# Uncertainty quantification for distributed regression

arXiv: https://arxiv.org/abs/2105.11425 · HTML: https://mlsanity.com/paper/2105.11425/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 40 references that are in the map.
- First posted on arXiv 24 May 2021.

## Builds on (most cited first, 7 of 7)

- [Less is More: Nystr"om Computational Regularization](https://mlsanity.com/paper/1507.04717/) (2015)
- [Distributed Gaussian Processes](https://mlsanity.com/paper/1502.02843/) (2015)
- [Distributed learning with regularized least squares](https://mlsanity.com/paper/1608.03339/) (2016)
- [Frequentist coverage and sup-norm convergence rate in Gaussian process regression](https://mlsanity.com/paper/1708.04753/) (2017)
- [On the Optimality of Averaging in Distributed Statistical Learning](https://mlsanity.com/paper/1407.2724/) (2014)
- [Bayesian model selection consistency and oracle inequality with intractable marginal likelihood](https://mlsanity.com/paper/1701.00311/) (2017)
- [Nonparametric Inference via Bootstrapping the Debiased Estimator](https://mlsanity.com/paper/1702.07027/) (2017)

## Abstract (arXiv)

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.