zoo.py

# MIT License
#
# Copyright (C) The Adversarial Robustness Toolbox (ART) Authors 2018
#
# Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated
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# Software.
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# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE
# WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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# SOFTWARE.
"""
This module implements the zeroth-order optimization attack `ZooAttack`. This is a black-box attack. This attack is a
variant of the Carlini and Wagner attack which uses ADAM coordinate descent to perform numerical estimation of
gradients.

| Paper link: https://arxiv.org/abs/1708.03999
"""
from __future__ import absolute_import, division, print_function, unicode_literals

import logging
from typing import Optional, Tuple, Any, TYPE_CHECKING

import numpy as np
from scipy.ndimage import zoom
from tqdm.auto import trange

from art.config import ART_NUMPY_DTYPE
from art.attacks.attack import EvasionAttack
from art.estimators.estimator import BaseEstimator
from art.estimators.classification.classifier import ClassifierMixin
from art.utils import (
    compute_success,
    get_labels_np_array,
    check_and_transform_label_format,
)

if TYPE_CHECKING:
    from art.utils import CLASSIFIER_TYPE

logger = logging.getLogger(__name__)


class ZooAttack(EvasionAttack):
    """
    The black-box zeroth-order optimization attack from Pin-Yu Chen et al. (2018). This attack is a variant of the
    C&W attack which uses ADAM coordinate descent to perform numerical estimation of gradients.

    | Paper link: https://arxiv.org/abs/1708.03999
    """

    attack_params = EvasionAttack.attack_params + [
        "confidence",
        "targeted",
        "learning_rate",
        "max_iter",
        "binary_search_steps",
        "initial_const",
        "abort_early",
        "use_resize",
        "use_importance",
        "nb_parallel",
        "batch_size",
        "variable_h",
        "verbose",
    ]
    _estimator_requirements = (BaseEstimator, ClassifierMixin)

    def __init__(
        self,
        classifier: "CLASSIFIER_TYPE",
        confidence: float = 0.0,
        targeted: bool = False,
        learning_rate: float = 1e-2,
        max_iter: int = 10,
        binary_search_steps: int = 1,
        initial_const: float = 1e-3,
        abort_early: bool = True,
        use_resize: bool = True,
        use_importance: bool = True,
        nb_parallel: int = 128,
        batch_size: int = 1,
        variable_h: float = 1e-4,
        verbose: bool = True,
    ):
        """
        Create a ZOO attack instance.

        :param classifier: A trained classifier.
        :param confidence: Confidence of adversarial examples: a higher value produces examples that are farther
               away, from the original input, but classified with higher confidence as the target class.
        :param targeted: Should the attack target one specific class.
        :param learning_rate: The initial learning rate for the attack algorithm. Smaller values produce better
               results but are slower to converge.
        :param max_iter: The maximum number of iterations.
        :param binary_search_steps: Number of times to adjust constant with binary search (positive value).
        :param initial_const: The initial trade-off constant `c` to use to tune the relative importance of distance
               and confidence. If `binary_search_steps` is large, the initial constant is not important, as discussed in
               Carlini and Wagner (2016).
        :param abort_early: `True` if gradient descent should be abandoned when it gets stuck.
        :param use_resize: `True` if to use the resizing strategy from the paper: first, compute attack on inputs
               resized to 32x32, then increase size if needed to 64x64, followed by 128x128.
        :param use_importance: `True` if to use importance sampling when choosing coordinates to update.
        :param nb_parallel: Number of coordinate updates to run in parallel. A higher value for `nb_parallel` should
               be preferred over a large batch size.
        :param batch_size: Internal size of batches on which adversarial samples are generated. Small batch sizes are
               encouraged for ZOO, as the algorithm already runs `nb_parallel` coordinate updates in parallel for each
               sample. The batch size is a multiplier of `nb_parallel` in terms of memory consumption.
        :param variable_h: Step size for numerical estimation of derivatives.
        :param verbose: Show progress bars.
        """
        super().__init__(estimator=classifier)

        if len(classifier.input_shape) == 1:
            self.input_is_feature_vector = True
            if batch_size != 1:
                raise ValueError(
                    "The current implementation of Zeroth-Order Optimisation attack only supports "
                    "`batch_size=1` with feature vectors as input."
                )
        else:
            self.input_is_feature_vector = False

        self.confidence = confidence
        self._targeted = targeted
        self.learning_rate = learning_rate
        self.max_iter = max_iter
        self.binary_search_steps = binary_search_steps
        self.initial_const = initial_const
        self.abort_early = abort_early
        self.use_resize = use_resize
        self.use_importance = use_importance
        self.nb_parallel = nb_parallel
        self.batch_size = batch_size
        self.variable_h = variable_h
        self.verbose = verbose
        self._check_params()

