LODA¶

LODA (Lightweight on-line detector of anomalies).

LODA ¹ is an ensemble of one-dimensional histograms. Each histogram approximates the probability density of the data once it has been projected onto a sparse random vector. The anomaly score of a sample is the average negative log-likelihood of its projections across the ensemble: rare projected values yield low densities and therefore high scores.

Pevný showed that aggregating many such deliberately weak detectors yields a strong anomaly detector, competitive with much heavier methods while remaining cheap to update online.

Each projection vector is sparse: only ⌊√d⌋ of the d features have a non-zero weight, drawn from a standard normal distribution. The feature set and the projections are fixed the first time learn_one is called. Features that appear later are ignored, and missing features are treated as zeros.

Unlike the histograms used in the original paper, this implementation relies on River's streaming sketch.Histogram, which maintains a bounded number of adaptive-width bins. The density of a projected value is estimated as (count / n) / width of the bin that contains it, where width is the bin's span (or, for not-yet-merged singleton bins, the distance to the nearest neighbouring bin). Projected values that fall outside every bin are assigned a floor density, making them maximally anomalous. This keeps the detector fully online and free of any numpy dependency.

Parameters¶

• n_bins

  Type → int

  Default → 10

  Maximum number of bins in each histogram.

• n_random_cuts

  Type → int

  Default → 100

  Number of random projections (the ensemble size).

• seed

  Type → int | None

  Default → None

  Random number seed, for reproducible projections.

Attributes¶

• n_features

  Number of features seen during the first call to learn_one.

Examples¶

from river import anomaly
from river import datasets

loda = anomaly.LODA(n_bins=10, n_random_cuts=100, seed=42)

for x, y in datasets.CreditCard().take(2500):
    loda.learn_one(x)

loda.n_features

30

score = loda.score_one(x)
print(f"{score:.3f}")

3.670

Methods¶