Computing p-values of LiNGAM outputs via Multiscale Bootstrap

TL;DR

This paper introduces a novel multiscale bootstrap approach to accurately compute p-values for LiNGAM causal discovery outputs, improving statistical reliability over traditional bootstrap methods.

Contribution

The paper develops and applies a multiscale bootstrap method to obtain unbiased p-values for LiNGAM, enhancing confidence assessment in causal inference results.

Findings

Multiscale bootstrap provides more accurate p-values for LiNGAM.

Experiments show improved reliability of causal inference.

Method outperforms ordinary bootstrap in bias reduction.

Abstract

Structural equation models and Bayesian networks have been widely used to study causal relationships between continuous variables. Recently, a non-Gaussian method called LiNGAM was proposed to discover such causal models and has been extended in various directions. An important problem with LiNGAM is that the results are affected by the random sampling of the data as with any statistical method. Thus, some analysis of the statistical reliability or confidence level should be conducted. A common method to evaluate a confidence level is a bootstrap method. However, a confidence level computed by ordinary bootstrap method is known to be biased as a probability-value ($p$-value) of hypothesis testing. In this paper, we propose a new procedure to apply an advanced bootstrap method called multiscale bootstrap to compute confidence levels, i.e., p-values, of LiNGAM outputs. The multiscale bootstrap method gives unbiased $p$-values with asymptotic much higher accuracy. Experiments on artificial data demonstrate the utility of our approach.