Related papers: Nuclear mass predictions with anisotropic kernel r…
In this paper, we consider the nonparametric least square regression in a Reproducing Kernel Hilbert Space (RKHS). We propose a new randomized algorithm that has optimal generalization error bounds with respect to the square loss, closing a…
While quantum annealing (QA) has been developed for combinatorial optimization, practical QA devices operate at finite temperature and under noise, and their outputs can be regarded as stochastic samples close to a Gibbs--Boltzmann…
Robust regression aims to develop methods for estimating an unknown regression function in the presence of outliers, heavy-tailed distributions, or contaminated data, which can severely impact performance. Most existing theoretical results…
This chapter discusses the importance of incorporating three-dimensional symmetries in the context of statistical learning models geared towards the interpolation of the tensorial properties of atomic-scale structures. We focus on Gaussian…
The Garvey-Kelson relations are used in an iterative process to predict nuclear masses in the neighborhood of nuclei with measured masses. Average errors in the predicted masses for the first three iteration shells are smaller than those…
In this paper, we propose a novel adaptive kernel for the radial basis function (RBF) neural networks. The proposed kernel adaptively fuses the Euclidean and cosine distance measures to exploit the reciprocating properties of the two. The…
We present a novel scheme to accurately predict atomic forces as vector quantities, rather than sets of scalar components, by Gaussian Process (GP) Regression. This is based on matrix-valued kernel functions, on which we impose the…
The divide-and-conquer method has been widely used for estimating large-scale kernel ridge regression estimates. Unfortunately, when the response variable is highly skewed, the divide-and-conquer kernel ridge regression (dacKRR) may…
Regression analysis-based approaches have been widely studied for face recognition (FR) in the past several years. More recently, to better deal with some difficult conditions such as occlusions and illumination, nuclear norm based matrix…
Random Fourier features is one of the most popular techniques for scaling up kernel methods, such as kernel ridge regression. However, despite impressive empirical results, the statistical properties of random Fourier features are still not…
The Garvey-Kelson relations (GKRs) are algebraic expressions originally developed to predict nuclear masses. In this letter we show that the GKRs provide a fruitful framework for the prediction of other physical observables that also…
This paper introduces algorithms to select/design kernels in Gaussian process regression/kriging surrogate modeling techniques. We adopt the setting of kernel method solutions in ad hoc functional spaces, namely Reproducing Kernel Hilbert…
Parameter selection without communicating local data is quite challenging in distributed learning, exhibing an inconsistency between theoretical analysis and practical application of it in tackling distributively stored data. Motivated by…
The large amount of online data and vast array of computing resources enable current researchers in both industry and academia to employ the power of deep learning with neural networks. While deep models trained with massive amounts of data…
This article gives a new insight of kernel-based (approximation) methods to solve the high-dimensional stochastic partial differential equations. We will combine the techniques of meshfree approximation and kriging interpolation to extend…
Kernel methods provide a principled approach to nonparametric learning. While their basic implementations scale poorly to large problems, recent advances showed that approximate solvers can efficiently handle massive datasets. A shortcoming…
It has been recently shown that supervised machine learning (ML) algorithms can accurately and efficiently predict the long-time populations dynamics of dissipative quantum systems given only short-time population dynamics. In the present…
An asymptotic theory is established for linear functionals of the predictive function given by kernel ridge regression, when the reproducing kernel Hilbert space is equivalent to a Sobolev space. The theory covers a wide variety of linear…
In this paper, we present a study of a kernel-based consensual aggregation on randomly projected high-dimensional features of predictions for regression. The aggregation scheme is composed of two steps: the high-dimensional features of…
The radial basis function (RBF) approach has been used to improve the mass predictions of nuclear models. However, systematic deviations exist between the improved masses and the experimental data for nuclei with different odd-even parities…