def infer(self, x: np.ndarray, y: np.ndarray | None = None, **kwargs) -> np.ndarray:
        """
        Infer the attacked feature.

        If the model's prediction coincides with the real prediction for the sample for a single value, choose it as the
        predicted value. If not, fall back to the Fredrikson method (without phi)

        :param x: Input to attack. Includes all features except the attacked feature.
        :param y: Original model's predictions for x.
        :param values: Possible values for attacked feature.
        :type values: list
        :param priors: Prior distributions of attacked feature values. Same size array as `values`.
        :type priors: list
        :return: The inferred feature values.
        """
        if "priors" not in kwargs:  # pragma: no cover
            raise ValueError("Missing parameter `priors`.")
        if "values" not in kwargs:  # pragma: no cover
            raise ValueError("Missing parameter `values`.")
        priors: list | None = kwargs.get("priors")
        values: list | None = kwargs.get("values")

        if self.estimator.input_shape[0] != x.shape[1] + 1:  # pragma: no cover
            raise ValueError("Number of features in x + 1 does not match input_shape of classifier")
        if priors is None or values is None:  # pragma: no cover
            raise ValueError("`priors` and `values` are required as inputs.")
        if len(priors) != len(values):  # pragma: no cover
            raise ValueError("Number of priors does not match number of values")
        if y is not None and y.shape[0] != x.shape[0]:  # pragma: no cover
            raise ValueError("Number of rows in x and y do not match")
        if self.attack_feature >= x.shape[1]:  # pragma: no cover
            raise ValueError("attack_feature must be a valid index to a feature in x")

        n_values = len(values)
        n_samples = x.shape[0]

        # Will contain the model's predictions for each value
        pred_values = []
        # Will contain the probability of each value
        prob_values = []

        for i, value in enumerate(values):
            # prepare data with the given value in the attacked feature
            v_full = np.full((n_samples, 1), value).astype(x.dtype)
            x_value = np.concatenate((x[:, : self.attack_feature], v_full), axis=1)
            x_value = np.concatenate((x_value, x[:, self.attack_feature :]), axis=1)

            # Obtain the model's prediction for each possible value of the attacked feature
            pred_value = [np.argmax(arr) for arr in self.estimator.predict(x_value)]
            pred_values.append(pred_value)

            # find the relative probability of this value for all samples being attacked
            prob_value = [
                (
                    (self.estimator.get_samples_at_node(self.estimator.get_decision_path([row])[-1]) / n_samples)
                    * priors[i]
                )
                for row in x_value
            ]
            prob_values.append(prob_value)

        # Find the single value that coincides with the real prediction for the sample (if it exists)
        pred_rows = zip(*pred_values)
        predicted_pred = []
        for row_index, row in enumerate(pred_rows):
            if y is not None:
                matches = [1 if row[value_index] == y[row_index] else 0 for value_index in range(n_values)]
                match_values = [
                    values[value_index] if row[value_index] == y[row_index] else 0 for value_index in range(n_values)
                ]
            else:
                matches = [0 for _ in range(n_values)]
                match_values = [0 for _ in range(n_values)]
            predicted_pred.append(sum(match_values) if sum(matches) == 1 else None)

        # Choose the value with the highest probability for each sample
        predicted_prob = [np.argmax(list(prob)) for prob in zip(*prob_values)]

        return np.array(
            [
                value if value is not None else values[predicted_prob[index]]
                for index, value in enumerate(predicted_pred)
            ]
        )

        Infer the attacked feature.

        If the model's prediction coincides with the real prediction for the sample for a single value, choose it as the
        predicted value. If not, fall back to the Fredrikson method (without phi)

        :param x: Input to attack. Includes all features except the attacked feature.
        :param y: Original model's predictions for x.
        :param values: Possible values for attacked feature.
        :type values: list
        :param priors: Prior distributions of attacked feature values. Same size array as `values`.
        :type priors: list
        :return: The inferred feature values.
        
art/attacks/inference/attribute_inference/white_box_decision_tree.py