In genomic selection (GS), genotype × environment interaction (G × E) can be modeled by a marker × environment interaction (M × E). The G × E may be modeled through a linear kernel or a nonlinear (Gaussian) kernel. In this study, we propose using two nonlinear Gaussian kernels: the reproducing kernel Hilbert space with kernel averaging (RKHS KA) and the Gaussian kernel with the bandwidth estima...

Alzheimer’s disease is a major cause of dementia. Its diagnosis requires accurate biomarkers that are sensitive to disease stages. In this respect, we regard probabilistic classification as a method of designing a probabilistic biomarker for disease staging. Probabilistic biomarkers naturally support the interpretation of decisions and evaluation of uncertainty associated with them. In this pap...

Multi-output Gaussian processes provide a convenient framework for multi-task problems. An illustrative and motivating example of a multi-task problem is multi-region electrophysiological time-series data, where experimentalists are interested in both power and phase coherence between channels. Recently, Wilson and Adams (2013) proposed the spectral mixture (SM) kernel to model the spectral den...

A function on R with multiple local minima is approximated from below, via linear programming, by a linear combination of convex kernel functions using sample points from the given function. The resulting convex kernel underestimator is then minimized, using either a linear equation solver for a linear-quadratic kernel or by a Newton method for a Gaussian kernel, to obtain an approximation to a...

We provide faster algorithms for the problem of Gaussian summation, which occurs in many machine learning methods. We develop two new extensions an O(D) Taylor expansion for the Gaussian kernel with rigorous error bounds and a new error control scheme integrating any arbitrary approximation method within the best discretealgorithmic framework using adaptive hierarchical data structures. We rigo...

In recent years, a number of kernel-based learning algorithms such as the regularization networks [1], the support vector machines [7, 4, 5], and the Gaussian process regression [8] have been investigated. These kernel machines are shown to work very well on real-world problems, given appropriate kernel functions. For general purposes, the Gaussian kernel is widely used and seems to work well [...

Since mammography images are in low-contrast, applying enhancement techniques as a pre-processing step are wisely recommended in the classification of the abnormal lesions into benign or malignant. A new kind of structural enhancement is proposed by morphological operator, which introduces an optimal Gaussian Kernel primitive, the kernel parameters are optimized the use of Genetic Algorithm. We...