Related papers: A Two-Stage Dimension Reduction Method for Induced…
Gradient-based dimension reduction decreases the cost of Bayesian inference and probabilistic modeling by identifying maximally informative (and informed) low-dimensional projections of the data and parameters, allowing high-dimensional…
Improvements in computational and experimental capabilities are rapidly increasing the amount of scientific data that is routinely generated. In applications that are constrained by memory and computational intensity, excessively large…
The mathematical theory of compressed sensing (CS) asserts that one can acquire signals from measurements whose rate is much lower than the total bandwidth. Whereas the CS theory is now well developed, challenges concerning hardware…
Predictive estimation, which comprises model calibration, model prediction, and validation, is a common objective when performing inverse uncertainty quantification (UQ) in diverse scientific applications. These techniques typically require…
In an era where big and high-dimensional data is readily available, data scientists are inevitably faced with the challenge of reducing this data for expensive downstream computation or analysis. To this end, we present here a new method…
Compressive sensing (CS) exploits sparsity to recover sparse or compressible signals from dimensionality reducing, non-adaptive sensing mechanisms. Sparsity is also used to enhance interpretability in machine learning and statistics…
Subspace clustering methods have been widely studied recently. When the inputs are 2-dimensional (2D) data, existing subspace clustering methods usually convert them into vectors, which severely damages inherent structures and relationships…
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…
A key limitation in using various modern methods of machine learning in developing feedback control policies is the lack of appropriate methodologies to analyze their long-term dynamics, in terms of making any sort of guarantees (even…
In a frequency division duplex (FDD) massive multiple input multiple output (MIMO) system, the channel state information (CSI) feedback causes a significant bandwidth resource occupation. In order to save the uplink bandwidth resources, a…
Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled numerical models is…
Randomized dimensionality reduction is a widely-used algorithmic technique for speeding up large-scale Euclidean optimization problems. In this paper, we study dimension reduction for a variety of maximization problems, including…
We consider the problem of sufficient dimensionality reduction (SDR), where the high-dimensional observation is transformed to a low-dimensional sub-space in which the information of the observations regarding the label variable is…
Compressed sensing (CS) is a signal processing framework for efficiently reconstructing a signal from a small number of measurements, obtained by linear projections of the signal. Block-based CS is a lightweight CS approach that is mostly…
Multidimensional scaling (MDS) is a popular dimensionality reduction techniques that has been widely used for network visualization and cooperative localization. However, the traditional stress minimization formulation of MDS necessitates…
As a successful approach to self-supervised learning, contrastive learning aims to learn invariant information shared among distortions of the input sample. While contrastive learning has yielded continuous advancements in sampling strategy…
Boosting has garnered significant interest across both machine learning and statistical communities. Traditional boosting algorithms, designed for fully observed random samples, often struggle with real-world problems, particularly with…
In this paper, we study randomized reduction methods, which reduce high-dimensional features into low-dimensional space by randomized methods (e.g., random projection, random hashing), for large-scale high-dimensional classification.…
The present paper introduces a method for substantial reduction of the number of diffusion encoding gradients required for reliable reconstruction of HARDI signals. The method exploits the theory of compressed sensing (CS), which…
In this paper, we propose a feedback reduction scheme for full-duplex relay-aided multiuser networks. The proposed scheme permits the base station (BS) to obtain channel state information (CSI) from a subset of strong users under…