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The Importance of Being Positive in Causal Statistical Fault Localization: Important Properties of Baah et al.'s CSFL Regression Model

This paper investigates the performance of Baah et al.'s causal regression model for fault localization when an important precondition for causal inference, called positivity, is violated. Two kinds of positivity violations are considered: structural and random ones. We prove that random, but not structural nonpositivity may harm the performance of Baah et al.'s causal estimator. To address the problem of random nonpositivity, we propose a modification to the way suspiciousness scores are assigned. Empirical results are presented that indicate it improves the performance of Baah et al.'s technique. We also present a probabilistic characterization of Baah et al.'s estimator, which provides a more efficient way to compute it.