        # Initialize some internal variables
        self._init_size = 32
        if self.abort_early:
            self._early_stop_iters = self.max_iter // 10 if self.max_iter >= 10 else self.max_iter

        # Initialize noise variable to zero
        if self.input_is_feature_vector:
            self.use_resize = False
            self.use_importance = False
            logger.info(  # pragma: no cover
                "Disable resizing and importance sampling because feature vector input has been detected."
            )

        if self.use_resize:
            if not self.estimator.channels_first:
                dims = (batch_size, self._init_size, self._init_size, self.estimator.input_shape[-1])
            else:  # pragma: no cover
                dims = (batch_size, self.estimator.input_shape[0], self._init_size, self._init_size)
            self._current_noise = np.zeros(dims, dtype=ART_NUMPY_DTYPE)
        else:
            self._current_noise = np.zeros((batch_size,) + self.estimator.input_shape, dtype=ART_NUMPY_DTYPE)
        self._sample_prob = np.ones(self._current_noise.size, dtype=ART_NUMPY_DTYPE) / self._current_noise.size

        self.adam_mean: Optional[np.ndarray] = None
        self.adam_var: Optional[np.ndarray] = None
        self.adam_epochs: Optional[np.ndarray] = None

    def _loss(
        self, x: np.ndarray, x_adv: np.ndarray, target: np.ndarray, c_weight: np.ndarray
    ) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
        """
        Compute the loss function values.

        :param x: An array with the original input.
        :param x_adv: An array with the adversarial input.
        :param target: An array with the target class (one-hot encoded).
        :param c_weight: Weight of the loss term aiming for classification as target.
        :return: A tuple holding the current logits, `L_2` distortion and overall loss.
        """
        l2dist = np.sum(np.square(x - x_adv).reshape(x_adv.shape[0], -1), axis=1)
        ratios = [1.0] + [
            int(new_size) / int(old_size) for new_size, old_size in zip(self.estimator.input_shape, x.shape[1:])
        ]
        preds = self.estimator.predict(np.array(zoom(x_adv, zoom=ratios)), batch_size=self.batch_size)
        z_target = np.sum(preds * target, axis=1)
        z_other = np.max(
            preds * (1 - target) + (np.min(preds, axis=1) - 1)[:, np.newaxis] * target,
            axis=1,
        )

        if self.targeted:
            # If targeted, optimize for making the target class most likely
            loss = np.maximum(z_other - z_target + self.confidence, 0)
        else:
            # If untargeted, optimize for making any other class most likely
            loss = np.maximum(z_target - z_other + self.confidence, 0)

        return preds, l2dist, c_weight * loss + l2dist

    def generate(self, x: np.ndarray, y: Optional[np.ndarray] = None, **kwargs) -> np.ndarray:
        """
        Generate adversarial samples and return them in an array.

        :param x: An array with the original inputs to be attacked.
        :param y: Target values (class labels) one-hot-encoded of shape (nb_samples, nb_classes) or indices of shape
                  (nb_samples,).
        :return: An array holding the adversarial examples.
        """
        if y is not None:
            y = check_and_transform_label_format(y, nb_classes=self.estimator.nb_classes)

        # Check that `y` is provided for targeted attacks
        if self.targeted and y is None:  # pragma: no cover
            raise ValueError("Target labels `y` need to be provided for a targeted attack.")

        # No labels provided, use model prediction as correct class
        if y is None:
            y = get_labels_np_array(self.estimator.predict(x, batch_size=self.batch_size))

        if self.estimator.nb_classes == 2 and y.shape[1] == 1:  # pragma: no cover
            raise ValueError(
                "This attack has not yet been tested for binary classification with a single output classifier."
            )

        # Compute adversarial examples with implicit batching
        nb_batches = int(np.ceil(x.shape[0] / float(self.batch_size)))
        x_adv_list = []
        for batch_id in trange(nb_batches, desc="ZOO", disable=not self.verbose):
            batch_index_1, batch_index_2 = batch_id * self.batch_size, (batch_id + 1) * self.batch_size
            x_batch = x[batch_index_1:batch_index_2]
            y_batch = y[batch_index_1:batch_index_2]
            res = self._generate_batch(x_batch, y_batch)
            x_adv_list.append(res)
        x_adv = np.vstack(x_adv_list)

