Related papers: High-Dimensional Partial Least Squares: Spectral A…
The method of ``Total Least Squares'' is proposed as a more natural way (than ordinary least squares) to approximate the data if both the matrix and and the right-hand side are contaminated by ``errors''. In this tutorial note, we give a…
This paper presents novel adaptive space-time reduced-rank interference suppression least squares algorithms based on joint iterative optimization of parameter vectors. The proposed space-time reduced-rank scheme consists of a joint…
Multidimensional Scaling (MDS) is one of the most popular methods for dimensionality reduction and visualization of high dimensional data. Apart from these tasks, it also found applications in the field of geometry processing for the…
Predictive modelling of multivariate data where both the covariates and responses are high-dimensional is becoming an increasingly popular task in many data mining applications. Partial Least Squares (PLS) regression often turns out to be a…
Principal component analysis (PCA) is a well-known linear dimension-reduction method that has been widely used in data analysis and modeling. It is an unsupervised learning technique that identifies a suitable linear subspace for the input…
Multivariate cortico-muscular analysis has recently emerged as a promising approach for evaluating the corticospinal neural pathway. However, current multivariate approaches encounter challenges such as high dimensionality and limited…
In this paper, we introduce principal asymmetric least squares (PALS) as a unified framework for linear and nonlinear sufficient dimension reduction. Classical methods such as sliced inverse regression (Li, 1991) and principal support…
Methods based on partial least squares (PLS) regression, which has recently gained much attention in the analysis of high-dimensional genomic datasets, have been developed since the early 2000s for performing variable selection. Most of…
As data-privacy requirements are becoming increasingly stringent and statistical models based on sensitive data are being deployed and used more routinely, protecting data-privacy becomes pivotal. Partial Least Squares (PLS) regression is…
We investigate the theoretical performances of the Partial Least Square (PLS) algorithm in a high dimensional context. We provide upper bounds on the risk in prediction for the statistical linear model when considering the PLS estimator.…
Detecting Earth twins remains challenging because their shallow, long-period transits are difficult to distinguish from background noise. Motivated by the challenge, we developed Segmented-Polynomial-fitting Least Squares (SPLS), a new…
A full parametric and linear specification may be insufficient to capture complicated patterns in studies exploring complex features, such as those investigating age-related changes in brain functional abilities. Alternatively, a partially…
Deep models have achieved impressive progress in solving partial differential equations (PDEs). A burgeoning paradigm is learning neural operators to approximate the input-output mappings of PDEs. While previous deep models have explored…
Partial least square regression (PLSR) is a widely-used statistical model to reveal the linear relationships of latent factors that comes from the independent variables and dependent variables. However, traditional methods to solve PLSR…
Shuffled linear regression (SLR) seeks to estimate latent features through a linear transformation, complicated by unknown permutations in the measurement dimensions. This problem extends traditional least-squares (LS) and Least Absolute…
Multi Task Learning (MTL) efficiently leverages useful information contained in multiple related tasks to help improve the generalization performance of all tasks. This article conducts a large dimensional analysis of a simple but, as we…
Principal component analysis (PCA) has well-documented merits for data extraction and dimensionality reduction. PCA deals with a single dataset at a time, and it is challenged when it comes to analyzing multiple datasets. Yet in certain…
A new statistical technique for constructing linear latent structure (LLS) models from available data, supported by well established theoretical results and an efficient algorithm, is presented. The method reduces the problem of estimating…
We propose a novel method to model nonlinear regression problems by adapting the principle of penalization to Partial Least Squares (PLS). Starting with a generalized additive model, we expand the additive component of each variable in…
We study the total least squares (TLS) problem that generalizes least squares regression by allowing measurement errors in both dependent and independent variables. TLS is widely used in applied fields including computer vision, system…