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DDM

Incremental, causal technical analysis documentation

Summary

DDM is RTTA's streaming implementation of: Drift Detection Method for Bernoulli prediction-error streams.

Update API

result = rtta.DDM().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

DDM 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.

\[p_t=\frac{1}{t}\sum_{i=1}^{t}\mathbf{1}[error_i>0], \qquad s_t=\sqrt{\frac{p_t(1-p_t)}{t}}, \qquad m_t=p_t+s_t\]
\[m^\*_t=\min_{i\le t}m_i, \qquad s^\*_t=s_{\arg\min_i m_i}\]
\[y_t = \begin{cases} 1, & m_t>m^\*_t+d\,s^\*_t\\ 0.5, & m_t>m^\*_t+w\,s^\*_t\\ 0, & \text{otherwise} \end{cases}\]

The detector resets its error counts after a drift signal.

The return value is the current scalar indicator value.

Implementation Notes

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

Reference