Comprehensible counterfactual explanation on Kolmogorov-Smirnov test

The Kolmogorov-Smirnov (KS) test is popularly used in many applications, such as anomaly detection, astronomy, database security and AI systems. One challenge remained untouched how we can obtain an explanation on why a set fails the KS test. In this paper, tackle problem of producing counterfactual explanations for data failing Concept-wise, propose notion most comprehensible explanations, which accommodates both user domain knowledge explanations. Computation-wise, develop efficient algorithm MOCHE (for <u>MO</u>st <u>C</u>ompre<u>H</u>ensible <u>E</u>xplanation) that avoids enumerating checking exponential number subsets not only guarantees to produce but also orders magnitudes faster than baselines. Experiment-wise, present systematic empirical study series benchmark real datasets verify effectiveness, efficiency scalability MOCHE.