Related papers: Beyond Generalized Eigenvalues in Lattice Quantum …
Machine learning (ML) is quickly emerging as a powerful tool with diverse applications across an extremely broad spectrum of disciplines and commercial endeavors. Typically, ML is used as a black box that provides little illuminating…
Efficient quantum Monte Carlo update schemes called directed loops have recently been proposed, which improve the efficiency of simulations of quantum lattice models. We propose to generalize the detailed balance equations at the local…
Generalized linear models and the quasi-likelihood method extend the ordinary regression models to accommodate more general conditional distributions of the response. Nonparametric methods need no explicit parametric specification, and the…
Moment based methods have produced efficient multiscale quantization algorithms for solving singular perturbation/strong coupling problems. One of these, the Eigenvalue Moment Method (EMM), developed by Handy et al (Phys. Rev. Lett.{\bf…
Projection predictive inference is a decision theoretic Bayesian approach that decouples model estimation from decision making. Given a reference model previously built including all variables present in the data, projection predictive…
The generalized eigenvalue problem (GEP) serves as a cornerstone in a wide range of applications in numerical linear algebra and scientific computing. However, traditional approaches that aim to maximize the classical Rayleigh quotient…
The Generalized Estimating Equations (GEE) approach is a widely used statistical method for analyzing longitudinal data and clustered data in clinic studies. In dentistry, due to multiple outcomes obtained from one patient, the outcomes…
A generalized matrix-pencil approach is proposed for the estimation of complex exponential components with segmented signal samples, which is very efficient and provides super-resolution estimations. It is applicable to the signals sampled…
Factorization machine (FM) is an effective model for feature-based recommendation which utilizes inner product to capture second-order feature interactions. However, one of the major drawbacks of FM is that it couldn't capture complex…
Gaussian Process Regression is a well-known machine learning technique for which several quantum algorithms have been proposed. We show here that in a wide range of scenarios these algorithms show no exponential speedup. We achieve this by…
A universal energy eigenvalue equation is proposed in this paper. It is proven that the unique set of eigenfunctions or preferred basis exists for any non-isolated sub-system. Applying the new eigenvalue equation to the relative motion of a…
Quantum Mechanics/Molecular Mechanics (QM/MM) simulations are a popular approach to study various features of large systems. A common application of QM/MM calculations is in the investigation of reaction mechanisms in condensed-phase and…
Many pre-trained models (PTMs) are available in modern applications. Because different PTMs are often trained on different datasets, their performances can vary substantially for different new tasks, and the ranking of the candidates may…
Periodic micromagnetic finite element method (PM-FEM) is introduced to solve periodic unit cell problems using the Landau-Lifshitz-Gilbert equation. PM-FEM is applicable to general problems with 1D, 2D, and 3D periodicities. PM-FEM is based…
This manuscript presents an approach to perform generalized linear regression with multiple high dimensional covariance matrices as the outcome. Model parameters are proposed to be estimated by maximizing a pseudo-likelihood. When the data…
This paper introduces an efficient algorithm for finding the dominant generalized eigenvectors of a pair of symmetric matrices. Combining tools from approximation theory and convex optimization, we develop a simple scalable algorithm with…
Generalized additive models (GAMs) are flexible non-linear regression models, which can be fitted efficiently using the approximate Bayesian methods provided by the mgcv R package. While the GAM methods provided by mgcv are based on the…
Generalized linear mixed-effects models (GLMMs) are widely used to analyze grouped and hierarchical data. In a GLMM, each response is assumed to follow an exponential-family distribution where the natural parameter is given by a linear…
Expectation-Maximization (EM) algorithm is a widely used iterative algorithm for computing (local) maximum likelihood estimate (MLE). It can be used in an extensive range of problems, including the clustering of data based on the Gaussian…
Finite differences, finite elements, and their generalizations are widely used for solving partial differential equations, and their high-order variants have respective advantages and disadvantages. Traditionally, these methods are treated…