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Fast variable selection under ℓ0 regularization in high-dimensions
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DOI：10.1007/s11222-026-10853-5.png)
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Abstract
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We adapt a classical associative memory learning algorithm, the Hopfield network, for variable selection involving information criteria, such as Akaike information criterion (AIC), in high-dimensional linear regression where the sample size n is large and the number of covariates p is also allowed to be large. This is known to be problematic due to the need to check 2p possible models. We show how the optimal penalized & ell;0 solution to this problem can be found in polynomial time via the Hopfield network. This enables efficient implementation of the class of Generalized information criteria (GIC), which includes the popular AIC and BIC, for variable selection in high-dimensional linear regression. Empirically, we conduct simulations to validate the efficiency and effectiveness of the proposed approach.
Keywords:
Variable selection
Finite-dimensional regression
Hopfield network optimization
Akaike Information Criterion
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