        # Apply clip
        if self.estimator.clip_values is not None:
            clip_min, clip_max = self.estimator.clip_values
            np.clip(x_adv, clip_min, clip_max, out=x_adv)

        # Log success rate of the ZOO attack
        logger.info(
            "Success rate of ZOO attack: %.2f%%",
            100 * compute_success(self.estimator, x, y, x_adv, self.targeted, batch_size=self.batch_size),
        )

        return x_adv

    def _generate_batch(self, x_batch: np.ndarray, y_batch: np.ndarray) -> np.ndarray:
        """
        Run the attack on a batch of images and labels.

        :param x_batch: A batch of original examples.
        :param y_batch: A batch of targets (0-1 hot).
        :return: A batch of adversarial examples.
        """
        # Initialize binary search
        c_current = self.initial_const * np.ones(x_batch.shape[0])
        c_lower_bound = np.zeros(x_batch.shape[0])
        c_upper_bound = 1e10 * np.ones(x_batch.shape[0])

        # Initialize best distortions and best attacks globally
        o_best_dist = np.inf * np.ones(x_batch.shape[0])
        o_best_attack = x_batch.copy()

        # Start with a binary search
        for bss in range(self.binary_search_steps):
            logger.debug(
                "Binary search step %i out of %i (c_mean==%f)",
                bss,
                self.binary_search_steps,
                np.mean(c_current),
            )

            # Run with 1 specific binary search step
            best_dist, best_label, best_attack = self._generate_bss(x_batch, y_batch, c_current)

            # Update best results so far
            o_best_attack[best_dist < o_best_dist] = best_attack[best_dist < o_best_dist]
            o_best_dist[best_dist < o_best_dist] = best_dist[best_dist < o_best_dist]

            # Adjust the constant as needed
            c_current, c_lower_bound, c_upper_bound = self._update_const(
                y_batch, best_label, c_current, c_lower_bound, c_upper_bound
            )

        return o_best_attack

    def _update_const(
        self,
        y_batch: np.ndarray,
        best_label: np.ndarray,
        c_batch: np.ndarray,
        c_lower_bound: np.ndarray,
        c_upper_bound: np.ndarray,
    ) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
        """
        Update constant `c_batch` from the ZOO objective. This characterizes the trade-off between attack strength and
        amount of noise introduced.

        :param y_batch: A batch of targets (0-1 hot).
        :param best_label: A batch of best labels.
        :param c_batch: A batch of constants.
        :param c_lower_bound: A batch of lower bound constants.
        :param c_upper_bound: A batch of upper bound constants.
        :return: A tuple of three batches of updated constants and lower/upper bounds.
        """

        comparison = [
            self._compare(best_label[i], np.argmax(y_batch[i])) and best_label[i] != -np.inf
            for i in range(len(c_batch))
        ]
        for i, comp in enumerate(comparison):
            if comp:
                # Successful attack
                c_upper_bound[i] = min(c_upper_bound[i], c_batch[i])
                if c_upper_bound[i] < 1e9:
                    c_batch[i] = (c_lower_bound[i] + c_upper_bound[i]) / 2
            else:
                # Failure attack
                c_lower_bound[i] = max(c_lower_bound[i], c_batch[i])
                c_batch[i] = (c_lower_bound[i] + c_upper_bound[i]) / 2 if c_upper_bound[i] < 1e9 else c_batch[i] * 10

        return c_batch, c_lower_bound, c_upper_bound

    def _compare(self, object1: Any, object2: Any) -> bool:
        """
        Check two objects for equality if the attack is targeted, otherwise check for inequality.

        :param object1: First object to compare.
        :param object2: Second object to compare.
        :return: When the attack is targeted, returns "True" if object are equal otherwise "False". When the attack is
                    untargeted, the function returns "True" when the objects are different otherwise "False".

        """
        return object1 == object2 if self.targeted else object1 != object2

    def _generate_bss(
        self, x_batch: np.ndarray, y_batch: np.ndarray, c_batch: np.ndarray
    ) -> Tuple[np.ndarray, np.ndarray, np.ndarray]:
        """
        Generate adversarial examples for a batch of inputs with a specific batch of constants.

