We establish the universal edge scaling limit of random partitions with infinite-parameter distribution called Schur measure. explore asymptotic behavior wave function, which is a building block corresponding kernel, based on Schrödinger-type differential equation. show that function in general to Airy and its higher-order analogs limit. construct kernel Tracy–Widom from discuss implication mul...

This paper proposes a set-membership approach to characterize the kernel of an intervalvalued function. In the context of a bounded-error estimation, this formulation makes it possible to embed all uncertainties of the problem inside the interval function and thus to avoid bisections with respect to all these uncertainties. To illustrate the principle of the approach, two testcases taken from r...

Upscaling based on the bandwidth of the kernel function is a flexible approach to upscale the data because the cells will be coarse-based on variability. The intensity of the coarsening of cells in this method can be controlled with bandwidth. In a smooth variability region, a large number of cells will be merged, and vice versa, they will remain fine with severe variability. Bandwidth variatio...

In this paper, a new approach is presented to fit arobust fuzzy regression model based on some fuzzy quantities. Inthis approach, we first introduce a new distance between two fuzzynumbers using the kernel function, and then, based on the leastsquares method, the parameters of fuzzy regression model isestimated. The proposed approach has a suitable performance to<b...

A covariance function estimate of a zero-mean nonstationary random process in discrete time is accomplished from one observed realization by weighting observations with a kernel function. Several kernel functions have been proposed in the literature. In this paper, we prove that the mean square error (MSE) optimal kernel function for any parameterized family of random processes can be computed ...

This study developed a novel model, HGA-SVR, for type of kernel function and kernel parameter value optimization in support vector regression (SVR), which is then applied to forecast the maximum electrical daily load. A novel hybrid genetic algorithm (HGA) was adapted to search for the optimal type of kernel function and kernel parameter values of SVR to increase the accuracy of SVR. The propos...

Kernel methods have become popular in many sub-fields of machine learning with the exception of reinforcement learning; they facilitate rich representations, and enable machine learning techniques to work in diverse input spaces. We describe a principled approach to the policy evaluation problem of reinforcement learning. We present a temporal difference (TD) learning using kernel functions. Ou...

Because k(·, x) is in the Stein class of p for any x , we can show that ∇ x k(·, x) is also in the Stein class, since x ∇ x (p(x)∇ x k(x, x))dx = ∇ x x ∇ x (p(x)k(x, x))dx = 0, and hence v(·, x) is also in the Stein class; apply Lemma 2.3 on v(·, x) with fixed x gives S(p, q) = E x,x ∼p [(s q (x) − s p (x)) v(x, x))] = E x,x ∼p [s q (x) v(x, x) + trace(∇ x v(x, x))] The result then follows by n...