Fast Mean Estimation with Sub-Gaussian Rates

Yeshwanth Cherapanamjeri; Nicolas Flammarion; Peter L. Bartlett

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arXiv · 1902.01998

Fast Mean Estimation with Sub-Gaussian Rates

Yeshwanth Cherapanamjeri·Nicolas Flammarion·Peter L. Bartlett

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Abstract

We propose an estimator for the mean of a random vector in $\mathbb{R}^d$ that can be computed in time $O(n^4+n^2d)$ for $n$ i.i.d.~samples and that has error bounds matching the sub-Gaussian case. The only assumptions we make about the data distribution are that it has finite mean and covariance; in particular, we make no assumptions about higher-order moments. Like the polynomial time estimator introduced by Hopkins, 2018, which is based on the sum-of-squares hierarchy, our estimator achieves optimal statistical efficiency in this challenging setting, but it has a significantly faster runtime and a simpler analysis.

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BibTeX RIS

Yeshwanth Cherapanamjeri, Nicolas Flammarion, Peter L. Bartlett. 2019-02-06. Fast Mean Estimation with Sub-Gaussian Rates. https://arxiv.org/abs/1902.01998

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