HDDM - RTTA

Summary

HDDM is RTTA's streaming implementation of: Hoeffding-bound drift detector for Bernoulli prediction-error streams.

Update API

result = rtta.HDDM().update(error)

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

Theory Of Operation

HDDM is a streaming classifier-error drift detector. It treats positive input values as errors and compares the current error process against the best historical baseline using the detector's bound: binomial standard error for DDM, distance-between-errors degradation for EDDM, and a Hoeffding bound for HDDM.

Recurrence

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

\[\bar{e}_t=\frac{1}{t}\sum_{i=1}^{t}\mathbf{1}[error_i>0], \qquad b_t(\delta)=\sqrt{\frac{\log(1/\delta)}{2t}}\]

\[(\bar{e}^\*_t,b^\*_t)= \arg\min_{i\le t}\left(\bar{e}_i+b_i(\delta_{drift})\right)\]

\[y_t = \begin{cases} 1, & \bar{e}_t-\bar{e}^\*_t>b_t(\delta_{drift})+b^\*_t\\ 0.5, & \bar{e}_t-\bar{e}^\*_t>b_t(\delta_{warning})+b^\*_t\\ 0, & \text{otherwise} \end{cases}\]

The return value is the current scalar indicator value.

Implementation Notes

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

Reference

Background reference