代码示例 / 计算机视觉 / 使用 Integrated Gradients 进行模型可解释性

使用 Integrated Gradients 进行模型可解释性

作者: A_K_Nain
创建日期 2020/06/02
最后修改 2020/06/02
描述: 如何获取分类模型的 Integrated Gradients。

ⓘ 本示例使用 Keras 3

在 Colab 中查看 GitHub 源代码


Integrated Gradients

Integrated Gradients 是一种将分类模型的预测归因于其输入特征的技术。它是一种模型可解释性技术:你可以使用它来可视化输入特征与模型预测之间的关系。

Integrated Gradients 是计算预测输出相对于输入特征的梯度的变体。要计算 Integrated Gradients,我们需要执行以下步骤:

  1. 确定输入和输出。在我们的例子中,输入是图像,输出是模型的最后一层(带有 softmax 激活的密集层)。

  2. 计算在特定数据点上进行预测时,哪些特征对神经网络是重要的。要识别这些特征,我们需要选择一个基线输入。基线输入可以是黑色图像(所有像素值都设置为零)或随机噪声。基线输入的形状需要与输入图像相同,例如 (299, 299, 3)。

  3. 对基线进行给定步数的插值。步数表示我们在给定输入图像的梯度近似中所需的步数。步数是一个超参数。作者建议使用 20 到 1000 之间的步数。

  4. 预处理这些插值图像并进行前向传播。

  5. 获取这些插值图像的梯度。
  6. 使用梯形法则近似梯度积分。

要深入了解 Integrated Gradients 以及此方法为何有效,请阅读这篇优秀的文章

参考文献


设置

import numpy as np
import matplotlib.pyplot as plt
from scipy import ndimage
from IPython.display import Image, display

import tensorflow as tf
import keras
from keras import layers
from keras.applications import xception


# Size of the input image
img_size = (299, 299, 3)

# Load Xception model with imagenet weights
model = xception.Xception(weights="imagenet")

# The local path to our target image
img_path = keras.utils.get_file("elephant.jpg", "https://i.imgur.com/Bvro0YD.png")
display(Image(img_path))

jpeg


Integrated Gradients 算法

def get_img_array(img_path, size=(299, 299)):
    # `img` is a PIL image of size 299x299
    img = keras.utils.load_img(img_path, target_size=size)
    # `array` is a float32 Numpy array of shape (299, 299, 3)
    array = keras.utils.img_to_array(img)
    # We add a dimension to transform our array into a "batch"
    # of size (1, 299, 299, 3)
    array = np.expand_dims(array, axis=0)
    return array


def get_gradients(img_input, top_pred_idx):
    """Computes the gradients of outputs w.r.t input image.

    Args:
        img_input: 4D image tensor
        top_pred_idx: Predicted label for the input image

    Returns:
        Gradients of the predictions w.r.t img_input
    """
    images = tf.cast(img_input, tf.float32)

    with tf.GradientTape() as tape:
        tape.watch(images)
        preds = model(images)
        top_class = preds[:, top_pred_idx]

    grads = tape.gradient(top_class, images)
    return grads


def get_integrated_gradients(img_input, top_pred_idx, baseline=None, num_steps=50):
    """Computes Integrated Gradients for a predicted label.

    Args:
        img_input (ndarray): Original image
        top_pred_idx: Predicted label for the input image
        baseline (ndarray): The baseline image to start with for interpolation
        num_steps: Number of interpolation steps between the baseline
            and the input used in the computation of integrated gradients. These
            steps along determine the integral approximation error. By default,
            num_steps is set to 50.

    Returns:
        Integrated gradients w.r.t input image
    """
    # If baseline is not provided, start with a black image
    # having same size as the input image.
    if baseline is None:
        baseline = np.zeros(img_size).astype(np.float32)
    else:
        baseline = baseline.astype(np.float32)

    # 1. Do interpolation.
    img_input = img_input.astype(np.float32)
    interpolated_image = [
        baseline + (step / num_steps) * (img_input - baseline)
        for step in range(num_steps + 1)
    ]
    interpolated_image = np.array(interpolated_image).astype(np.float32)

    # 2. Preprocess the interpolated images
    interpolated_image = xception.preprocess_input(interpolated_image)

    # 3. Get the gradients
    grads = []
    for i, img in enumerate(interpolated_image):
        img = tf.expand_dims(img, axis=0)
        grad = get_gradients(img, top_pred_idx=top_pred_idx)
        grads.append(grad[0])
    grads = tf.convert_to_tensor(grads, dtype=tf.float32)

    # 4. Approximate the integral using the trapezoidal rule
    grads = (grads[:-1] + grads[1:]) / 2.0
    avg_grads = tf.reduce_mean(grads, axis=0)

    # 5. Calculate integrated gradients and return
    integrated_grads = (img_input - baseline) * avg_grads
    return integrated_grads


def random_baseline_integrated_gradients(
    img_input, top_pred_idx, num_steps=50, num_runs=2
):
    """Generates a number of random baseline images.

