The classical two-sample test of Kolmogorov-Smirnov(KS) is widely used to test whether empirical samples come from the same distribution. Even though most statistical packages provide an implementation, carrying out the test in big data settings can be challenging because it requires a full sort of the data. The popular Apache Spark system for big data processing provides a 1-sample KS test, but not the 2-sample version. Moreover, recent Spark versions provide the approxQuantile method for querying $\epsilon$-approximate quantiles. We build on approxQuantile to propose a variation of the classical Kolmogorov-Smirnov two-sample test that constructs approximate cumulative distribution functions (CDF) from $\epsilon$-approximate quantiles. We derive error bounds of the approximate CDF and show how to use this information to carry out KS tests. Psuedocode for the approach requires 15 executable lines. A Python® implementation appears in the appendix.

Actively monitoring machine learning models during production operations helps ensure prediction quality and detection and remediation of unexpected or undesired conditions. Monitoring models already deployed in big data environments brings the additional challenges of adding monitoring in parallel to the existing modelling workflow and controlling resource requirements. In this paper, we describe (1) a framework for monitoring machine learning models; and, (2) its implementation for a big data supply chain application. We use our implementation to study drift in model features, predictions, and performance on three real data sets. We compare hypothesis test and information theoretic approaches to drift detection in features and predictions using the Kolmogorov-Smirnov distance and Bhattacharyya coefficient. Results showed that model performance was stable over the evaluation period. Features and predictions showed statistically significant drifts; however, these drifts were not linked to changes in model performance during the time of our study.