OXTRegressor

Online Extra Trees regressor.

The online Extra Trees¹ ensemble takes some steps further into randomization when compared to Adaptive Random Forests (ARF). A subspace of the feature space is considered at each split attempt, as ARF does, and online bagging or subbagging can also be (optionally) used. Nonetheless, Extra Trees randomizes the split candidates evaluated by each leaf node (just a single split is tested by numerical feature, which brings significant speedups to the ensemble), and might also randomize the maximum depth of the forest members, as well as the size of the feature subspace processed by each of its trees' leaves.

On the other hand, OXT suffers from a cold-start problem. As the splits are random, the predictive performance in small samples is usually worse than using a deterministic split approach, such as the one used by ARF.

Parameters

• n_models

  Type → int

  Default → 10

  The number of trees in the ensemble.

• max_features

  Type → bool | str | int

  Default → sqrt

  Max number of attributes for each node split.
  - If int, then consider max_features at each split.
  - If float, then max_features is a percentage and int(max_features * n_features) features are considered per split.
  - If "sqrt", then max_features=sqrt(n_features).
  - If "log2", then max_features=log2(n_features).
  - If "random", then max_features will assume a different random number in the interval [2, n_features] for each tree leaf.
  - If None, then max_features=n_features.

• resampling_strategy

  Type → str | None

  Default → subbagging

  The chosen instance resampling strategy:
  - If None, no resampling will be done and the trees will process all instances. - If 'baggging', online bagging will be performed (sampling with replacement). - If 'subbagging', online subbagging will be performed (sampling without replacement).

• resampling_rate

  Type → int | float

  Default → 0.5

  Only valid if resampling_strategy is not None. Controls the parameters of the resampling strategy.
  . - If resampling_strategy='bagging', must be an integer greater than or equal to 1 that parameterizes the poisson distribution used to simulate bagging in online learning settings. It acts as the lambda parameter of Oza Bagging and Leveraging Bagging.
  - If resampling_strategy='subbagging', must be a float in the interval \((0, 1]\) that controls the chance of each instance being used by a tree for learning.

• detection_mode

  Type → str

  Default → all

  The concept drift detection mode in which the forest operates. Valid values are:
  - "all": creates both warning and concept drift detectors. If a warning is detected, an alternate tree starts being trained in the background. If the warning trigger escalates to a concept drift, the affected tree is replaced by the alternate tree.
  - "drop": only the concept drift detectors are created. If a drift is detected, the affected tree is dropped and replaced by a new tree.
  - "off": disables the concept drift adaptation capabilities. The forest will act as if the processed stream is stationary.

• warning_detector

  Type → base.DriftDetector | None

  Default → None

  The detector that will be used to trigger concept drift warnings. Defaults to drift.ADWIN(0.01)`.

• drift_detector

  Type → base.DriftDetector | None

  Default → None

  The detector used to detect concept drifts. Defaults to drift.ADWIN(0.001)`.

• max_depth

  Type → int | None

  Default → None

  The maximum depth the ensemble members might reach. If None, the trees will grow indefinitely.

• randomize_tree_depth

  Type → bool

  Default → False

  Whether or not randomize the maximum depth of each tree in the ensemble. If max_depth is provided, it is going to act as an upper bound to generate the maximum depth for each tree.

• track_metric

  Type → metrics.base.RegressionMetric | None

  Default → None

  The performance metric used to weight predictions. Defaults to metrics.MAE()`.

• disable_weighted_vote

  Type → bool

  Default → True

  Defines whether or not to use predictions weighted by each trees' prediction performance.

• split_buffer_size

  Type → int

  Default → 5

  Defines the size of the buffer used by the tree splitters when determining the feature range and a random split point in this interval.

• seed

  Type → int | None

  Default → None

  Random seed to support reproducibility.

• grace_period

  Type → int

  Default → 50

  [Tree parameter] Number of instances a leaf should observe between split attempts.

• delta

  Type → float

  Default → 0.01

  [Tree parameter] Allowed error in split decision, a value closer to 0 takes longer to decide.

• tau

  Type → float

  Default → 0.05

  [Tree parameter] Threshold below which a split will be forced to break ties.

• leaf_prediction

  Type → str

  Default → adaptive

  [Tree parameter] Prediction mechanism used at leaves.
  - 'mean' - Target mean
  - 'model' - Uses the model defined in leaf_model
  - 'adaptive' - Chooses between 'mean' and 'model' dynamically
  

• leaf_model

  Type → base.Regressor | None

  Default → None

  [Tree parameter] The regression model used to provide responses if leaf_prediction='model'. If not provided, an instance of linear_model.LinearRegression with the default hyperparameters is used.

• model_selector_decay

  Type → float

  Default → 0.95

  [Tree parameter] The exponential decaying factor applied to the learning models' squared errors, that are monitored if leaf_prediction='adaptive'. Must be between 0 and 1. The closer to 1, the more importance is going to be given to past observations. On the other hand, if its value approaches 0, the recent observed errors are going to have more influence on the final decision.

• nominal_attributes

  Type → list | None

  Default → None

  [Tree parameter] List of Nominal attributes. If empty, then assume that all attributes are numerical.

• min_samples_split

  Type → int

  Default → 5

  [Tree parameter] The minimum number of samples every branch resulting from a split candidate must have to be considered valid.

• binary_split

  Type → bool

  Default → False

  [Tree parameter] If True, only allow binary splits.

• max_size

  Type → int

  Default → 500

  [Tree parameter] Maximum memory (MB) consumed by the tree.

• memory_estimate_period

  Type → int

  Default → 2000000

  [Tree parameter] Number of instances between memory consumption checks.

• stop_mem_management

  Type → bool

  Default → False

  [Tree parameter] If True, stop growing as soon as memory limit is hit.

• remove_poor_attrs

  Type → bool

  Default → False

  [Tree parameter] If True, disable poor attributes to reduce memory usage.

• merit_preprune

  Type → bool

  Default → True

  [Tree parameter] If True, enable merit-based tree pre-pruning.

Attributes

• instances_per_tree

  The number of instances processed by each one of the current forest members. Each time a concept drift is detected, the count corresponding to the affected tree is reset.

• models

• n_drifts

  The number of concept drifts detected per ensemble member.

• n_tree_swaps

  The number of performed alternate tree swaps. Not applicable if the warning detectors are disabled.

• n_warnings

  The number of warnings detected per ensemble member.

• total_instances

  The total number of instances processed by the ensemble.

Examples

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

dataset = datasets.synth.Friedman(seed=42).take(5000)

model = forest.OXTRegressor(n_models=3, seed=42)

metric = metrics.RMSE()

evaluate.progressive_val_score(dataset, model, metric)

RMSE: 3.127311

Methods

learn_one

predict_one

Predict the output of features x.

Parameters

• x — 'dict'

Returns

base.typing.RegTarget: The prediction.

Notes

As the Online Extra Trees change the way in which Hoeffding Trees perform split attempts and monitor numerical input features, some of the parameters of the vanilla Hoeffding Tree algorithms are not available.

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1. Mastelini, S. M., Nakano, F. K., Vens, C., & de Leon Ferreira, A. C. P. (2022). Online Extra Trees Regressor. IEEE Transactions on Neural Networks and Learning Systems. ↩