DWT_MLEAD

class dtaianomaly.anomaly_detection.DWT_MLEAD(start_level: int = 3, quantile_boundary_type: Literal['percentile'] = 'percentile', quantile_epsilon: float = 0.01, padding_mode: Literal['constant', 'edge', 'linear_ramp', 'maximum', 'mean', 'median', 'minimum', 'reflect', 'symmetric', 'wrap', 'empty'] = 'wrap')[source]

Anomaly detection based on the Discrete Wavelet Transform [36].

DWT-MLEAD (Discrete Wavelet Transform and Maximum Likelihood Estimation for Anomaly Detection) first performs multilevel DWT using Haar wavelets. Next, for each window in the obtained coefficients, a likelihood is estimated using a Guassian distribution. A boundary on the likelihood is computed within each DWT-level based on the quantiles, and the likelihood estimates that are below the boundary are flagged as anomalous. The final anomaly score is then computed as the number of times an observation was in an anomalous window.

Parameters:

start_levelint, default=3: The first level for computing the Discrete Wavelet Transform.
quantile_boundary_type{‘percentile’}, default=’percentile’: Method for putting a boundary on the likelihood estimates within each DWT-level. 'percentile' will consider a quantile_epsilon of the windows as anomalous.
quantile_epsilonfloat, default=0.01: The percentile used as threshold on the likelihood estimates.
padding_mode{‘constant’, ‘edge’, ‘linear_ramp’, ‘maximum’, ‘mean’, ‘median’, ‘minimum’, ‘reflect’, ‘symmetric’, ‘wrap’, ‘empty’}, default=’wrap’: Mode for padding the time series, which is passed to numpy.pad.

Notes

The implementation is based on aeon and TimeEval. These made the following modifications compared to original paper [36]:

We use window sizes for the DWT coefficients that decrease with the level number because otherwise we would have too few items to slide the window over.
We exclude the highest level coefficients because they contain only a single entry and are, thus, not suitable for sliding a window of length 2 over it.
We have not implemented the Monte Carlo quantile boundary type yet.
We do not perform the anomaly clustering step to determine the anomaly centers. Instead, we return the anomaly scores for each timestep in the original time series.

In addition, we add the following extension:

aeon uses 'wrap' padding and TimeEval uses 'periodic' padding. Initial experiments show that different values may lead to quite different anomaly scores. Therefore, we included the padding as a parameter of DWT-MLEAD.

Examples

>>> from dtaianomaly.anomaly_detection import DWT_MLEAD
>>> from dtaianomaly.data import demonstration_time_series
>>> x, y = demonstration_time_series()
>>> dwt_mlead = DWT_MLEAD()  # No fitting is necessary
>>> dwt_mlead.decision_function(x)
array([ 0.,  0.,  0., ..., 12., 12., 12.]...)

check_is_fitted() → None

Raise an error if this object is not fitted.

Check whether this object is fitted, and if it is not fitted, an exception is thrown.

Raises:

NotFittedError: If this object is not fitted.

decision_function(X: ndarray) → array

Compute anomaly scores.

Compute the anomaly scores for the given time series using this detector.

Parameters:

Xarray-like of shape (n_samples, n_attributes): Input time series.

Returns:

array-like of shape (n_samples): The computed anomaly scores.

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

Fit this detector.

Fit this detector to the given data.

Parameters:

Xarray-like of shape (n_samples, n_attributes): Input time series.
yarray-like, default=None: Ground-truth information.
**kwargs: Additional parameters to be used to fit the anomaly detector.

Returns:

BaseDetector: Returns the instance itself.

is_fitted() → bool

Check whether this object is fitted.

Check whether all the attributes of this object that end with an underscore (‘_’) has been initialized.

Returns:

bool: True if and only if all the attributes of this object ending with ‘_’ are initialized.

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 [26].

This method implements ExCeeD (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:

Xarray-like of shape (n_samples, n_attributes): The test time series for which the confidence of anomaly scores should be predicted.
X_trainarray-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.
contaminationfloat, default=0.05: The (estimated) contamination rate for the data, i.e., the expected percentage of anomalies.
decision_scores_givenbool, 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:

array-like of shape (n_samples): The confidence of this anomaly detector in each prediction in the given test time series.

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:

Xarray-like of shape (n_samples, n_attributes): Input time series.

Returns:

array-like of shape (n_samples): 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.

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.

requires_fitting() → bool

Check whether this object requires fitting.

Check whether any of the attributes of this object ends with an underscore (‘_’), which indicates that the attribute is set when the object is fitted. Note that this method does not check whether the object is fitted, i.e., whether the attributes have been set.

Returns:

bool: True if and only if this object has attributes that end with ‘_’.

save(path: str | Path) → None

Save this detector.

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:

pathstr or Path: Location where to store the detector.