Related papers: Principal Balances of Compositional Data for Regre…

This paper proposes a new method and algorithm for predicting multivariate responses in a regression setting. Research into classification of High Dimension Low Sample Size (HDLSS) data, in particular microarray data, has made considerable…

Sparse Partial Least Squares (sPLS) is a common dimensionality reduction technique for data fusion, which projects data samples from two views by seeking linear combinations with a small number of variables with the maximum variance.…

Sparse linear regression, which entails finding a sparse solution to an underdetermined system of linear equations, can formally be expressed as an $l_0$-constrained least-squares problem. The Orthogonal Least-Squares (OLS) algorithm…

In many applications, particularly in the natural sciences, the available high-dimensional set of features may contain variables that are not correlated with the response under consideration. Such irrelevant features can, in certain cases,…

The dramatic growth of big datasets presents a new challenge to data storage and analysis. Data reduction, or subsampling, that extracts useful information from datasets is a crucial step in big data analysis. We propose an orthogonal…

The identification of different homogeneous groups of observations and their appropriate analysis in PLS-SEM has become a critical issue in many appli- cation fields. Usually, both SEM and PLS-SEM assume the homogeneity of all units on…

We provide a rigorous random matrix theory analysis of spiked cross-covariance models where the signals across two high-dimensional data channels are partially aligned. These models are motivated by multi-modal learning and form the…

High dimensional data reduction techniques are provided by using partial least squares within deep learning. Our framework provides a nonlinear extension of PLS together with a disciplined approach to feature selection and architecture…

In the course of the last century, Principal Component Analysis (PCA) have become one of the pillars of modern scientific methods. Although PCA is normally addressed as a statistical tool aiming at finding orthogonal directions on which the…

Despite the rising prevalence of neural language models, recent empirical evidence suggests their deficiency in compositional generalization. One of the current de-facto solutions to this problem is compositional data augmentation, which…

High-dimensional spectral data -- routinely generated in dairy production -- are used to predict a range of traits in milk products. Partial least squares (PLS) regression is ubiquitously used for these prediction tasks. However, PLS…

Least squares (LS)-based subset selection methods are popular in linear regression modeling. Best subset selection (BS) is known to be NP-hard and has a computational cost that grows exponentially with the number of predictors. Recently,…

In current applied research the most-used route to an analysis of composition is through log-ratios -- that is, contrasts among log-transformed measurements. Here we argue instead for a more direct approach, using a statistical model for…

Many studies collect data that can be considered as a realization of a point process. Included are medical imaging data where photon counts are recorded by a gamma camera from patients being injected with a gamma emitting tracer. It is of…

In statistics, series of ordinary least squares problems (OLS) are used to study the linear correlation among sets of variables of interest; in many studies, the number of such variables is at least in the millions, and the corresponding…

The Classification on high-dimension low-sample-size data (HDLSS) is a challenging problem and it is common to have class-imbalanced data in most application fields. We term this as Imbalanced HDLSS (IHDLSS). Recent theoretical results…

In this paper, we propose deep partial least squares for the estimation of high-dimensional nonlinear instrumental variable regression. As a precursor to a flexible deep neural network architecture, our methodology uses partial least…

Principal Component Analysis (PCA) is a very successful dimensionality reduction technique, widely used in predictive modeling. A key factor in its widespread use in this domain is the fact that the projection of a dataset onto its first…

Uncertainty in estimating the log-law parameters is arguably the greatest obstacle to establishing definitive conclusions regarding their numerical values and universality. This challenge is exacerbated by the limited number of studies that…

Reduced-rank regression estimates regression coefficients by imposing a low-rank constraint on the matrix of regression coefficients, thereby accounting for correlations among response variables. To further improve predictive accuracy and…