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.
翻译:Gaussian 过程的光谱近似和变异引导学习是降低计算复杂性的两种流行方法。 但是,在以前的研究中,这些方法总是倾向于采用正正统基础功能,如Hilbert空间、频谱法或变异框架中脱钩的正方形元件。在本文中,受量子物理的启发,我们引入了一种新型的基础功能,即金枪鱼、局部和捆绑,以近似Gaussian 过程的内核函数。这些功能中有两个可调整参数,可以相互控制其正方形,限制其交界性。我们在开源数据集上进行了广泛的实验,以证明其性能。与几种最先进的方法相比,我们发现,拟议的方法可以取得满意或更好的结果,特别是在选取的内核功能很差的情况下。