DDM Concept Drift Detector

Background

DDM (Drift Detection Method, Gama et al. 2004) detects concept drift on a streaming classifier by tracking the running error rate $p$ and its standard error $s$. As new data arrives, if $p + s$ grows past historical minimums by enough, the detector raises warning or drift alerts. The canonical streaming-drift baseline.

Problem statement

Implement DDM(min_samples=30) as a class with update(is_error: int) -> "none" | "warn" | "drift":

• Track running $p$ (cumulative error rate) and $s = \sqrt{p(1-p)/n}$.
• Track minimums $p_{\min}, s_{\min}$ seen so far.
• Below min_samples: always return "none".
• p + s < p_{\min} + s_{\min}: update the minimums.
• p + s \ge p_{\min} + 3 s_{\min}: return "drift".
• p + s \ge p_{\min} + 2 s_{\min}: return "warn".
• Else: return "none".

Input

• min_samples — int, minimum samples before any verdict (default 30).
• update(is_error) — is_error is 0 (correct) or 1 (incorrect).

Output

update returns one of "none", "warn", "drift".

Examples

Example 1 — stable stream

Stream: 200 zeros
Verdicts: mostly "none" (no drift)

Example 2 — sudden drift triggers detection

Stream: 50 zeros, then 50 ones
Final verdict: "warn" or "drift"

Example 3 — below min_samples

Stream of length 5 with min_samples=100
Verdicts: all "none"

Constraints

• min_samples >= 2 (need at least 2 samples to compute $s$).
• State updates monotonically; the minimums never go up (they latch onto the lowest $p + s$ seen).
• Returns a str from a fixed alphabet {"none", "warn", "drift"}.

Notes

• Why 2σ / 3σ. Same Gaussian thresholds as control charts. Roughly: $> 2\sigma$ = unusual; $> 3\sigma$ = action.
• Slow recovery. DDM never lowers $p_{\min}$ after a drift event without a reset; production setups expose a reset() after retraining.