Related papers: Greedy regularized kernel interpolation
Subset selection, which aims to select a subset from a ground set to maximize some objective function, arises in various applications such as influence maximization and sensor placement. In real-world scenarios, however, one often needs to…
A major problem in data augmentation is to ensure that the generated new samples cover the search space. This is a challenging problem and requires exploration for data augmentation policies to ensure their effectiveness in covering the…
In this paper we present a locally and dimension-adaptive sparse grid method for interpolation and integration of high-dimensional functions with discontinuities. The proposed algorithm combines the strengths of the generalised sparse grid…
MapReduce has become the de facto standard model for designing distributed algorithms to process big data on a cluster. There has been considerable research on designing efficient MapReduce algorithms for clustering, graph optimization, and…
The randomized projection (RP) method is a simple iterative scheme for solving linear feasibility problems and has recently gained popularity due to its speed and low memory requirement. This paper develops an accelerated variant of the…
An approach to obtaining a parsimonious polynomial model from time series is proposed. An optimal minimal nonuniform time series embedding schema is used to obtain a time delay kernel. This scheme recursively optimizes an objective…
Given a straight-line program whose output is a polynomial function of the inputs, we present a new algorithm to compute a concise representation of that unknown function. Our algorithm can handle any case where the unknown function is a…
Motivated by, e.g., sensitivity analysis and end-to-end learning, the demand for differentiable optimization algorithms has been significantly increasing. In this paper, we establish a theoretically guaranteed versatile framework that makes…
We address the problem of approximating parametric Fourier imaging problems via interpolation/ extrapolation algorithms that impose smoothing constraints across contiguous values of the parameter. Previous works already proved that…
Reduced bases have been introduced for the approximation of parametrized PDEs in applications where many online queries are required. Their numerical efficiency for such problems has been theoretically confirmed in \cite{BCDDPW,DPW}, where…
In this paper, we propose a new framework for designing fast parallel algorithms for fundamental statistical subset selection tasks that include feature selection and experimental design. Such tasks are known to be weakly submodular and are…
The standard greedy algorithm has been recently shown to enjoy approximation guarantees for constrained non-submodular nondecreasing set function maximization. While these recent results allow to better characterize the empirical success of…
Numerical methods for the optimal feedback control of high-dimensional dynamical systems typically suffer from the curse of dimensionality. In the current presentation, we devise a mesh-free data-based approximation method for the value…
Sparse interpolation} refers to the exact recovery of a function as a short linear combination of basis functions from a limited number of evaluations. For multivariate functions, the case of the monomial basis is well studied, as is now…
We present a unified interpolation scheme that combines compactly-supported positive-definite kernels and multivariate polynomials. This unified framework generalizes interpolation with compactly-supported kernels and also classical…
In the absence of explicit regularization, Kernel "Ridgeless" Regression with nonlinear kernels has the potential to fit the training data perfectly. It has been observed empirically, however, that such interpolated solutions can still…
Sparse optimization is a central problem in machine learning and computer vision. However, this problem is inherently NP-hard and thus difficult to solve in general. Combinatorial search methods find the global optimal solution but are…
We consider the task of robust non-linear regression in the presence of both inlier noise and outliers. Assuming that the unknown non-linear function belongs to a Reproducing Kernel Hilbert Space (RKHS), our goal is to estimate the set of…
The aim of this paper is to extend the approximate quasi-interpolation on a uniform grid by dilated shifts of a smooth and rapidly decaying function on a uniform grid to scattered data quasi-interpolation. It is shown that high order…
We propose a data-driven sensor-selection algorithm for accurate estimation of the target variables from the selected measurements. The target variables are assumed to be estimated by a ridge-regression estimator which is trained based on…