code: from __future__ import annotations
  from typing import Tuple, NoReturn
  from ...base import BaseEstimator
  import numpy as np
  from ...metrics import misclassification_error
  from itertools import product
  
  
  class DecisionStump(BaseEstimator):
      """
      A decision stump classifier for {-1,1} labels according to the CART algorithm
  
      Attributes
      ----------
      self.threshold_ : float
          The threshold by which the data is split
  
      self.j_ : int
          The index of the feature by which to split the data
  
      self.sign_: int
          The label to predict for samples where the value of the j'th feature is about the threshold
      """
  
      def __init__(self) -> DecisionStump:
          """
          Instantiate a Decision stump classifier
          """
          super().__init__()
          self.threshold_, self.j_, self.sign_ = None, None, None
  
      def _fit(self, X: np.ndarray, y: np.ndarray) -> NoReturn:
          """
          fits a decision stump to the given data
  
          Parameters
          ----------
          X : ndarray of shape (n_samples, n_features)
              Input data to fit an estimator for
  
          y : ndarray of shape (n_samples, )
              Responses of input data to fit to
          """
          min_error = 1
          # Run on all sign combinations instead of determining the majority
          for feature_index, sign in product(range(X.shape[1]),
                                             np.unique(np.sign(y))):
              threshold, error = self._find_threshold(X[:, feature_index], y,
                                                      sign)
              if error <= min_error:
                  min_error = error
                  self.threshold_ = threshold
                  self.sign_ = sign
                  self.j_ = feature_index
  
      def _predict(self, X: np.ndarray) -> np.ndarray:
          """
          Predict responses for given samples using fitted estimator
  
          Parameters
          ----------
          X : ndarray of shape (n_samples, n_features)
              Input data to predict responses for
  
          Returns
          -------
          responses : ndarray of shape (n_samples, )
              Predicted responses of given samples
  
          Notes
          -----
          Feature values strictly below threshold are predicted as `-sign` whereas values which equal
          to or above the threshold are predicted as `sign`
          """
          return np.where(X[:, self.j_] < self.threshold_, -self.sign_,
                          self.sign_)
  
      def _find_threshold(self, values: np.ndarray, labels: np.ndarray,
                          sign: int) -> Tuple[float, float]:
          """
          Given a feature vector and labels, find a threshold by which to perform a split
          The threshold is found according to the value minimizing the misclassification
          error along this feature
  
          Parameters
          ----------
          values: ndarray of shape (n_samples,)
              A feature vector to find a splitting threshold for
  
          labels: ndarray of shape (n_samples,)
              The labels to compare against
  
          sign: int
              Predicted label assigned to values equal to or above threshold
  
          Returns
          -------
          thr: float
              Threshold by which to perform split
  
          thr_err: float between 0 and 1
              Misclassificaiton error of returned threshold
  
          Notes
          -----
          For every tested threshold, values strictly below threshold are predicted as `-sign` whereas values
          which equal to or above the threshold are predicted as `sign`
          """
          sorted_values = values[values.argsort()]
          sorted_labels = labels[values.argsort()]
          error_count = np.sum(np.abs(sorted_labels[
                                          np.not_equal(np.sign(sorted_labels),
                                                       np.ones(
                                                           sorted_values.shape[
                                                               0]) * sign)]))
  
          def calc_thr_value_error(i):
              """
              Calculates the misclassificaiton error of the threshold with
              The value in index i
  
              Parameters
              ----------
              i: int
                  The index of the value in the sorted_values array
  
              Returns
              -------
              thr_err: float between 0 and 1
                  Misclassificaiton error of the threshold
  
              """
              nonlocal error_count
              if i == 0:
                  return error_count
              if np.sign(sorted_labels[i - 1]) == -sign:
                  error_count -= np.abs(sorted_labels[i - 1])
              else:
                  error_count += np.abs(sorted_labels[i - 1])
              return error_count
  
          errors = np.vectorize(calc_thr_value_error)(
              np.arange(sorted_values.shape[0]))
          min_error_index = np.argmin(errors)
          return sorted_values[min_error_index], errors[min_error_index]
  
      def _loss(self, X: np.ndarray, y: np.ndarray) -> float:
          """
          Evaluate performance under misclassification loss function
  
          Parameters
          ----------
          X : ndarray of shape (n_samples, n_features)
              Test samples
  
          y : ndarray of shape (n_samples, )
              True labels of test samples
  
          Returns
          -------
          loss : float
              Performance under missclassification loss function
          """
          return misclassification_error(np.sign(y), np.sign(self.predict(X)))
  
apis: numpy.ones numpy.sign numpy.vectorize numpy.argmin numpy.abs numpy.arange numpy.where