Upper and Lower Bounds on the Learning Curve for Gaussian Processes

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Control functionals for Monte Carlo integration (2014, background): “ depend on the tail behaviour of ˇwhich may be complicated (Aad van der Vaart, personal communication). Indeed, even the case where D 0 is non-random poses signicant theoretical challenges (see also Williams and Vivarelli, 2000). For these reasons, here we state a general presistency condition that ”
Explaining neural scaling laws (2021, background): “Case 2 – bounded second derivative : The quadratic mean value theorem states that for any f T , there exists a c such that, Taking the expectation of (S2) and using the fact that f ′′ ( c ) is bounded yields the desired result.”
Multi-fidelity Gaussian process regression for computer experiments (2013, unknown): “, 1998], [Mockus, 1994], [Williams et al., 2000], [Mockus, 2002], [Huang et al.”
Generalization Errors and Learning Curves for Regression with Multi-task Gaussian Processes (2009, background): “Similar to the case of single-task learning, each training point creates a depression on the σ(2) T (x∗, ρ) surface [9, 13].”
Multi-Task Learning using Generalized t Process (2010, result): “There exist some previous research works on the asymptotic analysis and learning curve of GP, e.g., (Opper and Vivarelli, 1998; Sollich, 1998; Williams and Vivarelli, 2000; Sollich and Halees, 2002).”