标题： 关于高斯过程回归无法最优学习组合函数的无能性 显示英文标题

标题： On the inability of Gaussian process regression to optimally learn compositional functions

摘要： 我们严格证明，如果目标函数具有组合结构，深度高斯过程先验可以优于高斯过程先验。 为此，我们研究了连续回归模型中高斯过程回归的后验收缩率的信息理论下界。 我们表明，如果真实函数是一个广义加法函数，那么基于任何零均值高斯过程的后验只能以一个严格慢于最小最大率的速率恢复真实函数，该速率在样本量$n$上是多项式次优的。 显示英文摘要

摘要： We rigorously prove that deep Gaussian process priors can outperform Gaussian process priors if the target function has a compositional structure. To this end, we study information-theoretic lower bounds for posterior contraction rates for Gaussian process regression in a continuous regression model. We show that if the true function is a generalized additive function, then the posterior based on any mean-zero Gaussian process can only recover the truth at a rate that is strictly slower than the minimax rate by a factor that is polynomially suboptimal in the sample size $n$.