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A Theoretical Study of The Effects of Adversarial Attacks on Sparse Regression. (arXiv:2212.11209v1 [cs.LG])
Dec. 22, 2022, 2:10 a.m. | Deepak Maurya, Jean Honorio
cs.CR updates on arXiv.org arxiv.org
This paper analyzes $\ell_1$ regularized linear regression under the
challenging scenario of having only adversarially corrupted data for training.
We use the primal-dual witness paradigm to provide provable performance
guarantees for the support of the estimated regression parameter vector to
match the actual parameter. Our theoretical analysis shows the
counter-intuitive result that an adversary can influence sample complexity by
corrupting the irrelevant features, i.e., those corresponding to zero
coefficients of the regression parameter vector, which, consequently, do not
affect the …
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