Related papers: Nuclear masses in extended kernel ridge regression…
Calculations of nuclei are often carried out in finite model spaces. Thus, finite-size corrections enter, and it is necessary to extrapolate the computed observables to infinite model spaces. In this work, we employ extrapolation methods…
Kernel density estimation (KDE) is integral to a range of generative and discriminative tasks in machine learning. Drawing upon tools from the multidimensional calculus of variations, we derive an optimal weight function that reduces bias…
As modern machine learning models continue to advance the computational frontier, it has become increasingly important to develop precise estimates for expected performance improvements under different model and data scaling regimes.…
Kernel-based learning methods such as Kernel Logistic Regression (KLR) can substantially increase the storage capacity of Hopfield networks, but the principles governing their performance and stability remain largely uncharacterized. This…
A structure-preserving kernel ridge regression method is presented that allows the recovery of nonlinear Hamiltonian functions out of datasets made of noisy observations of Hamiltonian vector fields. The method proposes a closed-form…
We propose a method for nonparametric density estimation that exhibits robustness to contamination of the training sample. This method achieves robustness by combining a traditional kernel density estimator (KDE) with ideas from classical…
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…
The primary hyperparameter in kernel regression (KR) is the choice of kernel. In most theoretical studies of KR, one assumes the kernel is fixed before seeing the training data. Under this assumption, it is known that the optimal kernel is…
One central theme in machine learning is function estimation from sparse and noisy data. An example is supervised learning where the elements of the training set are couples, each containing an input location and an output response. In the…
We study the problem of estimating the derivatives of a regression function, which has a wide range of applications as a key nonparametric functional of unknown functions. Standard analysis may be tailored to specific derivative orders, and…
Quantum machine learning models have been gaining significant traction within atomistic simulation communities. Conventionally, relative model performances are being assessed and compared using learning curves (prediction error vs. training…
Given the importance of nuclear mass predictions, numerous models have been developed to extrapolate the measured data into unknown regions. While neural networks -- the core of modern artificial intelligence -- have been recently suggested…
A unified theoretical model reproducing charge radii of known atomic nuclei plays an essential role in making extrapolations for unknown nuclei. Recently developed new ansatz which phenomenologically takes into account the neutron-proton…
In this article a surprising result is demonstrated using the neural tangent kernel. This kernel is defined as the inner product of the vector of the gradient of an underlying model evaluated at training points. This kernel is used to…
Finding optimal measurement operators is crucial for the performance of quantum reservoir computers (QRCs), since they employ a fixed quantum feature map. We formulate the training of both stateless (quantum extreme learning machines,…
Distributed learning is an effective way to analyze big data. In distributed regression, a typical approach is to divide the big data into multiple blocks, apply a base regression algorithm on each of them, and then simply average the…
The problem of learning functions over spaces of probabilities - or distribution regression - is gaining significant interest in the machine learning community. A key challenge behind this problem is to identify a suitable representation…
This paper investigates preconditioned conjugate gradient techniques for solving kernel ridge regression (KRR) problems with a medium to large number of data points ($10^4 \leq N \leq 10^7$), and it describes two methods with the strongest…
One of the most fundamental aspects of any machine learning algorithm is the training data used by the algorithm. We introduce the novel concept of $\epsilon$-approximation of datasets, obtaining datasets which are much smaller than or are…
Mass is a fundamental property and an important fingerprint of atomic nucleus. It provides an extremely useful test ground for nuclear models and is crucial to understand energy generation in stars as well as the heavy elements synthesized…