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Data drift monitoring: hypothesis tests or statistical distances?

Today, I would like to talk about a tough and important subject in my opinion: data drift monitoring.

Data drift monitoring is critical. Data drift leads to model performance decrease. At the same time, IMHO, it’s hard to get a satisfactory solution for at least two reasons:

  • It’s challenging to develop a custom solution.
  • It’s laborious to know if it is preferable to compute statistical distances or try to reject a hypothesis test with a p-value?

What is data drift?

Data drift is when you get such a change in your coming data that it can impact the performance of the model.

What I name data drift has synonyms such as data shift. The word gets also many subnames to describe the specificities of each kind of data drift. You can get gradual drift, abrupt drift, extended drift, etc.

I think it’s important to understand that there are many kinds of drifts and that they don’t mean the same thing.

  • A short but abrupt drift can be due to a problem in your data.
  • An extended abrupt drift can be due to a recession.
  • A seasonal drift can be due to the seasons.

You can see all these nuances in the paper Characterizing Concept Drift by Geoffrey I Webb, Roy Hyde, Hong Cao, Hai-Long Nguyen and François Petitjean.

How to monitor data drift?

There are two solutions that are presented in the literature.

Statistical distances

I get the impression that the favourite one is computing a distance measure between your different distributions. You can use wasserstein distance, mahalanobis distance, euclidean distance etc. Among all of them, you must choose one. Hellinger distance is the preferred one of the paper Survey of distance measures for quantifying concept drift and shift in numeric data written by Igor Goldenberg and Geoffrey I Webb.

They built different tests and find Hellinger distance more suitable because this distance is robust and provide an “absolute” value, bounded between 0 and 1.

Martin Schmidtz, the author of the article How to Detect Drifting Models explains that he doesn’t think hypothesis tests useful for monitoring data drift:

A low p-value only means that we cannot confirm it. This does not mean that we can prove that these distributions are different! Not very useful… Martin Schmidtz

So I asked myself—isn’t there something else to use? And there is—distance measures for distributions! Martin Schmidtz

The big winner seems to be: statistical distances.

Hypothesis tests

A paper struck me recently: Monitoring and explainability of models in production written by Janis Klaise, Arnaud Van Looveren, Clive Cox, Giovanni Vacanti and Alexandru Coca.

The authors speak about hypothesis tests to monitor data drift.

I had a discussion with one of the authors and found his explanation quite clarifying.

The distance between two distributions doesn’t tell you when you have to be concerned. You must set a threshold to send an alert. This is what a statistical test does. p-value is surely not the best metric. But at least, it’s easier to understand a p-value than a wasserstein distance.

The paper talks about a library I definitely want to test: alibi-detect. It was designed to detect data drift with hypothesis tests: Kolmogorov-Smirnov and Maximum Mean Discrepancy.


To answer the question previously asked Data drift monitoring: hypothesis tests or statistical distances?, I don’t know. Data Drift is currently an open research area. I guess it’s normal not to know. What I definitely believe is that it’s a tough but important topic. Then I would say it’s better to do something - hypothesis tests or statistical distances - than nothing.

Azure Machine learning or Mona Labs proposes off-the-shelf solutions.

Thank you for reading.