class mars.learn.ensemble.IsolationForest(*, n_estimators=100, max_samples='auto', contamination='auto', max_features=1.0, bootstrap=False, random_state=None, warm_start=False)[source]

Isolation Forest Algorithm.

Return the anomaly score of each sample using the IsolationForest algorithm

The IsolationForest ‘isolates’ observations by randomly selecting a feature and then randomly selecting a split value between the maximum and minimum values of the selected feature.

Since recursive partitioning can be represented by a tree structure, the number of splittings required to isolate a sample is equivalent to the path length from the root node to the terminating node.

This path length, averaged over a forest of such random trees, is a measure of normality and our decision function.

Random partitioning produces noticeably shorter paths for anomalies. Hence, when a forest of random trees collectively produce shorter path lengths for particular samples, they are highly likely to be anomalies.

Read more in the User Guide.

  • n_estimators (int, default=100) – The number of base estimators in the ensemble.

  • max_samples ("auto", int or float, default="auto") –

    The number of samples to draw from X to train each base estimator.
    • If int, then draw max_samples samples.

    • If float, then draw max_samples * X.shape[0] samples.

    • If “auto”, then max_samples=min(256, n_samples).

    If max_samples is larger than the number of samples provided, all samples will be used for all trees (no sampling).

  • contamination ('auto' or float, default='auto') –

    The amount of contamination of the data set, i.e. the proportion of outliers in the data set. Used when fitting to define the threshold on the scores of the samples.

    • If ‘auto’, the threshold is determined as in the original paper.

    • If float, the contamination should be in the range (0, 0.5].

  • max_features (int or float, default=1.0) –

    The number of features to draw from X to train each base estimator.

    • If int, then draw max_features features.

    • If float, then draw max_features * X.shape[1] features.

  • bootstrap (bool, default=False) – If True, individual trees are fit on random subsets of the training data sampled with replacement. If False, sampling without replacement is performed.

  • random_state (int, RandomState instance or None, default=None) –

    Controls the pseudo-randomness of the selection of the feature and split values for each branching step and each tree in the forest.

    Pass an int for reproducible results across multiple function calls. See Glossary.

  • warm_start (bool, default=False) – When set to True, reuse the solution of the previous call to fit and add more estimators to the ensemble, otherwise, just fit a whole new forest. See the Glossary.


The child estimator template used to create the collection of fitted sub-estimators.


ExtraTreeRegressor instance


The collection of fitted sub-estimators.


list of ExtraTreeRegressor instances


The subset of drawn features for each base estimator.


list of ndarray


The actual number of samples.




Offset used to define the decision function from the raw scores. We have the relation: decision_function = score_samples - offset_. offset_ is defined as follows. When the contamination parameter is set to “auto”, the offset is equal to -0.5 as the scores of inliers are close to 0 and the scores of outliers are close to -1. When a contamination parameter different than “auto” is provided, the offset is defined in such a way we obtain the expected number of outliers (samples with decision function < 0) in training.




The implementation is based on an ensemble of ExtraTreeRegressor. The maximum depth of each tree is set to ceil(log_2(n)) where \(n\) is the number of samples used to build the tree (see (Liu et al., 2008) for more details).



Liu, Fei Tony, Ting, Kai Ming and Zhou, Zhi-Hua. “Isolation forest.” Data Mining, 2008. ICDM’08. Eighth IEEE International Conference on.


Liu, Fei Tony, Ting, Kai Ming and Zhou, Zhi-Hua. “Isolation-based anomaly detection.” ACM Transactions on Knowledge Discovery from Data (TKDD) 6.1 (2012): 3.

See also


An object for detecting outliers in a Gaussian distributed dataset.


Unsupervised Outlier Detection. Estimate the support of a high-dimensional distribution. The implementation is based on libsvm.


Unsupervised Outlier Detection using Local Outlier Factor (LOF).


>>> from mars.learn.ensemble import IsolationForest
>>> X = [[-1.1], [0.3], [0.5], [100]]
>>> clf = IsolationForest(random_state=0).fit(X)
>>> clf.predict([[0.1], [0], [90]])
array([ 1,  1, -1])
__init__(*, n_estimators=100, max_samples='auto', contamination='auto', max_features=1.0, bootstrap=False, random_state=None, warm_start=False)[source]


__init__(*[, n_estimators, max_samples, ...])

decision_function(X[, session, run_kwargs])

Average anomaly score of X of the base classifiers.

fit(X[, y, sample_weight, session, run_kwargs])

Fit estimator.

fit_predict(X[, y])

Perform fit on X and returns labels for X.

predict(X[, session, run_kwargs])

Predict if a particular sample is an outlier or not.

score_samples(X[, session, run_kwargs])

Opposite of the anomaly score defined in the original paper.