Towards Indefinite Gaussian Processes

Gaussian processes (GPs) enable probabilistic kernel-machines with remarkable modeling efficacy and GPML toolbox facilitates a widespread use by practitioners and researchers. Many modern applications demand non-metric (dis)similarities. As a result, Mercer’s condition for positive semidefiniteness is violated. Through a simple text categorization example that involves a KL-divergence based kernel function, we have demonstrated that, despite all the care taken for numerical stability, the current framework is vulnerable to indefiniteness. Learning a spectral transformation is an option to tackle the problem with. However, the need for a general and principled solution towards indefinite Gaussian processes is urgent.