arXiv research

We prove the statistical consistency of kernel Partial Least Squares Regression applied to a bounded regression learning problem on a reproducing kernel Hilbert space. Partial Least Squares stands out of well-known classical approaches as e.g. Ridge Regression or Principal Components Regression, as it is not defined as…

Randomized matrix compression techniques, such as the Johnson-Lindenstrauss transform, have emerged as an effective and practical way for solving large-scale problems efficiently. With a focus on computational efficiency, however, forsaking solutions quality and accuracy becomes the trade-off. In this paper, we investi…

This paper studies an unsupervised deep learning-based numerical approach for solving partial differential equations (PDEs). The approach makes use of the deep neural network to approximate solutions of PDEs through the compositional construction and employs least-squares functionals as loss functions to determine para…

Proposes a method for coarse graph alignment using sparse partial least squares.

This paper presents regression models obtained from a process of blind prediction of peptide binding affinity from provided descriptors for several distinct datasets as part of the 2006 Comparative Evaluation of Prediction Algorithms (COEPRA) contest. This paper finds that kernel partial least squares, a nonlinear part…

Unified multi-view learning framework using OPLS with regularization and deep extensions.

New algorithm extracts shared latent space for cortico-muscular interactions.

The derivation of statistical properties for Partial Least Squares regression can be a challenging task. The reason is that the construction of latent components from the predictor variables also depends on the response variable. While this typically leads to good performance and interpretable models in practice, it ma…

Functional PLS improves prediction and inference for scalar responses from functional predictors.

Dual-sPLS improves feature selection and prediction in high-dimensional data.

Improves Bayesian optimisation for engineering design problems with many variables.

This paper reviews and compares supervised linear dimension-reduction techniques.

Study reveals limits of PLS in multi-modal learning with correlated signals.

Improved Least-Squares Monte Carlo with finite-difference ansatz.

Estimates smooth functions and their derivatives from noisy data.

This study examines the relationship between PLS and OLS regression using eigenvalue distributions.

The paper analyzes PLS-SVD in high-dimensional data integration, revealing its strengths and limitations.

The runtime for Kernel Partial Least Squares (KPLS) to compute the fit is quadratic in the number of examples. However, the necessity of obtaining sensitivity measures as degrees of freedom for model selection or confidence intervals for more detailed analysis requires cubic runtime, and thus constitutes a computationa…

Matrix factorization is a popular approach to solving matrix estimation problems based on partial observations. Existing matrix factorization is based on least squares and aims to yield a low-rank matrix to interpret the conditional sample means given the observations. However, in many real applications with skewed and…

P3LS preserves privacy while integrating data across companies.

We prove rates of convergence in the statistical sense for kernel-based least squares regression using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is directly related to Kernel Partial Least Squares, a regression method that combines supervised dim…

The resolution and calibration of pure spectra of minority components in measurements of chemical mixtures without prior knowledge of the mixture is a challenging problem. In this work, a combination of band target entropy minimization (BTEM) and target partial least squares (T-PLS) was used to obtain estimates for sin…

This paper reviews SDR methods for multivariate response regression.

High-dimensional data common in genomics, proteomics, and chemometrics often contains complicated correlation structures. Recently, partial least squares (PLS) and Sparse PLS methods have gained attention in these areas as dimension reduction techniques in the context of supervised data analysis. We introduce a framewo…

We analyze a simple prefiltered variation of the least squares estimator for the problem of estimation with biased, semi-parametric noise, an error model studied more broadly in causal statistics and active learning. We prove an oracle inequality which demonstrates that this procedure provably mitigates the variance in…

DPLS improves asset pricing by capturing non-linear risk factor structures.

Motivated by the Bagging Partial Least Squares (PLS) and Principal Component Analysis (PCA) algorithms, we propose a Principal Model Analysis (PMA) method in this paper. In the proposed PMA algorithm, the PCA and the PLS are combined. In the method, multiple PLS models are trained on sub-training sets, derived from the…

JAXFit speeds up curve fitting on GPUs.

Proposes a new method for joint sample and feature selection in multi-view data.

PLS-Lasso integrates dimension reduction into regression for financial index tracking.

We prove statistical rates of convergence for kernel-based least squares regression from i.i.d. data using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping. This method is related to Kernel Partial Least Squares, a regression method that combines supervised dimensio…

In this paper we propose a computationally efficient algorithm for on-line variable selection in multivariate regression problems involving high dimensional data streams. The algorithm recursively extracts all the latent factors of a partial least squares solution and selects the most important variables for each facto…

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 $K$ principal components minimizes the sum of squared errors between the original …

Bayesian PINN improves estimation of PDE solutions from noisy data.

OLS predictions are shown to be similar to attention mechanisms in models.

CD converges linearly for MCP/SCAD penalized least squares.

The goal of semi-supervised learning is to improve supervised classifiers by using additional unlabeled training examples. In this work we study a simple self-learning approach to semi-supervised learning applied to the least squares classifier. We show that a soft-label and a hard-label variant of self-learning can be…

Bayesian optimization reduces hyperparameters for mixed variable design problems.

Most of the existing solutions to enterprise threat management are preventive approaches prescribing means to prevent policy violations with varying degrees of success. In this paper we consider the complementary scenario where a number of security violations have already occurred, or security threats, or vulnerabiliti…

In this paper, we implement multi-label neural networks with optimal thresholding to identify gas species among a multi gas mixture in a cluttered environment. Using infrared absorption spectroscopy and tested on synthesized spectral datasets, our approach outperforms conventional binary relevance - partial least squar…

This paper is concerned with the squared F(robenius)-norm regularized factorization form for noisy low-rank matrix recovery problems. Under a suitable assumption on the restricted condition number of the Hessian for the loss function, we derive an error bound to the true matrix for the non-strict critical points with r…

Illustrates interleaved learning with Kalman Filter for linear least squares.

We obtain an improved finite-sample guarantee on the linear convergence of stochastic gradient descent for smooth and strongly convex objectives, improving from a quadratic dependence on the conditioning $(L/μ)^2$ (where $L$ is a bound on the smoothness and $μ$ on the strong convexity) to a linear dependence on $L/μ$. …

We study randomized sketching methods for approximately solving least-squares problem with a general convex constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the quadratic objective function (cost approximation), or in terms of some distance meas…

Cross validation residuals are well known for the ordinary least squares model. Here leave-M-out cross validation is extended to generalised least squares. The relationship between cross validation residuals and Cook's distance is demonstrated, in terms of an approximation to the difference in the generalised residual …

We compare the risk of ridge regression to a simple variant of ordinary least squares, in which one simply projects the data onto a finite dimensional subspace (as specified by a Principal Component Analysis) and then performs an ordinary (un-regularized) least squares regression in this subspace. This note shows that …

This work improves SINDy-type algorithms for system identification using score-guided dictionary selection.

Deep learning solves complex volatility equations.