        :param x_batch: A batch of original examples.
        :param y_batch: A batch of targets (0-1 hot).
        :param c_batch: A batch of constants.
        :return: A tuple of best elastic distances, best labels, best attacks.
        """

        x_orig = x_batch.astype(ART_NUMPY_DTYPE)
        fine_tuning = np.full(x_batch.shape[0], False, dtype=bool)
        prev_loss = 1e6 * np.ones(x_batch.shape[0])
        prev_l2dist = np.zeros(x_batch.shape[0])

        # Resize and initialize Adam
        if self.use_resize:
            x_orig = self._resize_image(x_orig, self._init_size, self._init_size, True)
            assert (x_orig != 0).any()
            x_adv = x_orig.copy()
        else:
            x_orig = x_batch
            self._reset_adam(np.prod(self.estimator.input_shape).item())
            if x_batch.shape == self._current_noise.shape:
                self._current_noise.fill(0)
            else:
                self._current_noise = np.zeros(x_batch.shape, dtype=ART_NUMPY_DTYPE)
            x_adv = x_orig.copy()

        # Initialize best distortions, best changed labels and best attacks
        best_dist = np.inf * np.ones(x_adv.shape[0])
        best_label = -np.inf * np.ones(x_adv.shape[0])
        best_attack = np.array([x_adv[i] for i in range(x_adv.shape[0])])

        for iter_ in range(self.max_iter):
            logger.debug("Iteration step %i out of %i", iter_, self.max_iter)

            # Upscaling for very large number of iterations
            if self.use_resize:
                if iter_ == 2000:
                    x_adv = self._resize_image(x_adv, 64, 64)
                    x_orig = zoom(
                        x_orig,
                        [
                            1,
                            x_adv.shape[1] / x_orig.shape[1],
                            x_adv.shape[2] / x_orig.shape[2],
                            x_adv.shape[3] / x_orig.shape[3],
                        ],
                    )
                elif iter_ == 10000:
                    x_adv = self._resize_image(x_adv, 128, 128)
                    x_orig = zoom(
                        x_orig,
                        [
                            1,
                            x_adv.shape[1] / x_orig.shape[1],
                            x_adv.shape[2] / x_orig.shape[2],
                            x_adv.shape[3] / x_orig.shape[3],
                        ],
                    )

            # Compute adversarial examples and loss
            x_adv = self._optimizer(x_adv, y_batch, c_batch)
            preds, l2dist, loss = self._loss(x_orig, x_adv, y_batch, c_batch)

            # Reset Adam if a valid example has been found to avoid overshoot
            mask_fine_tune = (~fine_tuning) & (loss == l2dist) & (prev_loss != prev_l2dist)
            fine_tuning[mask_fine_tune] = True
            self._reset_adam(self.adam_mean.size, np.repeat(mask_fine_tune, x_adv[0].size))  # type: ignore
            prev_l2dist = l2dist

            # Abort early if no improvement is obtained
            if self.abort_early and iter_ % self._early_stop_iters == 0:
                if (loss > 0.9999 * prev_loss).all():
                    break
                prev_loss = loss

            # Adjust the best result
            labels_batch = np.argmax(y_batch, axis=1)
            for i, (dist, pred) in enumerate(zip(l2dist, np.argmax(preds, axis=1))):
                if dist < best_dist[i] and self._compare(pred, labels_batch[i]):
                    best_dist[i] = dist
                    best_attack[i] = x_adv[i]
                    best_label[i] = pred

        # Resize images to original size before returning
        best_attack = np.array(best_attack)
        if self.use_resize:
            if not self.estimator.channels_first:
                best_attack = zoom(
                    best_attack,
                    [
                        1,
                        int(x_batch.shape[1]) / best_attack.shape[1],
                        int(x_batch.shape[2]) / best_attack.shape[2],
                        1,
                    ],
                )
            else:
                best_attack = zoom(
                    best_attack,
                    [
                        1,
                        1,
                        int(x_batch.shape[2]) / best_attack.shape[2],
                        int(x_batch.shape[2]) / best_attack.shape[3],
                    ],
                )

        return best_dist, best_label, best_attack

    def _optimizer(self, x: np.ndarray, targets: np.ndarray, c_batch: np.ndarray) -> np.ndarray:
        # Variation of input for computing loss, same as in original implementation
        coord_batch = np.repeat(self._current_noise, 2 * self.nb_parallel, axis=0)
        coord_batch = coord_batch.reshape(2 * self.nb_parallel * self._current_noise.shape[0], -1)

