How is it possible to design a custom covariance/kernel function and ensure its positive definiteness?

03 March 2018 1 1K Report

In kernel-based learning, the covariance/kernel matrix defines the properties of the function being modeled from the data (smoothness, boundedness, etc.). How can I design a covariance function that models specific assumptions about the data? How can I guarantee this function's positive definiteness?

Ette Etuk

A covariance matrix is bound to be a square matrix. If it is of full rank, it is bound to be invertible and positive definite. Most real life data will naturally produce positive definite covariance matrices.

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