ChebyshevUnderSampler

Under-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: $P(|y-\bar{y}|=t)={\displaystyle \frac{{\sigma }^2}{|y-\bar{y}|}}$. The reciprocal of this probability is used for under-sampling¹ the most frequent cases. Extreme valued or rare cases have higher probabilities of selection, whereas the most frequent cases are likely to be discarded. Still, frequent cases have a small chance of being selected (controlled via the sp parameter) in case few rare instances were observed.

Parameters

• regressor (base.Regressor)

  The regression model that will receive the biased sample.

• sp (float) – defaults to 0.15

  Second chance probability. Even if an example is not initially selected for training, it still has a small chance of being selected in case the number of rare case observed so far is small.

• seed (int) – defaults to None

  Random seed to support reproducibility.

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.ChebyshevUnderSampler(
...         regressor=rules.AMRules(
...             n_min=50, delta=0.01,
...         ),
...         seed=42
...     )
... )

>>> evaluate.progressive_val_score(
...     datasets.TrumpApproval(),
...     model,
...     metrics.MAE(),
...     print_every=500
... )
[500] MAE: 1.787162
[1,000] MAE: 1.515711
[1,001] MAE: 1.515236
MAE: 1.515236

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. ↩