Asymmetric kernel in Gaussian Processes for learning target variance

• Published in: Pattern recognition letters 2018-06, Vol.108, p.70-77
• Main Authors: Pintea, S.L., van Gemert, J.C., Smeulders, A.W.M.
• Format: Article
• Language: English
• Subjects: Asymmetric kernel distances; Asymmetry; Computer centers; Data centers; Gaussian distribution; Gaussian process; Kernel metric learning; Learning; Normal distribution; Pattern recognition; Regression; Regression analysis; Regression models; Training; Variances
• ISSN: 0167-8655; 1872-7344
• DOI: 10.1016/j.patrec.2018.02.026

•Training the Gaussian Process regression model on training centers only, which makes is applicable on large datasets.•An asymmetric kernel formulation of the Gaussian Process regression model that adds to its descriptiveness.•Learning individualized kernel metrics per data center.•Effective use of the available training samples when learning the individualized kernel metrics.•Learning for each data center not only the appropriate size but also the shape in the kernel metric. [Display omitted] This work incorporates the multi-modality of the data distribution into a Gaussian Process regression model. We approach the problem from a discriminative perspective by learning, jointly over the training data, the target space variance in the neighborhood of a certain sample through metric learning. We start by using data centers rather than all training samples. Subsequently, each center selects an individualized kernel metric. This enables each center to adjust the kernel space in its vicinity in correspondence with the topology of the targets — a multi-modal approach. We additionally add descriptiveness by allowing each center to learn a precision matrix. We demonstrate empirically the reliability of the model.