis to study the relationship between two sets of random variables. However, there has been remarkably little theoretical…
Differential network is an important tool to capture the changes of conditional correlations under two sample cases. In this paper, we introduce a fast iterative algorithm to recover the differential network for high-dimensional data. The…
Hyperspectral images provide abundant spatial and spectral information that is very valuable for material detection in diverse areas of practical science. The high-dimensions of data lead to many processing challenges that can be addressed…
Although there is an extensive literature on the eigenvalues of high-dimensional sample covariance matrices, much of it is specialized to independent components (IC) models -- in which observations are represented as linear transformations…
We consider the problem of computationally-efficient prediction from high dimensional and highly correlated predictors in challenging settings where accurate variable selection is effectively impossible. Direct application of penalization…
Optimal prediction methods compensate for a lack of resolution in the numerical solution of time-dependent differential equations through the use of prior statistical information. We present a new derivation of the basic methodology, show…
The classical Canonical Correlation Analysis (CCA) identifies the correlations between two sets of multivariate variables based on their covariance, which has been widely applied in diverse fields such as computer vision, natural language…
In this paper, we propose a novel approach to hyperspectral image super-resolution by modeling the global spatial-and-spectral correlation and local smoothness properties over hyperspectral images. Specifically, we utilize the tensor…
Owing to their more extensive sky coverage and tighter control on systematic errors, future deep weak lensing surveys should provide a better statistical picture of the dark matter clustering beyond the level of the power spectrum. In this…
Line spectral estimation theory aims to estimate the off-the-grid spectral components of a time signal with optimal precision. Recent results have shown that it is possible to recover signals having sparse line spectra from few temporal…
Visible images offer rich texture details, while infrared images emphasize salient targets. Fusing these complementary modalities enhances scene understanding, particularly for advanced vision tasks under challenging conditions. Recently,…
This article presents a new search algorithm for the NP-hard problem of optimizing functions of binary variables that decompose according to a graphical model. It can be applied to models of any order and structure. The main novelty is a…
A unified approach to derive optimal finite differences is presented which combines three critical elements for numerical performance especially for multi-scale physical problems, namely, order of accuracy, spectral resolution and…
Sensitivity analysis is an important tool used in many domains of computational science to either gain insight into the mathematical model and interaction of its parameters or study the uncertainty propagation through the input-output…
While calculations and measurements of single-particle spectral properties often offer the most direct route to study correlated electron systems, the underlying physics may remain quite elusive, if information at higher particle levels is…
We study a spectral generalization of classical combinatorial graph spanners to the spectral setting. Given a set of vectors $V\subseteq \Re^d$, we say a set $U\subseteq V$ is an $\alpha$-spectral spanner if for all $v\in V$ there is a…
In Optimal Recovery, the task of learning a function from observational data is tackled deterministically by adopting a worst-case perspective tied to an explicit model assumption made on the functions to be learned. Working in the…
Context: New spectroscopic surveys will increase the number of astronomical objects requiring characterization by over tenfold.. Machine learning tools are required to address this data deluge in a fast and accurate fashion. Most machine…
Despite the huge spread and economical importance of configurable software systems, there is unsatisfactory support in utilizing the full potential of these systems with respect to finding performance-optimal configurations. Prior work on…