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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def calibrate_threshold(self, pairs_valid, y_valid, strategy='accuracy', min_rate=None, beta=1.):
 """Decision threshold calibration for pairwise binary classification Method that calibrates the decision threshold (cutoff point) of the metric learner. This threshold will then be used when calling the method `predict`. The methods for picking cutoff points make use of traditional binary classification evaluation statistics such as the true positive and true negative rates and F-scores. The threshold will be found to maximize the chosen score on the validation set ``(pairs_valid, y_valid)``. See more in the :ref:`User Guide <calibration>`. Parameters strategy : str, optional (default='accuracy') The strategy to use for choosing the cutoff threshold. 'accuracy' Selects a decision threshold that maximizes the accuracy. 'f_beta' Selects a decision threshold that maximizes the f_beta score, with beta given by the parameter `beta`. 'max_tpr' Selects a decision threshold that yields the highest true positive rate with true negative rate at least equal to the value of the parameter `min_rate`. 'max_tnr' Selects a decision threshold that yields the highest true negative rate with true positive rate at least equal to the value of the parameter `min_rate`. beta : float in [0, 1], optional (default=None) Beta value to be used in case strategy == 'f_beta'. min_rate : float in [0, 1] or None, (default=None) In case strategy is 'max_tpr' or 'max_tnr' this parameter must be set to specify the minimal value for the true negative rate or true positive rate respectively that needs to be achieved. pairs_valid : array-like, shape=(n_pairs_valid, 2, n_features) The validation set of pairs to use to set the threshold. y_valid : array-like, shape=(n_pairs_valid,) The labels of the pairs of the validation set to use to set the threshold. They must be +1 for positive pairs and -1 for negative pairs. References .. [1] Receiver-operating characteristic (ROC) plots: a fundamental evaluation tool in clinical medicine, MH Zweig, G Campbell - Clinical chemistry, 1993 .. [2] most of the code of this function is from scikit-learn's PR #10117 See Also -------- sklearn.calibration : scikit-learn's module for calibrating classifiers """


    self._validate_calibration_params(strategy, min_rate, beta)

    pairs_valid, y_valid = self._prepare_inputs(pairs_valid, y_valid,
                                                type_of_inputs='tuples')

    n_samples = pairs_valid.shape[0]
    if strategy == 'accuracy':
      scores = self.decision_function(pairs_valid)
      scores_sorted_idces = np.argsort(scores)[::-1]
      scores_sorted = scores[scores_sorted_idces]
      # true labels ordered by decision_function value: (higher first)
      y_ordered = y_valid[scores_sorted_idces]
      # we need to add a threshold that will reject all points
      scores_sorted = np.concatenate([[scores_sorted[0] + 1], scores_sorted])

      # finds the threshold that maximizes the accuracy:
      cum_tp = stable_cumsum(y_ordered == 1)  # cumulative number of true
      # positives
      # we need to add the point where all samples are rejected:
      cum_tp = np.concatenate([[0.], cum_tp])
      cum_tn_inverted = stable_cumsum(y_ordered[::-1] == -1)
      cum_tn = np.concatenate([[0.], cum_tn_inverted])[::-1]
      cum_accuracy = (cum_tp + cum_tn) / n_samples
      imax = np.argmax(cum_accuracy)
      # we set the threshold to the lowest accepted score
      # note: we are working with negative distances but we want the threshold
      # to be with respect to the actual distances so we take minus sign
      self.threshold_ = - scores_sorted[imax]
      # note: if the best is to reject all points it's already one of the
      # thresholds (scores_sorted[0])
      return self

    if strategy == 'f_beta':
      precision, recall, thresholds = precision_recall_curve(
          y_valid, self.decision_function(pairs_valid), pos_label=1)

      # here the thresholds are decreasing
      # We ignore the warnings here, in the same taste as
      # https://github.com/scikit-learn/scikit-learn/blob/62d205980446a1abc1065
      # f4332fd74eee57fcf73/sklearn/metrics/classification.py#L1284
      with np.errstate(divide='ignore', invalid='ignore'):
        f_beta = ((1 + beta**2) * (precision * recall) /
                  (beta**2 * precision + recall))
      # We need to set nans to zero otherwise they will be considered higher
      # than the others (also discussed in https://github.com/scikit-learn/
      # scikit-learn/pull/10117/files#r262115773)
      f_beta[np.isnan(f_beta)] = 0.
      imax = np.argmax(f_beta)
      # we set the threshold to the lowest accepted score
      # note: we are working with negative distances but we want the threshold
      # to be with respect to the actual distances so we take minus sign
      self.threshold_ = - thresholds[imax]
      # Note: we don't need to deal with rejecting all points (i.e. threshold =
      # max_scores + 1), since this can never happen to be optimal
      # (see a more detailed discussion in test_calibrate_threshold_extreme)
      return self

    fpr, tpr, thresholds = roc_curve(y_valid,
                                     self.decision_function(pairs_valid),
                                     pos_label=1)
    # here the thresholds are decreasing
    fpr, tpr, thresholds = fpr, tpr, thresholds

    if strategy in ['max_tpr', 'max_tnr']:
      if strategy == 'max_tpr':
        indices = np.where(1 - fpr >= min_rate)[0]
        imax = np.argmax(tpr[indices])

      if strategy == 'max_tnr':
        indices = np.where(tpr >= min_rate)[0]
        imax = np.argmax(1 - fpr[indices])

      imax_valid = indices[imax]
      # note: we are working with negative distances but we want the threshold
      # to be with respect to the actual distances so we take minus sign
      if indices[imax] == len(thresholds):  # we want to accept everything
        self.threshold_ = - (thresholds[imax_valid] - 1)
      else:
        # thanks to roc_curve, the first point will always be max_scores
        # + 1, see: https://github.com/scikit-learn/scikit-learn/pull/13523
        self.threshold_ = - thresholds[imax_valid]
      return self