ChebyshevOverSampler

Over-sampling for imbalanced regression using Chebyshev's inequality.

Chebyshev's inequality can be used to define the probability of target observations being frequent values (w.r.t. the distribution mean).

Let \(Y\) be a random variable with finite expected value \(\overline{y}\) and non-zero variance \(\sigma^2\). For any real number \(t > 0\), the Chebyshev's inequality states that, for a wide class of unimodal probability distributions: \(Pr(|y-\overline{y}| \ge t\sigma) \le \dfrac{1}{t^2}\).

Taking \(t=\dfrac{|y-\overline{y}|}{\sigma}\), and assuming \(t > 1\), the Chebyshev’s inequality for an observation \(y\) becomes: \(P(|y - \overline{y}|=t) = \dfrac{\sigma^2}{|y-\overline{y}|}\).

Alternatively, one can use \(t\) directly to estimate a frequency weight \(\kappa = \lceil t\rceil\) and define an over-sampling strategy for extreme and rare target values¹. Each incoming instance is used \(\kappa\) times to update the underlying regressor. Frequent target values contribute only once to the underlying regressor, whereas rares cases are used multiple times for training.

Parameters

• regressor (base.Regressor)

  The regression model that will receive the biased sample.

Examples

>>> from river import datasets
>>> from river import evaluate
>>> from river import imblearn
>>> from river import metrics
>>> from river import preprocessing
>>> from river import rules

>>> model = (
...     preprocessing.StandardScaler() |
...     imblearn.ChebyshevOverSampler(
...         regressor=rules.AMRules(
...             n_min=50, delta=0.01
...         )
...     )
... )

>>> evaluate.progressive_val_score(
...     datasets.TrumpApproval(),
...     model,
...     metrics.MAE(),
...     print_every=500
... )
[500] MAE: 1.682627
[1,000] MAE: 1.761306
MAE: 1.759576

Methods

learn_one

Fits to a set of features x and a real-valued target y.

Parameters

• x
• y
• kwargs

Returns

self

predict_one

Predict the output of features x.

Parameters

• x

Returns

The prediction.

References

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1. Aminian, Ehsan, Rita P. Ribeiro, and João Gama. "Chebyshev approaches for imbalanced data streams regression models." Data Mining and Knowledge Discovery 35.6 (2021): 2389-2466. ↩