On the inability of Gaussian process regression to optimally learn compositional functions
NeurIPS 2022(2022)
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 $n$.
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关键词
Gaussian processes,Bayesian nonparametrics,posterior contraction,minimax estimation,large-sample asymptotics
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