        # Sample indices to prioritize for optimization
        if self.use_importance and np.unique(self._sample_prob).size != 1:
            indices = (
                np.random.choice(
                    coord_batch.shape[-1] * x.shape[0],
                    self.nb_parallel * self._current_noise.shape[0],
                    replace=False,
                    p=self._sample_prob.flatten(),
                )
                % coord_batch.shape[-1]
            )
        else:
            try:
                indices = (
                    np.random.choice(
                        coord_batch.shape[-1] * x.shape[0],
                        self.nb_parallel * self._current_noise.shape[0],
                        replace=False,
                    )
                    % coord_batch.shape[-1]
                )
            except ValueError as error:  # pragma: no cover
                if "Cannot take a larger sample than population when 'replace=False'" in str(error):
                    raise ValueError(
                        "Too many samples are requested for the random indices. Try to reduce the number of parallel"
                        "coordinate updates `nb_parallel`."
                    ) from error

                raise error

        # Create the batch of modifications to run
        for i in range(self.nb_parallel * self._current_noise.shape[0]):
            coord_batch[2 * i, indices[i]] += self.variable_h
            coord_batch[2 * i + 1, indices[i]] -= self.variable_h

        # Compute loss for all samples and coordinates, then optimize
        expanded_x = np.repeat(x, 2 * self.nb_parallel, axis=0).reshape((-1,) + x.shape[1:])
        expanded_targets = np.repeat(targets, 2 * self.nb_parallel, axis=0).reshape((-1,) + targets.shape[1:])
        expanded_c = np.repeat(c_batch, 2 * self.nb_parallel)
        _, _, loss = self._loss(
            expanded_x,
            expanded_x + coord_batch.reshape(expanded_x.shape),
            expanded_targets,
            expanded_c,
        )
        if self.adam_mean is not None and self.adam_var is not None and self.adam_epochs is not None:
            self._current_noise = self._optimizer_adam_coordinate(
                loss,
                indices,
                self.adam_mean,
                self.adam_var,
                self._current_noise,
                self.learning_rate,
                self.adam_epochs,
                True,
            )
        else:
            raise ValueError("Unexpected `None` in `adam_mean`, `adam_var` or `adam_epochs` detected.")

        if self.use_importance and self._current_noise.shape[2] > self._init_size:
            self._sample_prob = self._get_prob(self._current_noise).flatten()

        return x + self._current_noise

    def _optimizer_adam_coordinate(
        self,
        losses: np.ndarray,
        index: np.ndarray,
        mean: np.ndarray,
        var: np.ndarray,
        current_noise: np.ndarray,
        learning_rate: float,
        adam_epochs: np.ndarray,
        proj: bool,
    ) -> np.ndarray:
        """
        Implementation of the ADAM optimizer for coordinate descent.

        :param losses: Overall loss.
        :param index: Indices of the coordinates to update.
        :param mean: The mean of the gradient (first moment).
        :param var: The uncentered variance of the gradient (second moment).
        :param current_noise: Current noise.
        :param learning_rate: Learning rate for Adam optimizer.
        :param adam_epochs: Epochs to run the Adam optimizer.
        :param proj: Whether to project the noise to the L_p ball.
        :return: Updated noise for coordinate descent.
        """
        beta1, beta2 = 0.9, 0.999

        # Estimate grads from loss variation (constant `h` from the paper is fixed to .0001)
        grads = np.array([(losses[i] - losses[i + 1]) / (2 * self.variable_h) for i in range(0, len(losses), 2)])

        # ADAM update
        mean[index] = beta1 * mean[index] + (1 - beta1) * grads
        var[index] = beta2 * var[index] + (1 - beta2) * grads ** 2

        corr = (np.sqrt(1 - np.power(beta2, adam_epochs[index]))) / (1 - np.power(beta1, adam_epochs[index]))
        orig_shape = current_noise.shape
        current_noise = current_noise.reshape(-1)
        current_noise[index] -= learning_rate * corr * mean[index] / (np.sqrt(var[index]) + 1e-8)
        adam_epochs[index] += 1

        if proj and hasattr(self.estimator, "clip_values") and self.estimator.clip_values is not None:
            clip_min, clip_max = self.estimator.clip_values
            current_noise[index] = np.clip(current_noise[index], clip_min, clip_max)

        return current_noise.reshape(orig_shape)

