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Sample-Efficient Linear Regression with Self-Selection Bias
Feb. 23, 2024, 5:42 a.m. | Jason Gaitonde, Elchanan Mossel
cs.LG updates on arXiv.org arxiv.org
Abstract: We consider the problem of linear regression with self-selection bias in the unknown-index setting, as introduced in recent work by Cherapanamjeri, Daskalakis, Ilyas, and Zampetakis [STOC 2023]. In this model, one observes $m$ i.i.d. samples $(\mathbf{x}_{\ell},z_{\ell})_{\ell=1}^m$ where $z_{\ell}=\max_{i\in [k]}\{\mathbf{x}_{\ell}^T\mathbf{w}_i+\eta_{i,\ell}\}$, but the maximizing index $i_{\ell}$ is unobserved. Here, the $\mathbf{x}_{\ell}$ are assumed to be $\mathcal{N}(0,I_n)$ and the noise distribution $\mathbf{\eta}_{\ell}\sim \mathcal{D}$ is centered and independent of $\mathbf{x}_{\ell}$. We provide a novel and near optimally sample-efficient (in …
abstract arxiv bias cs.ds cs.lg index linear linear regression math.st regression sample samples stat.th type work
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