Related papers: Hybrid hyperinterpolation over general regions
The task of hyper-parameter optimization (HPO) is burdened with heavy computational costs due to the intractability of optimizing both a model's weights and its hyper-parameters simultaneously. In this work, we introduce a new class of HPO…
Many modern machine learning models are trained to achieve zero or near-zero training error in order to obtain near-optimal (but non-zero) test error. This phenomenon of strong generalization performance for "overfitted" / interpolated…
This paper focuses on developing a framework for constructing quasi-interpolation with the highest achievable approximation order from generalized Gaussian kernels with the help of kernel restriction trick and periodization technique. We…
With the rapid growth of data, how to extract effective information from data is one of the most fundamental problems. In this paper, based on Tikhonov regularization, we propose an effective method for reconstructing the function and its…
We propose novel smooth approximations to the classical rounding function, suitable for differentiable optimization and machine learning applications. Our constructions are based on two approaches: (1) localized sigmoid window functions…
When approximating a function that depends on a parameter, one encounters many practical examples where linear interpolation or linear approximation with respect to the parameters prove ineffective. This is particularly true for responses…
In this work, we investigate data fitting problems with random noises. A randomized progressive iterative regularization method is proposed. It works well for large-scale matrix computations and converges in expectation to the least-squares…
Overparametrized models can exhibit an excellent generalization performance, although they should be prone to overfitting according to classical statistical theory. The discovery of the "double descent", indicating that the generalization…
A method based on orthogonal function series interpolation of the square root probability density to analyze higher dimensional scattered data is presented. The method is targeted for the use-case when the model and/or data are available…
We introduce a new implementation of hybridization expansion continuous time quantum impurity solver which is relevant to dynamical mean-field theory. It employs Newton interpolation at a sequence of real Leja points to compute the time…
Consider estimating a structured signal $\mathbf{x}_0$ from linear, underdetermined and noisy measurements $\mathbf{y}=\mathbf{A}\mathbf{x}_0+\mathbf{z}$, via solving a variant of the lasso algorithm: $\hat{\mathbf{x}}=\arg\min_\mathbf{x}\{…
This paper, the fourth part of a series of papers on the arithmetic average (AA) density fusion approach and its application for target tracking, addresses the intricate challenge of distributed heterogeneous multisensor multitarget…
Good generalization performance on high-dimensional data crucially hinges on a simple structure of the ground truth and a corresponding strong inductive bias of the estimator. Even though this intuition is valid for regularized models, in…
We introduce an interpolation framework for H-infinity model reduction founded on ideas originating in optimal-H2 interpolatory model reduction, realization theory, and complex Chebyshev approximation. By employing a Loewner "data-driven"…
This work is concerned with the kernel-based approximation of a complex-valued function from data, where the frequency response function of a partial differential equation in the frequency domain is of particular interest. In this setting,…
Generalized Fourier series with orthogonal polynomial bases have useful applications in several fields, including differential equations, pattern recognition, and image and signal processing. However, computing the generalized Fourier…
We propose a sparse regularization model for inversion of incomplete Fourier transforms and apply it to seismic wavefield modeling. The objective function of the proposed model employs the Moreau envelope of the $\ell_0$ norm under a tight…
The article concerns hybrid combinations of empirical and parametric likelihood functions. Combining the two allows classical parametric likelihood to be crucially modified via the nonparametric counterpart, making possible model…
Many inverse problems and signal processing problems involve low-rank regularizers based on the nuclear norm. Commonly, proximal gradient methods (PGM) are adopted to solve this type of non-smooth problems as they can offer fast and…
Data augmentation is one of the most popular techniques for improving the robustness of neural networks. In addition to directly training the model with original samples and augmented samples, a torrent of methods regularizing the distance…