Related papers: Exact Stiefel Optimization for Probabilistic PLS: …

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…

Uncertainty quantification is essential for scientific analysis, as it allows for the evaluation and interpretation of variability and reliability in complex systems and datasets. In their original form, multivariate statistical regression…

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.…

With a rapid increase in volume and complexity of data sets, there is a need for methods that can extract useful information, for example the relationship between two data sets measured for the same persons. The Partial Least Squares (PLS)…

Physics-Informed Neural Networks (PINNs) have shown promise in solving partial differential equations (PDEs), including the frequency-domain Helmholtz equation. However, standard training of PINNs using gradient descent (GD) suffers from…

Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving PDEs, yet existing uncertainty quantification (UQ) approaches for PINNs generally lack rigorous statistical guarantees. In this work, we bridge this…

Partial Least Square (PLS) is a dimension reduction method used to remove multicollinearities in a regression model. However contrary to Principal Components Analysis (PCA) the PLS components are also choosen to be optimal for predicting…

An asymptotically optimal blind calibration scheme of uniform linear arrays for narrowband Gaussian signals is proposed. Rather than taking the direct Maximum Likelihood (ML) approach for joint estimation of all the unknown model…

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…

Semi-supervised learning by self-training heavily relies on pseudo-label selection (PLS). The selection often depends on the initial model fit on labeled data. Early overfitting might thus be propagated to the final model by selecting…

We propose a Binary Robust Least Squares (BRLS) model that encompasses key robust least squares formulations, such as those involving uncertain binary labels and adversarial noise constrained within a hypercube. We show that the geometric…

We present a non-conforming least squares method for approximating solutions of second order elliptic problems with discontinuous coefficients. The method is based on a general Saddle Point Least Squares (SPLS) method introduced in previous…

Projected least squares (PLS) is an intuitive and numerically cheap technique for quantum state tomography. The method first computes the least-squares estimator (or a linear inversion estimator) and then projects the initial estimate onto…

Motivated by the need for efficient estimation of conditional expectations, we consider a least-squares function approximation problem with heavily polluted data. Existing methods that are effective in the small-noise regime are suboptimal…

Partial least squares (PLS) is a simple factorisation method that works well with high dimensional problems in which the number of observations is limited given the number of independent variables. In this article, we show that PLS can…

Motivated by renal imaging studies that combine renogram curves with pharmacokinetic and demographic covariates, we propose Hybrid partial least squares (Hybrid PLS) for simultaneous supervised dimension reduction and regression in the…

Partial least squares regression (PLSR) has been a popular technique to explore the linear relationship between two datasets. However, most of algorithm implementations of PLSR may only achieve a suboptimal solution through an optimization…

Brittle optimization has been observed to adversely impact model likelihoods for regression and VAEs when simultaneously fitting neural network mappings from a (random) variable onto the mean and variance of a dependent Gaussian variable.…

Partial-label learning (PLL) is a typical weakly supervised learning problem, where each training instance is equipped with a set of candidate labels among which only one is the true label. Most existing methods elaborately designed…

Accurate uncertainty quantification is critical for reliable predictive modeling. Existing methods typically address either aleatoric uncertainty due to measurement noise or epistemic uncertainty resulting from limited data, but not both in…