We study the theoretical properties of a variational Bayes method in the Gaussian Process regression model. We consider the inducing variables method introduced by Titsias (2009a) and derive sufficient conditions for obtaining contraction rates for the corresponding variational Bayes (VB) posterior. As examples we show that for three particular covariance kernels (Mat\'ern, squared exponential, random series prior) the VB approach can achieve optimal, minimax contraction rates for a sufficiently large number of appropriately chosen inducing variables. The theoretical findings are demonstrated by numerical experiments.

翻译：我们研究了高山进程回归模型中变式贝叶斯方法的理论属性。我们考虑了提齐亚斯(2009年a)采用的诱变变量方法,并为相应的变式贝叶斯后座获得收缩率创造了充分的条件。我们举例表明,对于三种特定的共变内核(马特尔恩,正方指数,前随机序列),VB方法可以为足够多的合适选择的诱变变量实现最佳、最小速率收缩率。理论结果通过数字实验得到证明。