Efficient List-Decodable Regression using Batches

• URL: http://arxiv.org/abs/2211.12743v1
• Date: Wed, 23 Nov 2022 07:08:00 GMT
• Title: Efficient List-Decodable Regression using Batches
• Authors: Abhimanyu Das, Ayush Jain, Weihao Kong and Rajat Sen
• Abstract summary: We begin the study of list-decodable linear regression using batches. In this setting only an $alpha in (0,1]$ fraction of the batches are genuine. Each genuine batch contains $ge n$ i.i.d samples from a common unknown distribution and the remaining batches may contain arbitrary or even adversarial samples.
• Score: 33.300073775123835
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We begin the study of list-decodable linear regression using batches. In this setting only an $\alpha \in (0,1]$ fraction of the batches are genuine. Each genuine batch contains $\ge n$ i.i.d. samples from a common unknown distribution and the remaining batches may contain arbitrary or even adversarial samples. We derive a polynomial time algorithm that for any $n\ge \tilde \Omega(1/\alpha)$ returns a list of size $\mathcal O(1/\alpha^2)$ such that one of the items in the list is close to the true regression parameter. The algorithm requires only $\tilde{\mathcal{O}}(d/\alpha^2)$ genuine batches and works under fairly general assumptions on the distribution. The results demonstrate the utility of batch structure, which allows for the first polynomial time algorithm for list-decodable regression, which may be impossible for the non-batch setting, as suggested by a recent SQ lower bound \cite{diakonikolas2021statistical} for the non-batch setting.

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