Related papers: Eigenvalue and Generalized Eigenvalue Problems: Tu…
The aim of this paper is to develop an algebraic multigrid method to solve eigenvalue problems based on the combination of the multilevel correction scheme and the algebraic multigrid method for linear equations. Our approach uses the…
We propose a new algorithm for sparse estimation of eigenvectors in generalized eigenvalue problems (GEP). The GEP arises in a number of modern data-analytic situations and statistical methods, including principal component analysis (PCA),…
We establish central limit theorems for principal eigenvalues and eigenvectors under a large factor model setting, and develop two-sample tests of both principal eigenvalues and principal eigenvectors. One important application is to detect…
Optimization is a ubiquitous modeling tool and is often deployed in settings which repeatedly solve similar instances of the same problem. Amortized optimization methods use learning to predict the solutions to problems in these settings,…
Estimating the eigenvalues of non-normal matrices is a foundational problem with far-reaching implications, from modeling non-Hermitian quantum systems to analyzing complex fluid dynamics. Yet, this task remains beyond the reach of standard…
Emulators that can bypass computationally expensive scientific calculations with high accuracy and speed can enable new studies of fundamental science as well as more potential applications. In this work we discuss solving a system of…
In this paper we present the notions of trail (pseudo-)division, generalized subresultants and generalized subresultant algorithm.
Recent years have seen growing interest in learning disentangled representations, in which distinct features, such as size or shape, are represented by distinct neurons. Quantifying the extent to which a given representation is disentangled…
The challenge of learning disentangled representation has recently attracted much attention and boils down to a competition using a new real world disentanglement dataset (Gondal et al., 2019). Various methods based on variational…
The standard approach for finding eigenvalues and eigenvectors of matrix polynomials starts by embedding the coefficients of the polynomial into a matrix pencil, known as linearization. Building on the pioneering work of Nakatsukasa and…
In this paper, we consider a nonlinear integral eigenvalue problem, which is a reformulation of the transmission eigenvalue problem arising in the inverse scattering theory. The boundary element method is employed for discretization, which…
A fundamental challenge for machine learning models is generalizing to out-of-distribution (OOD) data, in part due to spurious correlations. To tackle this challenge, we first formalize the OOD generalization problem as constrained…
In this article we study eigenvalues and minimizers of a fractional non-standard growth problem. We prove several properties on this quantities and their corresponding eigenfunctions.
As machine learning applications grow increasingly ubiquitous and complex, they face an increasing set of requirements beyond accuracy. The prevalent approach to handle this challenge is to aggregate a weighted combination of requirement…
An a posteriori verification method is proposed for the generalized real-symmetric eigenvalue problem and is applied to densely clustered eigenvalue problems in large-scale electronic state calculations. The proposed method is realized by a…
We discuss two approaches to solving the parametric (or stochastic) eigenvalue problem. One of them uses a Taylor expansion and the other a Chebyshev expansion. The parametric eigenvalue problem assumes that the matrix $A$ depends on a…
The parallel orbital-updating approach is an orbital/eigenfunction iteration based approach for solving eigenvalue problems when many eigenpairs are required. It has been proven to be efficient, for instance, in electronic structure…
We propose and analyze a finite element method for the Oseen eigenvalue problem. This problem is an extension of the Stokes eigenvalue problem, where the presence of the convective term leads to a non-symmetric problem and hence, to complex…
To provide mathematically rigorous eigenvalue bounds for the Steklov eigenvalue problem, an enhanced version of the eigenvalue estimation algorithm developed by the third author is proposed, which removes the requirements of the positive…
Deep Reinforcement Learning has shown significant progress in extracting useful representations from high-dimensional inputs albeit using hand-crafted auxiliary tasks and pseudo rewards. Automatically learning such representations in an…