Related papers: Hybrid kernel polynomial method
Multivariate global polynomial approximations - such as polynomial chaos or stochastic collocation methods - are now in widespread use for sensitivity analysis and uncertainty quantification. The pseudospectral variety of these methods uses…
Obtaining a rigorous and reliable method for linking computer simulations of polymer blends and composites at different length scales of interest is a highly desirable goal in soft matter physics. In this paper a multiscale modeling…
Kernel method in machine learning consists of encoding input data into a vector in a Hilbert space called the feature space and modeling the target function as a linear map on the feature space. Given a cost function, computing such an…
A spectral mixture (SM) kernel is a flexible kernel used to model any stationary covariance function. Although it is useful in modeling data, the learning of the SM kernel is generally difficult because optimizing a large number of…
Integral equation methods for the solution of partial differential equations, when coupled with suitable fast algorithms, yield geometrically flexible, asymptotically optimal and well-conditioned schemes in either interior or exterior…
This work presents an efficient numerical method to evaluate the free energy density and associated thermodynamic quantities of (quasi) one-dimensional classical systems, by combining the transfer operator approach with a numerical…
We consider the problem of simultaneously learning to linearly combine a very large number of kernels and learn a good predictor based on the learnt kernel. When the number of kernels $d$ to be combined is very large, multiple kernel…
Local polynomial regression of order at least one often performs poorly in regions of sparse data. Local constant regression is exceptional in this regard, though it is the least accurate method in general, especially at the boundaries of…
Quantum signal processing (QSP) is a framework which was proven to unify and simplify a large number of known quantum algorithms, as well as discovering new ones. QSP allows one to transform a signal embedded in a given unitary using…
In this paper, we propose a variable selection method for general nonparametric kernel-based estimation. The proposed method consists of two-stage estimation: (1) construct a consistent estimator of the target function, (2) approximate the…
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…
Feature preprocessing continues to play a critical role when applying machine learning and statistical methods to tabular data. In this paper, we propose the use of the kernel density integral transformation as a feature preprocessing step.…
Subsampling methods aim to select a subsample as a surrogate for the observed sample. Such methods have been used pervasively in large-scale data analytics, active learning, and privacy-preserving analysis in recent decades. Instead of…
A new method of estimating higher order perturbative coefficients is discussed. It exploits the rapid, asymptotic growth of perturbative coefficients and the information on the singularities in the complex Borel plane. A comparison with…
We present methods that can provide an exponential savings in the resources required to perform dynamic parameter estimation using quantum systems. The key idea is to merge classical compressive sensing techniques with quantum control…
Quantum states and measurements exhibit wave-like --- continuous, or particle-like --- discrete, character. Hybrid discrete-continuous photonic systems are key to investigating fundamental quantum phenomena, generating superpositions of…
Data visualization is important in understanding the characteristics of data that are difficult to see directly. It is used to visualize loss landscapes and optimization trajectories to analyze optimization performance. Popular optimization…
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…
Quantum sensing encompasses highly promising techniques with diverse applications including noise-reduced imaging, super-resolution microscopy as well as imaging and spectroscopy in challenging spectral ranges. These detection schemes use…
We consider scattered data approximation on product regions of equal and different dimensionality. On each of these regions, we assume quasi-uniform but unstructured data sites and construct optimal sparse grids for scattered data…