Uncertainty quantification for distributed regression

• URL: http://arxiv.org/abs/2105.11425v1
• Date: Mon, 24 May 2021 17:33:19 GMT
• Title: Uncertainty quantification for distributed regression
• Authors: Valeriy Avanesov
• Abstract summary: We propose a fully data-driven approach to quantify uncertainty of the averaged estimator. Namely, we construct simultaneous element-wise confidence bands for the predictions yielded by the averaged estimator on a given deterministic prediction set. As a by-product of our analysis we also obtain a sup-norm consistency result for the divide-and-conquer Kernel Ridge Regression.
• Score: 2.28438857884398
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The ever-growing size of the datasets renders well-studied learning techniques, such as Kernel Ridge Regression, inapplicable, posing a serious computational challenge. Divide-and-conquer is a common remedy, suggesting to split the dataset into disjoint partitions, obtain the local estimates and average them, it allows to scale-up an otherwise ineffective base approach. In the current study we suggest a fully data-driven approach to quantify uncertainty of the averaged estimator. Namely, we construct simultaneous element-wise confidence bands for the predictions yielded by the averaged estimator on a given deterministic prediction set. The novel approach features rigorous theoretical guaranties for a wide class of base learners with Kernel Ridge regression being a special case. As a by-product of our analysis we also obtain a sup-norm consistency result for the divide-and-conquer Kernel Ridge Regression. The simulation study supports the theoretical findings.

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