Handling negative conditional mutual information estimates from the KSG estimator in IDTxl

Determine a principled, theoretically justified procedure for handling small negative estimates of conditional mutual information produced by the Kraskov–Stögbauer–Grassberger (KSG) nearest-neighbor estimator during the PRUNE-phase significance testing in the IDTxl transfer entropy pipeline, so as to avoid false-positive links without ad hoc rejection rules.

Background

The paper employs the IDTxl library to infer information flow using transfer entropy and conditional mutual information estimated with the Kraskov–Stögbauer–Grassberger (KSG) nearest-neighbor method. In practice, during the PRUNE phase of the algorithm's hypothesis testing, the KSG estimator sometimes yields small negative values of conditional mutual information, which are theoretically impossible but arise due to estimation artifacts.

The authors note that they have heuristically treated these negative values by automatically rejecting them as significant, which appears to reduce false-positive links in their experiments. However, they acknowledge that there is no clear principled basis for this choice, indicating a methodological gap in how best to treat such estimator pathologies.