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<p>This study investigates five prevalent identifiability conditions for linear additive noise models (ANMs): (i) equal error variance (EV), (ii) the conditional variance-based (CV), (iii) the diagonal entries of the inverse covariance matrix-based (DI), (iv) LiNGAM, and (v) variance-sortability conditions. It demonstrates that the CV condition identifies a strictly larger set of models than the DI condition. Hence, when it is unclear which condition holds for a given dataset, an algorithm based on the CV condition is expected to be more reliable for causal structure recovery than one based on the DI condition. Furthermore, we show that none of the EV, DI, or CV conditions has a nested (subset or superset) relationship with the other identifiability conditions such as LiNGAM or variance-sortability. The real dataset, 2022 Baseball Statistics, analyzed in Section 5 is available at http://eng.koreabaseball.com.</p>

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Comparison of identifiability conditions in linear additive noise models

  • 期刊论文

  • 发表日期：

    2026年6月29日

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  • Gunwoong Park

摘要

This study investigates five prevalent identifiability conditions for linear additive noise models (ANMs): (i) equal error variance (EV), (ii) the conditional variance-based (CV), (iii) the diagonal entries of the inverse covariance matrix-based (DI), (iv) LiNGAM, and (v) variance-sortability conditions. It demonstrates that the CV condition identifies a strictly larger set of models than the DI condition. Hence, when it is unclear which condition holds for a given dataset, an algorithm based on the CV condition is expected to be more reliable for causal structure recovery than one based on the DI condition. Furthermore, we show that none of the EV, DI, or CV conditions has a nested (subset or superset) relationship with the other identifiability conditions such as LiNGAM or variance-sortability. The real dataset, 2022 Baseball Statistics, analyzed in Section 5 is available at http://eng.koreabaseball.com.