    def _reset_adam(self, nb_vars: int, indices: Optional[np.ndarray] = None) -> None:
        # If variables are already there and at the right size, reset values
        if self.adam_mean is not None and self.adam_mean.size == nb_vars:
            if indices is None:
                self.adam_mean.fill(0)
                self.adam_var.fill(0)  # type: ignore
                self.adam_epochs.fill(1)  # type: ignore
            else:
                self.adam_mean[indices] = 0
                self.adam_var[indices] = 0  # type: ignore
                self.adam_epochs[indices] = 1  # type: ignore
        else:
            # Allocate Adam variables
            self.adam_mean = np.zeros(nb_vars, dtype=ART_NUMPY_DTYPE)
            self.adam_var = np.zeros(nb_vars, dtype=ART_NUMPY_DTYPE)
            self.adam_epochs = np.ones(nb_vars, dtype=int)

    def _resize_image(self, x: np.ndarray, size_x: int, size_y: int, reset: bool = False) -> np.ndarray:
        if not self.estimator.channels_first:
            dims = (x.shape[0], size_x, size_y, x.shape[-1])
        else:
            dims = (x.shape[0], x.shape[1], size_x, size_y)
        nb_vars = np.prod(dims).item()

        if reset:
            # Reset variables to original size and value
            if dims == x.shape:
                resized_x = x
                if x.shape == self._current_noise.shape:
                    self._current_noise.fill(0)
                else:
                    self._current_noise = np.zeros(x.shape, dtype=ART_NUMPY_DTYPE)
            else:
                resized_x = zoom(
                    x,
                    (
                        1,
                        dims[1] / x.shape[1],
                        dims[2] / x.shape[2],
                        dims[3] / x.shape[3],
                    ),
                )
                self._current_noise = np.zeros(dims, dtype=ART_NUMPY_DTYPE)
            self._sample_prob = np.ones(nb_vars, dtype=ART_NUMPY_DTYPE) / nb_vars
        else:
            # Rescale variables and reset values
            resized_x = zoom(x, (1, dims[1] / x.shape[1], dims[2] / x.shape[2], dims[3] / x.shape[3]))
            self._sample_prob = self._get_prob(self._current_noise, double=True).flatten()
            self._current_noise = np.zeros(dims, dtype=ART_NUMPY_DTYPE)

        # Reset Adam
        self._reset_adam(nb_vars)

        return resized_x

    def _get_prob(self, prev_noise: np.ndarray, double: bool = False) -> np.ndarray:
        dims = list(prev_noise.shape)
        channel_index = 1 if self.estimator.channels_first else 3

        # Double size if needed
        if double:
            dims = [2 * size if i not in [0, channel_index] else size for i, size in enumerate(dims)]

        prob = np.empty(shape=dims, dtype=np.float32)
        image = np.abs(prev_noise)

        for channel in range(prev_noise.shape[channel_index]):
            if not self.estimator.channels_first:
                image_pool = self._max_pooling(image[:, :, :, channel], dims[1] // 8)
                if double:
                    prob[:, :, :, channel] = np.abs(zoom(image_pool, [1, 2, 2]))
                else:
                    prob[:, :, :, channel] = image_pool
            elif self.estimator.channels_first:
                image_pool = self._max_pooling(image[:, channel, :, :], dims[2] // 8)
                if double:
                    prob[:, channel, :, :] = np.abs(zoom(image_pool, [1, 2, 2]))
                else:
                    prob[:, channel, :, :] = image_pool

        prob /= np.sum(prob)

        return prob

    @staticmethod
    def _max_pooling(image: np.ndarray, kernel_size: int) -> np.ndarray:
        img_pool = np.copy(image)
        for i in range(0, image.shape[1], kernel_size):
            for j in range(0, image.shape[2], kernel_size):
                img_pool[:, i : i + kernel_size, j : j + kernel_size] = np.max(
                    image[:, i : i + kernel_size, j : j + kernel_size],
                    axis=(1, 2),
                    keepdims=True,
                )

        return img_pool

    def _check_params(self) -> None:
        if not isinstance(self.binary_search_steps, int) or self.binary_search_steps < 0:
            raise ValueError("The number of binary search steps must be a non-negative integer.")

        if not isinstance(self.max_iter, int) or self.max_iter < 0:
            raise ValueError("The number of iterations must be a non-negative integer.")

        if not isinstance(self.nb_parallel, int) or self.nb_parallel < 1:
            raise ValueError("The number of parallel coordinates must be an integer greater than zero.")

        if not isinstance(self.batch_size, int) or self.batch_size < 1:
            raise ValueError("The batch size must be an integer greater than zero.")

        if not isinstance(self.verbose, bool):
            raise ValueError("The argument `verbose` has to be of type bool.")