Information Rates of Nonparametric Gaussian Process Methods

By A. van der Vaart, Harry van Zanten. 2011

231 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Control and Systems Engineering

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Citations in the corpus

Entropy Search for Information-Efficient Global Optimization (2011, background): “But thanks to the consistency of Bayesian inference in general, and Gaussian process priors in particular (van der Vaart and van Zanten, 2011), no decision can lead to an evaluation that somehow makes it impossible to learn the true function afterward.”
Convergence Types and Rates in Generic Karhunen-Loève Expansions with Applications to Sample Path Properties (2014, background): “It is in particular interesting for certain statistical methods, see [34, 28, 27, 40, 13, 39, 33], since the considered family of covariance functions allows for a high flexibility in these methods.”
Bayesian Nonparametric Causal Inference: Information Rates and Learning Algorithms (2017, methodology): “The analyses in Appendix E was based on the work of van der Vaart and van Zanten in [27].”
Thomas Bayes’ walk on manifolds (2012, background): “Nevertheless, similar to what happens for the squared exponential prior on the real line [33], the paths of the corresponding Gaussian process are infinitely differentiable almost surely, which would lead to slow rates of convergence for the posterior, see [30].”
Frequentist coverage and sup-norm convergence rate in Gaussian process regression (2017, methodology): “…the L 2 norm, our result shows that by introducing the scaling ( nλ ) − 1 in the covariance kernel of the prior GP, we can eliminate the mismatch [44, 46] between the smoothness level (which is α + 1 / 2 for the univariate case and α + d/ 2 for the d -variate case) of the RKHS of the α -Mat´ern…”
Limits of Estimating Heterogeneous Treatment Effects: Guidelines for Practical Algorithm Design (2018, unknown): “H¨older for all (cid:22) (cid:12) (cid:20) (cid:12) (Vaart & Zanten, 2011).”