    Args:
        img_input (ndarray): 3D image
        top_pred_idx: Predicted label for the input image
        num_steps: Number of interpolation steps between the baseline
            and the input used in the computation of integrated gradients. These
            steps along determine the integral approximation error. By default,
            num_steps is set to 50.
        num_runs: number of baseline images to generate

    Returns:
        Averaged integrated gradients for `num_runs` baseline images
    """
    # 1. List to keep track of Integrated Gradients (IG) for all the images
    integrated_grads = []

    # 2. Get the integrated gradients for all the baselines
    for run in range(num_runs):
        baseline = np.random.random(img_size) * 255
        igrads = get_integrated_gradients(
            img_input=img_input,
            top_pred_idx=top_pred_idx,
            baseline=baseline,
            num_steps=num_steps,
        )
        integrated_grads.append(igrads)

    # 3. Return the average integrated gradients for the image
    integrated_grads = tf.convert_to_tensor(integrated_grads)
    return tf.reduce_mean(integrated_grads, axis=0)

用于可视化梯度和 Integrated Gradients 的辅助类

class GradVisualizer:
    """Plot gradients of the outputs w.r.t an input image."""

    def __init__(self, positive_channel=None, negative_channel=None):
        if positive_channel is None:
            self.positive_channel = [0, 255, 0]
        else:
            self.positive_channel = positive_channel

        if negative_channel is None:
            self.negative_channel = [255, 0, 0]
        else:
            self.negative_channel = negative_channel

    def apply_polarity(self, attributions, polarity):
        if polarity == "positive":
            return np.clip(attributions, 0, 1)
        else:
            return np.clip(attributions, -1, 0)

    def apply_linear_transformation(
        self,
        attributions,
        clip_above_percentile=99.9,
        clip_below_percentile=70.0,
        lower_end=0.2,
    ):
        # 1. Get the thresholds
        m = self.get_thresholded_attributions(
            attributions, percentage=100 - clip_above_percentile
        )
        e = self.get_thresholded_attributions(
            attributions, percentage=100 - clip_below_percentile
        )

        # 2. Transform the attributions by a linear function f(x) = a*x + b such that
        # f(m) = 1.0 and f(e) = lower_end
        transformed_attributions = (1 - lower_end) * (np.abs(attributions) - e) / (
            m - e
        ) + lower_end

        # 3. Make sure that the sign of transformed attributions is the same as original attributions
        transformed_attributions *= np.sign(attributions)

        # 4. Only keep values that are bigger than the lower_end
        transformed_attributions *= transformed_attributions >= lower_end

        # 5. Clip values and return
        transformed_attributions = np.clip(transformed_attributions, 0.0, 1.0)
        return transformed_attributions

    def get_thresholded_attributions(self, attributions, percentage):
        if percentage == 100.0:
            return np.min(attributions)

        # 1. Flatten the attributions
        flatten_attr = attributions.flatten()

        # 2. Get the sum of the attributions
        total = np.sum(flatten_attr)

        # 3. Sort the attributions from largest to smallest.
        sorted_attributions = np.sort(np.abs(flatten_attr))[::-1]

        # 4. Calculate the percentage of the total sum that each attribution
        # and the values about it contribute.
        cum_sum = 100.0 * np.cumsum(sorted_attributions) / total

        # 5. Threshold the attributions by the percentage
        indices_to_consider = np.where(cum_sum >= percentage)[0][0]

        # 6. Select the desired attributions and return
        attributions = sorted_attributions[indices_to_consider]
        return attributions

    def binarize(self, attributions, threshold=0.001):
        return attributions > threshold

    def morphological_cleanup_fn(self, attributions, structure=np.ones((4, 4))):
        closed = ndimage.grey_closing(attributions, structure=structure)
        opened = ndimage.grey_opening(closed, structure=structure)
        return opened

    def draw_outlines(
        self,
        attributions,
        percentage=90,
        connected_component_structure=np.ones((3, 3)),
    ):
        # 1. Binarize the attributions.
        attributions = self.binarize(attributions)

        # 2. Fill the gaps
        attributions = ndimage.binary_fill_holes(attributions)

        # 3. Compute connected components
        connected_components, num_comp = ndimage.label(
            attributions, structure=connected_component_structure
        )

        # 4. Sum up the attributions for each component
        total = np.sum(attributions[connected_components > 0])
        component_sums = []
        for comp in range(1, num_comp + 1):
            mask = connected_components == comp
            component_sum = np.sum(attributions[mask])
            component_sums.append((component_sum, mask))

