Convergence Analysis of Deterministic Kernel-Based Quadrature Rules in Misspecified Settings

Convergence Analysis of Deterministic Kernel-Based Quadrature Rules in Misspecified Settings

This paper presents convergence analysis of kernel-based quadrature rules in misspecified settings, focusing on deterministic quadrature in Sobolev spaces. In particular, we deal with misspecified settings where a test integrand is less smooth than a Sobolev RKHS based on which a quadrature rule is constructed. We provide convergence guarantees based on two different assumptions on a quadrature...

Convergence guarantees for kernel-based quadrature rules in misspecified settings

Kernel-based quadrature rules are becoming important in machine learning and statistics, as they achieve super√ n convergence rates in numerical integration, and thus provide alternatives to Monte Carlo integration in challenging settings where integrands are expensive to evaluate or where integrands are high dimensional. These rules are based on the assumption that the integrand has a certain ...

Varinace-Based Sensitivity Analysis of Deterministic Model

‎The study of many scientific and natural phenomena in laboratory condition is sometimes impossible‎, ‎therefore theire expresed by mathemathical models and simulated by complex computer models (codes)‎. ‎Running a computer model with different inputs is called a computer expriment‎. ‎Statistical issues allocated a wide range of applications for computer expriment to itself‎. ‎In this paper‎, ‎...

Quadrature Rules for Fuzzy Integrals

Quadrature-based features for kernel approximation

We consider the problem of improving kernel approximation via randomized feature maps. These maps arise as Monte Carlo approximation to integral representations of kernel functions and scale up kernel methods for larger datasets. We propose to use more efficient numerical integration technique to obtain better estimates of the integrals compared to the state-of-the-art methods. Our approach all...