Related papers: Nuclear masses in extended kernel ridge regression…

In this note we extend kernel function approximation results for neural networks with Gaussian-distributed weights to single-layer networks initialized using Haar-distributed random orthogonal matrices (with possible rescaling). This is…

Regularized least-squares (kernel-ridge / Gaussian process) regression is a fundamental algorithm of statistics and machine learning. Because generic algorithms for the exact solution have cubic complexity in the number of datapoints, large…

The semi-empirical macroscopic-microscopic mass formula is further improved by considering some residual corrections. The rms deviation from 2149 known nuclear masses is significantly reduced to 336 keV, even lower than that achieved with…

We perform a study on kernel regression for large-dimensional data (where the sample size $n$ is polynomially depending on the dimension $d$ of the samples, i.e., $n\asymp d^{\gamma}$ for some $\gamma >0$ ). We first build a general tool to…

In this paper, we propose a random projection approach to estimate variance in kernel ridge regression. Our approach leads to a consistent estimator of the true variance, while being computationally more efficient. Our variance estimator is…

We propose an optimal algorithm for estimating conditional average treatment effects (CATEs) when response functions lie in a reproducing kernel Hilbert space (RKHS). We study settings in which the contrast function is structurally simpler…

Matrix completion and extrapolation (MCEX) are dealt with here over reproducing kernel Hilbert spaces (RKHSs) in order to account for prior information present in the available data. Aiming at a faster and low-complexity solver, the task is…

The emergence of Quantum Machine Learning (QML) to enhance traditional classical learning methods has seen various limitations to its realisation. There is therefore an imperative to develop quantum models with unique model hypotheses to…

Besides their intrinsic nuclear-structure value, nuclear mass models are essential for astrophysical applications, such as r-process nucleosynthesis and neutron-star structure. To overcome the intrinsic limitations of existing…

Predicting nuclear masses is a longstanding challenge. One path forward is machine learning (ML) which trains on experimental data, but can suffer large errors when extrapolating toward neutron-rich species. In nature, such masses shape…

We present a Kernel Ridge Regression (KRR) based supervised learning method combined with Genetic Algorithms (GAs) for the calculation of quasiparticle energies within Many-Body Green's Functions Theory. These energies representing…

These notes provide a self-contained introduction to kernel methods and their geometric foundations in machine learning. Starting from the construction of Hilbert spaces, we develop the theory of positive definite kernels, reproducing…

Meta-learning involves training models on a variety of training tasks in a way that enables them to generalize well on new, unseen test tasks. In this work, we consider meta-learning within the framework of high-dimensional multivariate…

Reinforcement learning utilizing kernel ridge regression to predict the expected value function represents a powerful method with great representational capacity. This setting is a highly versatile framework amenable to analytical results.…

We propose a new method for feature learning and function estimation in supervised learning via regularised empirical risk minimisation. Our approach considers functions as expectations of Sobolev functions over all possible one-dimensional…

Hopfield networks using Hebbian learning suffer from limited storage capacity. While supervised methods like Linear Logistic Regression (LLR) offer some improvement, kernel methods like Kernel Logistic Regression (KLR) significantly enhance…

Kernel regression is a popular non-parametric fitting technique. It aims at learning a function which estimates the targets for test inputs as precise as possible. Generally, the function value for a test input is estimated by a weighted…

Most machine learning algorithms, such as classification or regression, treat the individual data point as the object of interest. Here we consider extending machine learning algorithms to operate on groups of data points. We suggest…

In practice, encoding invariances into models improves sample complexity. In this work, we study this phenomenon from a theoretical perspective. In particular, we provide minimax optimal rates for kernel ridge regression on compact…

The single-layer feedforward neural network with random weights is a recurring motif in the neural networks literature. The advantage of these networks is their simplified training, which reduces to solving a ridge-regression problem. A…