# HDDM_W¶

Drift Detection Method based on Hoeffding's bounds with moving weighted average-test.

HDDM_W is an online drift detection method based on McDiarmid's bounds. HDDM_W uses the Exponentially Weighted Moving Average (EWMA) statistic as estimator.

Input: x is an entry in a stream of bits, where 1 indicates error/failure and 0 represents correct/normal values.

For example, if a classifier's prediction $$y'$$ is right or wrong w.r.t. the true target label $$y$$:

• 0: Correct, $$y=y'$$

• 1: Error, $$y \neq y'$$

Implementation based on MOA.

## Parameters¶

• drift_confidence β defaults to 0.001

Confidence to the drift

• warning_confidence β defaults to 0.005

Confidence to the warning

• lambda_val β defaults to 0.05

The weight given to recent data. Smaller values mean less weight given to recent data.

• two_sided_test β defaults to False

If True, will monitor error increments and decrements (two-sided). By default will only monitor increments (one-sided).

## Attributes¶

• drift_detected

Whether or not a drift is detected following the last update.

• warning_detected

Whether or not a drift is detected following the last update.

## Examples¶

>>> import random
>>> from river import drift

>>> rng = random.Random(42)
>>> hddm_w = drift.binary.HDDM_W()

>>> # Simulate a data stream where the first 1000 instances come from a uniform distribution
>>> # of 1's and 0's
>>> data_stream = rng.choices([0, 1], k=1000)
>>> # Increase the probability of 1's appearing in the next 1000 instances
>>> data_stream = data_stream + rng.choices([0, 1], k=1000, weights=[0.3, 0.7])

>>> print_warning = True
>>> # Update drift detector and verify if change is detected
>>> for i, x in enumerate(data_stream):
...     _ = hddm_w.update(x)
...     if hddm_w.warning_detected and print_warning:
...         print(f"Warning detected at index {i}")
...         print_warning = False
...     if hddm_w.drift_detected:
...         print(f"Change detected at index {i}")
...         print_warning = True
Warning detected at index 451
Change detected at index 1077


## Methods¶

update

Update the change detector with a single data point.

Parameters

• x (bool)

Returns

BinaryDriftDetector: self

## References¶

1. FrΓ­as-Blanco I, del Campo-Γvila J, Ramos-Jimenez G, et al. Online and non-parametric drift detection methods based on Hoeffdingβs bounds. IEEE Transactions on Knowledge and Data Engineering, 2014, 27(3): 810-823.

2. Albert Bifet, Geoff Holmes, Richard Kirkby, Bernhard Pfahringer. MOA: Massive Online Analysis; Journal of Machine Learning Research 11: 1601-1604, 2010.