Related papers: Sufficient principal component regression for patt…

Unsupervised feature selection is an important method to reduce dimensions of high dimensional data without labels, which is benefit to avoid ``curse of dimensionality'' and improve the performance of subsequent machine learning tasks, like…

Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…

Compressed sensing provided a data-acquisition paradigm for sparse signals. Remarkably, it has been shown that practical algorithms provide robust recovery from noisy linear measurements acquired at a near optimal sampling rate. In many…

Compressed sensing of simultaneously sparse and low-rank matrices enables recovery of sparse signals from a few linear measurements of their bilinear form. One important question is how many measurements are needed for a stable…

Among semiparametric regression models, partially linear additive models provide a useful tool to include additive nonparametric components as well as a parametric component, when explaining the relationship between the response and a set…

Transformer-based large language models (LLMs) are comprised of billions of parameters arranged in deep and wide computational graphs, but it is not clear that they exploit their full capacity for all inputs. We introduce the s-Trace method…

Sparse PCA provides a linear combination of small number of features that maximizes variance across data. Although Sparse PCA has apparent advantages compared to PCA, such as better interpretability, it is generally thought to be…

Feature selection with specific multivariate performance measures is the key to the success of many applications, such as image retrieval and text classification. The existing feature selection methods are usually designed for…

Subsampling is a computationally efficient and scalable method to draw inference in large data settings based on a subset of the data rather than needing to consider the whole dataset. When employing subsampling techniques, a crucial…

Background: Understanding the relationship between the Omics and the phenotype is a central problem in precision medicine. The high dimensionality of metabolomics data challenges learning algorithms in terms of scalability and…

High-dimensional learning problems, where the number of features exceeds the sample size, often require sparse regularization for effective prediction and variable selection. While established for fully supervised data, these techniques…

While deep learning offers powerful capabilities for scientific research, its application is often hindered by a lack of quantitative reliability. To address this, we introduce a probabilistic denoising framework that simultaneously…

The problem of best subset selection in linear regression is considered with the aim to find a fixed size subset of features that best fits the response. This is particularly challenging when the total available number of features is very…

Principal component analysis (PCA) is possibly one of the most widely used statistical tools to recover a low-rank structure of the data. In the high-dimensional settings, the leading eigenvector of the sample covariance can be nearly…

Recently, introducing Tensor Decomposition (TD) techniques into unsupervised feature selection (UFS) has been an emerging research topic. A tensor structure is beneficial for mining the relations between different modes and helps relieve…

Principal Component Analysis (PCA) has been widely used for dimensionality reduction and feature extraction. Robust PCA (RPCA), under different robust distance metrics, such as l1-norm and l2, p-norm, can deal with noise or outliers to some…

To successfully work on variable selection, sparse model structure has become a basic assumption for all existing methods. However, this assumption is questionable as it is hard to hold in most of cases and none of existing methods may…

The development of single-cell and spatial transcriptomics has revolutionized our capacity to investigate cellular properties, functions, and interactions in both cellular and spatial contexts. However, the analysis of single-cell and…

We introduce a new methodology 'charcoal' for estimating the location of sparse changes in high-dimensional linear regression coefficients, without assuming that those coefficients are individually sparse. The procedure works by…

Dimension reduction for high-dimensional compositional data plays an important role in many fields, where the principal component analysis of the basis covariance matrix is of scientific interest. In practice, however, the basis variables…