We analyze a variational method for reconstructing a bar code signal from a blurry and noisy measurement. The bar code is modeled as a binary function with a finite number of transitions and a parameter controlling minimal feature size. The measured signal is the convolution of this binary function with a Gaussian kernel. In this work, we assume that the blur kernel is known and establish condi...

In Bayesian nonparametric models, Gaussian processes provide a popular prior choice for regression function estimation. Existing literature on the theoretical investigation of the resulting posterior distribution almost exclusively assume a fixed design for covariates. The only random design result we are aware of (van der Vaart and van Zanten, 2011) assumes the assigned Gaussian process to be ...

Many unsupervised learning algorithms make use of kernels that rely on the Euclidean distance between two samples. However, the Euclidean distance is optimal for Gaussian distributed data. In this paper, we relax the global Gaussian assumption made by the Euclidean distance, and propose a locale Gaussian modelling for the immediate neighbourhood of the samples, resulting in an augmented data sp...

Kernel k-means is useful for performing clustering on nonlinearly separable data. The kernel k-means is hard to scale to large data due to the quadratic complexity. In this paper, we propose an approach which utilizes the low-dimensional feature approximation of the Gaussian kernel function to capitalize a fast linear k-means solver to perform the nonlinear kernel k-means. This approach takes a...

The phenomenon of genotype × environment (G × E) interaction in plant breeding decreases selection accuracy, thereby negatively affecting genetic gains. Several genomic prediction models incorporating G × E have been recently developed and used in genomic selection of plant breeding programs. Genomic prediction models for assessing multi-environment G × E interaction are extensions of a single-...

The role of width of Gaussians in two types of computational models is investigated: Gaussian radial-basis-functions (RBFs) where both widths and centers vary and Gaussian kernel networks which have fixed widths but varying centers. The effect of width on functional equivalence, universal approximation property, and form of norms in reproducing kernel Hilbert spaces (RKHS) is explored. It is pr...

Can We Trust Bayesian Uncertainty Quantification from Gaussian Process Priors with Squared Exponential Covariance Kernel?

Regression problems on massive data sets are ubiquitous in many application domains including the Internet, earth and space sciences, and finances. Gaussian Process regression is a popular technique for modeling the input-output relations of a set of variables under the assumption that the weight vector has a Gaussian prior. However, it is challenging to apply Gaussian Process regression to lar...

This paper deals with the identification of nonlinear systems using multi-kernel approach. In this context, we have improved the Support Vector Regression (SVR) method in order to identify nonlinear complex system. Our idea consists in dividing the regressor vector in several blocks, and, for each one a kernel function is used. This blockwise SVR approach is called Support Kernel Regression (SK...