where K is the kernel of the integral. Given the input signal X , Y represents the output signal. The smoothness of the output depends on the smoothness of the kernel. We assume the kernel to be unimodal and isotropic. When the kernel is isotropic, it has radial symmetry and should be invariant under rotation. So it has the form K(t, s) = f(‖t− s‖) for some smooth function f . Since the kernel ...

Although Gaussian process inference is usually formulated for a single output, in many machine learning problems the objective is to infer multiple tasks jointly, possibly exploring the dependencies between them to improve results. Real world examples of this problem include ore mining where the objective is to infer the concentration of several chemical components to assess the ore quality. Si...

This paper aims to investigate a Bayesian sampling approach to parameter estimation in the GARCH model with an unknown conditional error density, which we approximate by a mixture of Gaussian densities centered at individual errors and scaled by a common standard deviation. This mixture density has the form of a kernel density estimator of the errors with its bandwidth being the standard deviat...

This paper describes the derivation of a sequence kernel that transforms speech utterances into probabilistic vectors for classification in an expanded feature space. The sequence kernel is built upon a set of Gaussian basis functions, where half of the basis functions contain speaker specific information while the other half implicates the common characteristics of the competing background spe...

Some linkages between kernel and penalty methods of density estimation are explored. It is recalled that classical Gaussian kernel density estimation can be viewed as the solution of the heat equation with initial condition given by data. We then observe that there is a direct relationship between the kernel method and a particular penalty method of density estimation. For this penalty method, ...

In most kernel based machine learning algorithms and non-parametric statistics the key computational task is to compute a linear combination of local kernel functions centered on the training data, i.e., f(x) = ∑N i=1 qik(x, xi), which is the discrete Gauss transform for the Gaussian kernel. f is the regression/classification function in case of regularized least squares, Gaussian process regre...

The generalization performance of kernel based extreme learning machine (KELM) with Gaussian kernel are sensitive to the parameters combination (C, γ). The best generalization performance of KELM with Gaussian kernel is usually achieved in a very narrow range of such combinations. In order to achieve optimal generalization performance, the parameters of KELM with Gaussian kernel were optimized ...

In this paper, extended approach to Gaussian kernel algorithm for text segmentation, reference text line and skew rate extractions is presented. It assumes creation of boundary growing area around text based on Gaussian kernel algorithm extended by anisotropic approach. Those boundary growing areas form control image with distinct objects that are prerequisite for text segmentation. After text ...

We evaluate three link functions (square root, logit, and copula) and Matérn kernel in the kernel-based estimation of reflectance spectra of the Munsell Matte collection in the 400-700 nm region. We estimate reflectance spectra from RGB camera responses in case of real and simulated responses and show that a combination of link function and a kernel regression model with a Matérn kernel decreas...

This paper proposes a novel approach for directly tuning the gaussian kernel matrix for one class learning. The popular gaussian kernel includes a free parameter, σ, that requires tuning typically performed through validation. The value of this parameter impacts model performance significantly. This paper explores an automated method for tuning this kernel based upon a hill climbing optimizatio...