class_docstr: Probabilistic Classifier Chains.
  
  The Probabilistic Classifier Chains (PCC) [^1] is a Bayes-optimal method
  based on the Classifier Chains (CC).
  
  Consider the concept of chaining classifiers as searching a path in a
  binary tree whose leaf nodes are associated with a label $y \in Y$. While
  CC searches only a single path in the aforementioned binary tree, PCC looks
  at each of the $2^l$ paths, where $l$ is the number of labels. This limits
  the applicability of the method to data sets with a small to moderate
  number of labels. The authors recommend no more than about 15 labels for
  real-world applications.
  
  Parameters
  ----------
  model
  
  Examples
  --------
  
  >>> from river import linear_model
  >>> from river import metrics
  >>> from river import multioutput
  >>> from river.datasets import synth
  
  >>> dataset = synth.Logical(seed=42, n_tiles=100)
  
  >>> model = multioutput.ProbabilisticClassifierChain(
  ...     model=linear_model.LogisticRegression()
  ... )
  
  >>> metric = metrics.multioutput.MicroAverage(metrics.Jaccard())
  
  >>> for x, y in dataset:
  ...    y_pred = model.predict_one(x)
  ...    y_pred = {k: y_pred.get(k, 0) for k in y}
  ...    metric.update(y, y_pred)
  ...    model.learn_one(x, y)
  
  >>> metric
  MicroAverage(Jaccard): 51.84%
  
  References
  ----------
  [^1]: Cheng, W., Hüllermeier, E., & Dembczynski, K. J. (2010).
        Bayes optimal multilabel classification via probabilistic classifier
        chains. In Proceedings of the 27th international conference on
        machine learning (ICML-10) (pp. 279-286).
code: def __init__(self, model: base.Classifier):
      super().__init__(model)
  
imports: from __future__ import annotations
  import collections
  import copy
  import functools
  import random
  from river import base, linear_model
  from river.utils.math import minkowski_distance, prod
label_desc: Use image node_id 1 to create a new ProbabilisticClassifierChain object from inherited base classes: ClassifierChain with example: obj = ProbabilisticClassifierChain(model)