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Adaptation Using Spatially Distributed Gaussian Processes
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DOI：10.1080/01621459.2025.2501717.png)
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We consider the accuracy of an approximate posterior distribution in nonparametric regression problems by combining posterior distributions computed on subsets of the data defined by the locations of the independent variables. We show that this approximate posterior retains the rate of recovery of the full data posterior distribution, where the rate of recovery adapts to the smoothness of the true regression function. As particular examples we consider Gaussian process priors based on integrated Brownian motion and the Matérn kernel augmented with a prior on the length scale. Besides theoretical guarantees we present a numerical study of the methods both on synthetic and real world data. We also propose a new aggregation technique, which numerically outperforms previous approaches. Finally, we demonstrate empirically that spatially distributed methods can adapt to local regularities, potentially outperforming the original Gaussian process. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.
Keyword:
Adaptation
Bayesian asymptotics
Distributed computation
Gaussian processes
Nonparametric Bayes
期刊
J
IF:
3
论文数:
5.2K
被引数:
4.8W
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分享收藏Rates of contraction of posterior distributions based on Gaussian process priors.png)
ANNALS OF STATISTICS
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ANNALS OF STATISTICSIF3.7
OAAI分享收藏ASYMPTOTIC BEHAVIOUR OF THE EMPIRICAL BAYES POSTERIORS ASSOCIATED TO MAXIMUM MARGINAL LIKELIHOOD ESTIMATORANNALS OF STATISTICSOAAI
ANNALS OF STATISTICSIF3.7
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