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Aggregated Mondrian Forest classifier for online learning.

This implementation is truly online1, in the sense that a single pass is performed, and that predictions can be produced anytime.

Each node in a tree predicts according to the distribution of the labels it contains. This distribution is regularized using a "Jeffreys" prior with parameter dirichlet. For each class with count labels in the node and n_samples samples in it, the prediction of a node is given by

\(\frac{count + dirichlet}{n_{samples} + dirichlet \times n_{classes}}\).

The prediction for a sample is computed as the aggregated predictions of all the subtrees along the path leading to the leaf node containing the sample. The aggregation weights are exponential weights with learning rate step and log-loss when use_aggregation is True.

This computation is performed exactly thanks to a context tree weighting algorithm. More details can be found in the paper cited in the references below.

The final predictions are the average class probabilities predicted by each of the n_estimators trees in the forest.


  • n_estimators

    Type → int

    Default → 10

    The number of trees in the forest.

  • step

    Type → float

    Default → 1.0

    Step-size for the aggregation weights. Default is 1 for classification with the log-loss, which is usually the best choice.

  • use_aggregation

    Type → bool

    Default → True

    Controls if aggregation is used in the trees. It is highly recommended to leave it as True.

  • dirichlet

    Type → float

    Default → 0.5

    Regularization level of the class frequencies used for predictions in each node. A rule of thumb is to set this to 1 / n_classes, where n_classes is the expected number of classes which might appear. Default is dirichlet = 0.5, which works well for binary classification problems.

  • split_pure

    Type → bool

    Default → False

    Controls if nodes that contains only sample of the same class should be split ("pure" nodes). Default is False, namely pure nodes are not split, but True can be sometimes better.

  • seed

    Type → int | None

    Default → None

    Random seed for reproducibility.


  • models


from river import datasets
from river import evaluate
from river import forest
from river import metrics

dataset = datasets.Bananas().take(500)

model = forest.AMFClassifier(

metric = metrics.Accuracy()

evaluate.progressive_val_score(dataset, model, metric)
Accuracy: 85.37%



Update the model with a set of features x and a label y.


  • x
  • y


Predict the label of a set of features x.


  • x — 'dict'
  • kwargs


base.typing.ClfTarget | None: The predicted label.


Predict the probability of each label for a dictionary of features x.


  • x


A dictionary that associates a probability which each label.


Only log_loss used for the computation of the aggregation weights is supported for now, namely the log-loss for multi-class classification.

  1. Mourtada, J., Gaïffas, S., & Scornet, E. (2021). AMF: Aggregated Mondrian forests for online learning. Journal of the Royal Statistical Society Series B: Statistical Methodology, 83(3), 505-533.