I'm looking for a rigorous proof that the $L_1$ regularization really produces sparsity, there are multiple intuitive ones like these which I understand but all of these feel like they just explain why coefficients shrink towards zero, not why they produce exact zero elements. Does this proof exist or is using the $L_1$ regularization just a heuristic approach to solve the $L_0$ regularization efficiently
2026-03-27 06:09:50.1774591790
Is there a rigorous proof that $L_1$ regularization produces sparse results
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