Kernel Learning by Quantum Annealer

The Boltzmann machine is one of the various applications using quantum annealer. We propose an application of the Boltzmann machine to the kernel matrix used in various machine-learning techniques. We focus on the fact that shift-invariant kernel functions can be expressed in terms of the expected value of a spectral distribution by the Fourier transformation. Using this transformation, random Fourier feature (RFF) samples the frequencies and approximates the kernel function. In this paper, furthermore, we propose a method to obtain a spectral distribution suitable for the data using a Boltzmann machine. As a result, we show that the prediction accuracy is comparable to that of the method using the Gaussian distribution. We also show that it is possible to create a spectral distribution that could not be feasible with the Gaussian distribution.