Related papers: Nuclear masses in extended kernel ridge regression…
In this work, we investigate high-dimensional kernel ridge regression (KRR) on i.i.d. Gaussian data with anisotropic power-law covariance. This setting differs fundamentally from the classical source & capacity conditions for KRR, where…
The classical kernel ridge regression problem aims to find the best fit for the output $Y$ as a function of the input data $X\in \mathbb{R}^d$, with a fixed choice of regularization term imposed by a given choice of a reproducing kernel…
In this paper, we investigate a divide and conquer approach to Kernel Ridge Regression (KRR). Given n samples, the division step involves separating the points based on some underlying disjoint partition of the input space (possibly via…
Kernel ridge regression is an important nonparametric method for estimating smooth functions. We introduce a new set of conditions, under which the actual rates of convergence of the kernel ridge regression estimator under both the L_2 norm…
We investigate the properties of random feature ridge regression (RFRR) given by a two-layer neural network with random Gaussian initialization. We study the non-asymptotic behaviors of the RFRR with nearly orthogonal deterministic…
We present tight lower bounds on the number of kernel evaluations required to approximately solve kernel ridge regression (KRR) and kernel $k$-means clustering (KKMC) on $n$ input points. For KRR, our bound for relative error approximation…
Taking into account nucleon-nucleon gravitational interaction, higher-order terms of symmetry energy, pairing interaction, and neural network corrections, a new BW4 mass model has been developed, which more accurately reflects the…
We study the cost of overfitting in noisy kernel ridge regression (KRR), which we define as the ratio between the test error of the interpolating ridgeless model and the test error of the optimally-tuned model. We take an "agnostic" view in…
Bayesian neural network (BNN) approach is employed to improve the nuclear mass predictions of various models. It is found that the noise error in the likelihood function plays an important role in the predictive performance of the BNN…
The exploration of nuclear mass or binding energy, a fundamental property of atomic nuclei, remains at the forefront of nuclear physics research due to limitations in experimental studies and uncertainties in model calculations,…
We propose new reproducing kernel-based tests for model checking in conditional moment restriction models. By regressing estimated residuals on kernel functions via kernel ridge regression (KRR), we obtain a coefficient function in a…
Machine learning offers a powerful framework for validating and predicting atomic mass. We compare three improved neural network methods for representation and extrapolation for atomic mass prediction. The powerful method, adopting a…
A recent proposed method for $\alpha$-decay energies ($Q_\alpha$) [J.M. Dong, W. Zuo, and W. Scheid, Phys. Rev. Lett. \textbf{107}, 012501 (2011)] can reproduce experimental data of superheavy nuclei (SHN) with an $rms$-value of less than…
Distributed machine learning systems have been receiving increasing attentions for their efficiency to process large scale data. Many distributed frameworks have been proposed for different machine learning tasks. In this paper, we study…
In the multivariate regression, also referred to as multi-task learning in machine learning, the goal is to recover a vector-valued function based on noisy observations. The vector-valued function is often assumed to be of low rank.…
Random Feature (RF) models are used as efficient parametric approximations of kernel methods. We investigate, by means of random matrix theory, the connection between Gaussian RF models and Kernel Ridge Regression (KRR). For a Gaussian RF…
A neural-network model is developed to reproduce the differences between experimental nuclear mass-excess values and the theoretical values given by the Finite Range Droplet Model. The results point to the existence of subtle regularities…
We study the problem of estimating the effect function for a continuous treatment, which maps each treatment value to a population-averaged outcome. A central challenge in this setting is confounding: treatment assignment often depends on…
A deep neural network (DNN) has been developed to generate the distributions of nuclear charge density, utilizing the training data from the relativistic density functional theory and incorporating available experimental charge radii of…
We introduce a global nuclear mass formula which is based on the macroscopic-microscopic method, the Skyrme energy-density functional and the isospin symmetry in nuclear physics. The rms deviation with respect to 2149 known nuclear masses…