FeatureDistributionDriftDetector

Summary

FeatureDistributionDriftDetector is RTTA's streaming implementation of: Bounded ADWIN-style drift detector for a single streaming feature distribution.

Update API

result = rtta.FeatureDistributionDriftDetector().update(feature)

The update(...) call consumes one observation using feature. advance(...) uses the same inputs when the caller wants to update state without materializing a Python return value.

Theory Of Operation

FeatureDistributionDriftDetector maintains an adaptive recent window and searches every admissible split for a statistically meaningful difference between the old and new subwindow means. The signal direction is the sign of the best accepted mean shift; accepting a split discards the older prefix.

Recurrence

Let \(z_t = feature_t\) denote the observation consumed by one update(...) call and let \(\theta\) denote constructor parameters such as window lengths, thresholds, and smoothing constants.

\[W_t=\operatorname{tail}_{max\_window}(W_{t-1}\cup\{x_t\})\]

\[\epsilon(c)=R_t \sqrt{\frac{1}{2}\log\left(\frac{4}{\delta}\right) \left(\frac{1}{c}+\frac{1}{|W_t|-c}\right)}\]

\[c^\*=\arg\max_c |\bar{x}_{c:|W_t|}-\bar{x}_{1:c}| \quad \text{s.t.}\quad |\bar{x}_{c:|W_t|}-\bar{x}_{1:c}|>\epsilon(c)\]

\[y_t = \begin{cases} \operatorname{sgn}(\bar{x}_{c^\*:|W_t|}-\bar{x}_{1:c^\*}), & c^\* \text{ exists}\\ 0, & \text{otherwise} \end{cases}\]

When a cut is accepted, the older prefix is discarded and the retained suffix becomes the next adaptive window.

The return value is the current scalar indicator value.

Implementation Notes

The recurrence is implemented in src/rtta/indicator.cpp in class FeatureDistributionDriftDetector.

Reference

Background reference