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<p>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 <i>n</i> is large and the number of covariates <i>p</i> is also allowed to be large. This is known to be problematic due to the need to check <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(2^p\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>2</mn> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation> possible models. We show how the optimal penalized <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\ell _0\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ℓ</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation> 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.</p>

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Fast variable selection under \(\ell _0\) regularization in high-dimensions

  • 期刊论文

  • 发表日期：

    2026年3月3日

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  • Yuchen Xiao,
  • Stephen Walker

摘要

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 \(2^p\) 2 p possible models. We show how the optimal penalized \(\ell _0\) ℓ 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.