Reduced Label Complexity For Tight ℓ_2 Regression

05/12/2023
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by   Alex Gittens, et al.
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Given data X∈ℝ^n× d and labels 𝐲∈ℝ^n the goal is find 𝐰∈ℝ^d to minimize ‖ X𝐰-𝐲‖^2. We give a polynomial algorithm that, oblivious to 𝐲, throws out n/(d+√(n)) data points and is a (1+d/n)-approximation to optimal in expectation. The motivation is tight approximation with reduced label complexity (number of labels revealed). We reduce label complexity by Ω(√(n)). Open question: Can label complexity be reduced by Ω(n) with tight (1+d/n)-approximation?

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