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 $\bar{y}$ 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: $Pr(|y-\bar{y}|\ge t\sigma )\le {\displaystyle \frac{1}{t^2}}$.

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

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
[1,001] MAE: 1.759576
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
• kwargs

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. ↩