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arXiv · 2511.22524

List-Decodable Regression via Expander Sketching

Herbod Pourali·Sajjad Hashemian·Ebrahim Ardeshir-Larijani
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Abstract

We introduce an expander-sketching framework for list-decodable linear regression that achieves sample complexity $\tilde{O}((d+\log(1/\delta))/\alpha)$, list size $O(1/\alpha)$, and near input-sparsity running time $\tilde{O}(\mathrm{nnz}(X)+d^{3}/\alpha)$ under standard sub-Gaussian assumptions. Our method uses lossless expanders to synthesize lightly contaminated batches, enabling robust aggregation and a short spectral filtering stage that matches the best known efficient guarantees while avoiding SoS machinery and explicit batch structure.

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Herbod Pourali, Sajjad Hashemian, Ebrahim Ardeshir-Larijani. 2025-11-27. List-Decodable Regression via Expander Sketching. https://arxiv.org/abs/2511.22524

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