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

  Type → 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: 1.673902
[1,000] MAE: 1.743046
[1,001] MAE: 1.741335
MAE: 1.741335

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.

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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. ↩