# Detecting model drift using polynomial relations

Machine learning (ML) models serve critical functions, such as classifying loan applicants as good or bad risks. Each model is trained under the assumption that the data used in training, and the data used in field come from the same underlying unknown distribution. Often this assumption is broken in practice. It is desirable to identify when this occurs in order to minimize the impact on model performance. We suggest a new approach to detect change in the data distribution by identifying polynomial relations between the data features. We measure the strength of each identified relation using its R-square value. A strong polynomial relation captures a significant trait of the data which should remain stable if the data distribution does not change. We thus use a set of learned strong polynomial relations to identify drift. For a set of polynomial relations that are stronger than a given desired threshold, we calculate the amount of drift observed for that relation. The amount of drift is estimated by calculating the Bayes Factor for the polynomial relation likelihood of the baseline data versus field data. We empirically validate the approach by simulating a range of changes in three publicly-available data sets, and demonstrate the ability to identify drift using the Bayes Factor of the polynomial relation likelihood change.

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