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Abstract <p> We propose a new formulation of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(p\)</EquationSource> </InlineEquation>-adic optimisation as the infinitesimal limit of the least squares method, and introduce several algorithms for <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(p\)</EquationSource> </InlineEquation>-adic optimisation. Since the optimisation problem includes the maximal feasible subsystem problem of linear equations over the finite field <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathbb{F}_p\)</EquationSource> </InlineEquation>, which is APX-complete, i.e. complete for the class of problems which allow constant-factor approximations, by E. Amaldi and V. Kann, we mainly deal with heuristic approaches to the <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(p\)</EquationSource> </InlineEquation>-adic optimisation under mild assumptions. In particular, we deal with <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(p\)</EquationSource> </InlineEquation>-adic polynomial regression under the assumption that noise occurs digitwise sparsely. </p>

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\(p\)-Adic Polynomial Regression Detecting Digitwise Noise

  • 期刊论文

  • 发表日期：

    2026年3月10日

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  • Tomoki Mihara

摘要

Abstract

We propose a new formulation of \(p\) -adic optimisation as the infinitesimal limit of the least squares method, and introduce several algorithms for \(p\) -adic optimisation. Since the optimisation problem includes the maximal feasible subsystem problem of linear equations over the finite field \(\mathbb{F}_p\) , which is APX-complete, i.e. complete for the class of problems which allow constant-factor approximations, by E. Amaldi and V. Kann, we mainly deal with heuristic approaches to the \(p\) -adic optimisation under mild assumptions. In particular, we deal with \(p\) -adic polynomial regression under the assumption that noise occurs digitwise sparsely.