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arXiv · 2305.11165

The noise level in linear regression with dependent data

Ingvar Ziemann·Stephen Tu·George J. Pappas·Nikolai Matni
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Abstract

We derive upper bounds for random design linear regression with dependent ($β$-mixing) data absent any realizability assumptions. In contrast to the strictly realizable martingale noise regime, no sharp instance-optimal non-asymptotics are available in the literature. Up to constant factors, our analysis correctly recovers the variance term predicted by the Central Limit Theorem -- the noise level of the problem -- and thus exhibits graceful degradation as we introduce misspecification. Past a burn-in, our result is sharp in the moderate deviations regime, and in particular does not inflate the leading order term by mixing time factors.

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Ingvar Ziemann, Stephen Tu, George J. Pappas, Nikolai Matni. 2023-10-27. The noise level in linear regression with dependent data. https://arxiv.org/abs/2305.11165

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