Related papers: Exact Stiefel Optimization for Probabilistic PLS: …
Partial least squares (PLS) is a dimensionality reduction technique introduced in the field of chemometrics and successfully employed in many other areas. The PLS components are obtained by maximizing the covariance between linear…
Linear programming on the Stiefel manifold (LPS) is studied for the first time. It aims at minimizing a linear objective function over the set of all $p$-tuples of orthonormal vectors in ${\mathbb R}^n$ satisfying $k$ additional linear…
Public Safety Power Shutoffs (PSPS) force rapid topology changes that can render standard operating points infeasible, requiring operators to quickly identify corrective transmission switching actions that reduce load shedding while…
Regression by composition provides a flexible framework for constructing conditional distributions through sequential group actions. However, when multiple flows act on the same distribution, the model becomes non-identifiable, leading to…
A new exact projective penalty method is proposed for the equivalent reduction of constrained optimization problems to nonsmooth unconstrained ones. In the method, the original objective function is extended to infeasible points by summing…
Physics-informed neural networks (PINNs) have recently emerged as an alternative way of solving partial differential equations (PDEs) without the need of building elaborate grids, instead, using a straightforward implementation. In…
Driven by a wide range of applications, many principal subspace estimation problems have been studied individually under different structural constraints. This paper presents a unified framework for the statistical analysis of a general…
Dimensionality reduction plays an important role in computer vision problems since it reduces computational cost and is often capable of yielding more discriminative data representation. In this context, Partial Least Squares (PLS) has…
A general approach to provide approximate parameterizations of the "small" scales by the "large" ones, is developed for stochastic partial differential equations driven by linear multiplicative noise. This is accomplished via the concept of…
The explicit regularization and optimality of deep neural networks estimators from independent data have made considerable progress recently. The study of such properties on dependent data is still a challenge. In this paper, we carry out…
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…
We motivate weakly supervised learning as an effective learning paradigm for problems where curating perfectly annotated datasets is expensive and may require domain expertise such as fine-grained classification. We focus on Partial Label…
Robust subspace estimation is fundamental to many machine learning and data analysis tasks. Iteratively Reweighted Least Squares (IRLS) is an elegant and empirically effective approach to this problem, yet its theoretical properties remain…
Affine projection algorithm (APA) is a well-known algorithm in adaptive filtering applications such as audio echo cancellation. APA relies on three parameters: $P$ (projection order), $\mu$ (step size) and $\delta$ (regularization…
The inherent nonlinearity of the power flow equations poses significant challenges in accurately modeling power systems, particularly when employing linearized approximations. Although power flow linearizations provide computational…
Under the reproducing kernel Hilbert spaces (RKHS), we consider the penalized least-squares of the partially functional linear models (PFLM), whose predictor contains both functional and traditional multivariate parts, and the multivariate…
Filtering and parameter estimation under partial information for multiscale problems is studied in this paper. After proving mean square convergence of the nonlinear filter to a filter of reduced dimension, we establish that the conditional…
We propose a predictor-corrector adaptive method for the simulation of hyperbolic partial differential equations (PDEs) on networks under general uncertainty in parameters, initial conditions, or boundary conditions. The approach is based…
The recent paper \cite{GSZ2023} on estimation and inference for top-ranking problem in Bradley-Terry-Lice (BTL) model presented a surprising result: component-wise estimation and inference can be done under much weaker conditions on the…
The heavy-tailed distributions of corrupted outliers and singular values of all channels in low-level vision have proven effective priors for many applications such as background modeling, photometric stereo and image alignment. And they…