Histogram Based Outlier Score

class dtaianomaly.anomaly_detection.HistogramBasedOutlierScore(window_size: int | str, stride: int = 1, n_bins: int | Literal['auto'] = 10, alpha: float = 0.1, tol: float = 0.5, **kwargs)

Anomaly detector based on the Histogram Based Outlier Score (HBOS) algorithm [10].

Histogram Based Outlier Score (HBOS) constructs for each feature a univariate histogram. Bins with a small height (for static bin widths) or wider bins (for dynamic bin widths) correspond to sparse regions of the feature space. Thus, values falling in these bins lay in sparse regions of the feature space and are considered more anomalous.

In this implementation, it is possible to set a window size to take the past observations into account. However, HBOS assumes feature independence. Therefore, for a time series with \(D\) attributes and a window size \(w\), HBOS constructs \(D \times w\) independent histograms, from which the anomaly score is computed.

Parameters:

• window_size (int or str) – The window size to use for extracting sliding windows from the time series. This value will be passed to compute_window_size().

• stride (int, default=1) – The stride, i.e., the step size for extracting sliding windows from the time series.

• n_bins (int or 'auto', default=10) – The number of bins for each feature. If 'auto', the birge-rozenblac method is used for automatically selecting the number of bins for each feature.

• alpha (float in [0, 1], default=0.1) – The regularizer for preventing overlfow.

• tol (float in [0, 1], default=0.5) – Parameter defining the flexibility for dealing with samples that fall outside the bins.

• **kwargs – Arguments to be passed to the PyOD histogram based outlier score.

window_size_

The effectively used window size for this anomaly detector

Type:

int

pyod_detector_

An HBOS detector of PyOD

Type:

HBOS

Examples

>>> from dtaianomaly.anomaly_detection import HistogramBasedOutlierScore
>>> from dtaianomaly.data import demonstration_time_series
>>> x, y = demonstration_time_series()
>>> hbos = HistogramBasedOutlierScore(1).fit(x)
>>> hbos.decision_function(x)
array([0.51808795, 0.51808795, 0.51808795, ..., 0.48347552, 0.48347552, 0.48347552]...)

Notes

The HBOS detector inherets from PyODAnomalyDetector.

check_is_fitted() → None

Check whether this anomaly detector is fitted or not.

Raises:

NotFittedError – If this detector is not fitted yet.

decision_function(X: ndarray) → array

Abstract method, compute anomaly scores.

Parameters:

X (array-like of shape (n_samples, n_attributes)) – Input time series.

Returns:

decision_scores – The computed anomaly scores.

Return type:

array-like of shape (n_samples)

fit(X: ndarray, y: ndarray = None, **kwargs) → BaseDetector

Abstract method, fit this detector to the given data.

Parameters:

• X (array-like of shape (n_samples, n_attributes)) – Input time series.

• y (array-like, default=None) – Ground-truth information.

Returns:

self – Returns the instance itself.

Return type:

BaseDetector

is_fitted() → bool

Return whether this anomaly detector is fitted.

Returns:

is_fitted – True if and only if this detector is fitted, and can be used for detecting anomalies.

Return type:

bool

predict_confidence(X: ndarray, X_train: ndarray = None, contamination: float = 0.05, decision_scores_given: bool = False)

Predict the confidence of the anomaly scores on the test given test data.

This method implements ExCeeD [perini2020quantifying] (Example-wise Confidence of anomaly Detectors) to estimate the confidence. ExCeed transforms the predicted decision scores to probability estimates using a Bayesian approach, which enables to assign a confidence score to each prediction which captures the uncertainty of the anomaly detector in that prediction.

Parameters:

• X (array-like of shape (n_samples, n_attributes)) – The test time series for which the confidence of anomaly scores should be predicted.

• X_train (array-like of shape (n_samples_train, n_attributes), default=None) – The training time series, which can be used as reference. If X_train=None, the test set is used as reference set.

• contamination (float, default=0.05) – The (estimated) contamination rate for the data, i.e., the expected percentage of anomalies.

• decision_scores_given (bool, default=False) – Whether the given X and X_train represent time series data or decision scores. If decision_scores_given=False (default), then the given arrays are interpreted as time series. Otherwise, they are interpreted as decision scores, as computed by decision_function().

Returns:

confidence – The confidence of this anomaly detector in each prediction in the given test time series.

Return type:

array-like of shape (n_samples)

References

[perini2020quantifying]

Perini, L., Vercruyssen, V., Davis, J. Quantifying the Confidence of Anomaly Detectors in Their Example-Wise Predictions. In: Machine Learning and Knowledge Discovery in Databases. ECML PKDD 2020. Springer, Cham, doi: 10.1007/978-3-030-67664-3_14.

predict_proba(X: ndarray) → ndarray

Predict anomaly probabilities

Estimate the probability of a sample of X being anomalous, based on the anomaly scores obtained from decision_function by rescaling them to the range of [0, 1] via min-max scaling.

Parameters:

X (array-like of shape (n_samples, n_attributes)) – Input time series.

Returns:

anomaly_scores – 1D array with the same length as X, with values in the interval [0, 1], in which a higher value implies that the instance is more likely to be anomalous.

Return type:

array-like of shape (n_samples)

Raises:

• ValueError – If scores is not a valid array.

• ValueError – If the prediction scores from ‘decision_function’ are constant, but not in the interval [0, 1], because these values can not unambiguously be transformed to an anomaly probability.

save(path: str | Path) → None

Save detector to disk as a pickle file with extension .dtai. If the given path consists of multiple subdirectories, then the not existing subdirectories are created.

Parameters:

path (str or Path) – Location where to store the detector.