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<p>Noise contrastive estimation (NCE) is a popular approach for parameter estimation of unnormalized statistical models. NCE is based on a maximum likelihood estimation framework for a classification task, which makes the parameter estimation of unnormalized models sensitive to outlier noise included in the dataset. To cope with this problem, a robust version of NCE called <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10463_2025_963_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\gamma\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>γ</mi> </math></EquationSource> </InlineEquation>-NCE (GNCE) has been proposed. In this paper, we investigate asymptotic statistical properties of GNCE and propose an information criterion for GNCE, which enables us to select an appropriate model even when the dataset is contaminated by outlier noise.</p>

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An information criterion for robust estimation with unnormalized statistical models

  • 期刊论文

  • 发表日期：

    2025年10月29日

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  • Takashi Takenouchi,
  • Hiroaki Sasaki

摘要

Noise contrastive estimation (NCE) is a popular approach for parameter estimation of unnormalized statistical models. NCE is based on a maximum likelihood estimation framework for a classification task, which makes the parameter estimation of unnormalized models sensitive to outlier noise included in the dataset. To cope with this problem, a robust version of NCE called \(\gamma\) γ -NCE (GNCE) has been proposed. In this paper, we investigate asymptotic statistical properties of GNCE and propose an information criterion for GNCE, which enables us to select an appropriate model even when the dataset is contaminated by outlier noise.