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

Key Points

• The research aims to understand why Gaussian process regression may fail with compositional functions.
• Proved theoretical bounds for Gaussian processes in regression contexts.
• Studied posterior contraction rates for Gaussian process regression in continuous models.
• Analyzed the performance of generalized additive functions using Gaussian process priors.
• Demonstrated that deep Gaussian process priors can outperform traditional Gaussian process priors.
• Established that general mean-zero Gaussian process recovery rates are strictly slower than minimax rates by a polynomial factor.