  Spectral approximation and variational inducing learning for the Gaussian
process are two popular methods to reduce computational complexity. However, in
previous research, those methods always tend to adopt the orthonormal basis
functions, such as eigenvectors in the Hilbert space, in the spectrum method,
or decoupled orthogonal components in the variational framework. In this paper,
inspired by quantum physics, we introduce a novel basis function, which is
tunable, local and bounded, to approximate the kernel function in the Gaussian
process. There are two adjustable parameters in these functions, which control
their orthogonality to each other and limit their boundedness. And we conduct
extensive experiments on open-source datasets to testify its performance.
Compared to several state-of-the-art methods, it turns out that the proposed
method can obtain satisfactory or even better results, especially with poorly
chosen kernel functions.
