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 \(\overline{y}\) 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: \(P(|y - \overline{y}|=t) = \dfrac{\sigma^2}{|y-\overline{y}|}\). 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

  Type → base.Regressor

  The regression model that will receive the biased sample.

• sp

  Type → float

  Default → 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

  Type → int | None

  Default → 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.

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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. ↩