Related papers: Kernel Learning for Regression via Quantum Anneali…

Energy-based generative models, such as restricted Boltzmann machines (RBMs), require unbiased Boltzmann samples for effective training. Classical Markov chain Monte Carlo methods, however, converge slowly and yield correlated samples,…

Approximations based on random Fourier features have recently emerged as an efficient and formally consistent methodology to design large-scale kernel machines. By expressing the kernel as a Fourier expansion, features are generated based…

Quantum computers have the opportunity to be transformative for a variety of computational tasks. Recently, there have been proposals to use the unsimulatably of large quantum devices to perform regression, classification, and other machine…

Conditional expectiles are becoming an increasingly important tool in finance as well as in other areas of applications. We analyse a support vector machine type approach for estimating conditional expectiles and establish learning rates…

The celebrated Nadaraya-Watson kernel estimator is among the most studied method for nonparametric regression. A classical result is that its rate of convergence depends on the number of covariates and deteriorates quickly as the dimension…

In this work, we introduce kernels with random Fourier features in the meta-learning framework to leverage their strong few-shot learning ability. We propose meta variational random features (MetaVRF) to learn adaptive kernels for the…

We introduce a novel kernel-based framework for learning differential equations and their solution maps that is efficient in data requirements, in terms of solution examples and amount of measurements from each example, and computational…

We propose several approaches for solving differential equations (DEs) with quantum kernel methods. We compose quantum models as weighted sums of kernel functions, where variables are encoded using feature maps and model derivatives are…

Data scarcity remains a central challenge in materials discovery, where finding meaningful descriptors and tuning models for generalization is critical but inherently a discrete optimization problem prone to multiple local minima…

There is currently a huge effort to understand the potential and limitations of variational quantum machine learning (QML) based on the optimization of parameterized quantum circuits. Recent proposals toward dequantizing variational QML…

A hybrid quantum-classical method for learning Boltzmann machines (BM) for a generative and discriminative task is presented. Boltzmann machines are undirected graphs with a network of visible and hidden nodes where the former is used as…

In this article, we introduce a kernel-based consensual aggregation method for regression problems. We aim to flexibly combine individual regression estimators $r_1, r_2, \ldots, r_M$ using a weighted average where the weights are defined…

Modest statistical differences between the sampling performances of the D-Wave quantum annealer (QA) and the classical Markov Chain Monte Carlo (MCMC), when applied to Restricted Boltzmann Machines (RBMs), are explored to explain, and…

Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…

Associated kernels have been introduced to improve the classical continuous kernels for smoothing any functional on several kinds of supports such as bounded continuous and discrete sets. This work deals with the effects of combined…

Various Graph Neural Networks (GNNs) have been successful in analyzing data in non-Euclidean spaces, however, they have limitations such as oversmoothing, i.e., information becomes excessively averaged as the number of hidden layers…

Incorporating nonlinearity into quantum machine learning is essential for learning a complicated input-output mapping. We here propose quantum algorithms for nonlinear regression, where nonlinearity is introduced with feature maps when…

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…

To accelerate kernel methods, we propose a near input sparsity time algorithm for sampling the high-dimensional feature space implicitly defined by a kernel transformation. Our main contribution is an importance sampling method for…

The Nadaraya-Watson kernel estimator is among the most popular nonparameteric regression technique thanks to its simplicity. Its asymptotic bias has been studied by Rosenblatt in 1969 and has been reported in a number of related literature.…