# HDDM_A¶

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

HDDM_A is a drift detection method based on the Hoeffding’s inequality. HDDM_A uses the average as estimator. It receives as input a stream of real values and returns the estimated status of the stream: STABLE, WARNING or DRIFT.

Input: value must be a binary signal, where 1 indicates error. 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 – defaults to 0.001

Confidence to the drift

• warning_confidence – defaults to 0.005

Confidence to the warning

• two_sided_test – defaults to False

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

## Attributes¶

• change_detected

Concept drift alarm. True if concept drift is detected.

• warning_detected

Warning zone alarm. Indicates if the drift detector is in the warning zone. Applicability depends on each drift detector implementation. True if the change detector is in the warning zone.

## Examples¶

>>> import numpy as np
>>> from river.drift import HDDM_A
>>> np.random.seed(12345)

>>> hddm_a = HDDM_A()

>>> # Simulate a data stream as a normal distribution of 1's and 0's
>>> data_stream = np.random.randint(2, size=2000)
>>> # Change the data distribution from index 999 to 1500, simulating an
>>> # increase in error rate (1 indicates error)
>>> data_stream[999:1500] = 1

>>> # Update drift detector and verify if change is detected
>>> for i, val in enumerate(data_stream):
...     in_drift, in_warning = hddm_a.update(val)
...     if in_drift:
...         print(f"Change detected at index {i}, input value: {val}")
Change detected at index 1013, input value: 1


## Methods¶

clone

Return a fresh estimator with the same parameters.

The clone has the same parameters but has not been updated with any data. This works by looking at the parameters from the class signature. Each parameter is either - recursively cloned if it's a River classes. - deep-copied via copy.deepcopy if not. If the calling object is stochastic (i.e. it accepts a seed parameter) and has not been seeded, then the clone will not be idempotent. Indeed, this method's purpose if simply to return a new instance with the same input parameters.

reset

Reset the change detector.

update

Update the change detector with a single data point.

Parameters

• value (numbers.Number)

Returns

tuple: A tuple (drift, warning) where its elements indicate if a drift or a warning is detected.

## References¶

1. Frías-Blanco I, del Campo-Ávila J, Ramos-Jimenez G, et al. Online and non-parametric drift detection methods based on Hoeffding’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.