        # 5. Compute the percentage of top components to keep
        sorted_sums_and_masks = sorted(component_sums, key=lambda x: x[0], reverse=True)
        sorted_sums = list(zip(*sorted_sums_and_masks))[0]
        cumulative_sorted_sums = np.cumsum(sorted_sums)
        cutoff_threshold = percentage * total / 100
        cutoff_idx = np.where(cumulative_sorted_sums >= cutoff_threshold)[0][0]
        if cutoff_idx > 2:
            cutoff_idx = 2

        # 6. Set the values for the kept components
        border_mask = np.zeros_like(attributions)
        for i in range(cutoff_idx + 1):
            border_mask[sorted_sums_and_masks[i][1]] = 1

        # 7. Make the mask hollow and show only the border
        eroded_mask = ndimage.binary_erosion(border_mask, iterations=1)
        border_mask[eroded_mask] = 0

        # 8. Return the outlined mask
        return border_mask

    def process_grads(
        self,
        image,
        attributions,
        polarity="positive",
        clip_above_percentile=99.9,
        clip_below_percentile=0,
        morphological_cleanup=False,
        structure=np.ones((3, 3)),
        outlines=False,
        outlines_component_percentage=90,
        overlay=True,
    ):
        if polarity not in ["positive", "negative"]:
            raise ValueError(
                f""" Allowed polarity values: 'positive' or 'negative'
                                    but provided {polarity}"""
            )
        if clip_above_percentile < 0 or clip_above_percentile > 100:
            raise ValueError("clip_above_percentile must be in [0, 100]")

        if clip_below_percentile < 0 or clip_below_percentile > 100:
            raise ValueError("clip_below_percentile must be in [0, 100]")

        # 1. Apply polarity
        if polarity == "positive":
            attributions = self.apply_polarity(attributions, polarity=polarity)
            channel = self.positive_channel
        else:
            attributions = self.apply_polarity(attributions, polarity=polarity)
            attributions = np.abs(attributions)
            channel = self.negative_channel

        # 2. Take average over the channels
        attributions = np.average(attributions, axis=2)

        # 3. Apply linear transformation to the attributions
        attributions = self.apply_linear_transformation(
            attributions,
            clip_above_percentile=clip_above_percentile,
            clip_below_percentile=clip_below_percentile,
            lower_end=0.0,
        )

        # 4. Cleanup
        if morphological_cleanup:
            attributions = self.morphological_cleanup_fn(
                attributions, structure=structure
            )
        # 5. Draw the outlines
        if outlines:
            attributions = self.draw_outlines(
                attributions, percentage=outlines_component_percentage
            )

        # 6. Expand the channel axis and convert to RGB
        attributions = np.expand_dims(attributions, 2) * channel

        # 7.Superimpose on the original image
        if overlay:
            attributions = np.clip((attributions * 0.8 + image), 0, 255)
        return attributions

    def visualize(
        self,
        image,
        gradients,
        integrated_gradients,
        polarity="positive",
        clip_above_percentile=99.9,
        clip_below_percentile=0,
        morphological_cleanup=False,
        structure=np.ones((3, 3)),
        outlines=False,
        outlines_component_percentage=90,
        overlay=True,
        figsize=(15, 8),
    ):
        # 1. Make two copies of the original image
        img1 = np.copy(image)
        img2 = np.copy(image)

        # 2. Process the normal gradients
        grads_attr = self.process_grads(
            image=img1,
            attributions=gradients,
            polarity=polarity,
            clip_above_percentile=clip_above_percentile,
            clip_below_percentile=clip_below_percentile,
            morphological_cleanup=morphological_cleanup,
            structure=structure,
            outlines=outlines,
            outlines_component_percentage=outlines_component_percentage,
            overlay=overlay,
        )

        # 3. Process the integrated gradients
        igrads_attr = self.process_grads(
            image=img2,
            attributions=integrated_gradients,
            polarity=polarity,
            clip_above_percentile=clip_above_percentile,
            clip_below_percentile=clip_below_percentile,
            morphological_cleanup=morphological_cleanup,
            structure=structure,
            outlines=outlines,
            outlines_component_percentage=outlines_component_percentage,
            overlay=overlay,
        )

        _, ax = plt.subplots(1, 3, figsize=figsize)
        ax[0].imshow(image)
        ax[1].imshow(grads_attr.astype(np.uint8))
        ax[2].imshow(igrads_attr.astype(np.uint8))

        ax[0].set_title("Input")
        ax[1].set_title("Normal gradients")
        ax[2].set_title("Integrated gradients")
        plt.show()

让我们来试用一下

# 1. Convert the image to numpy array
img = get_img_array(img_path)

# 2. Keep a copy of the original image
orig_img = np.copy(img[0]).astype(np.uint8)

# 3. Preprocess the image
img_processed = tf.cast(xception.preprocess_input(img), dtype=tf.float32)

# 4. Get model predictions
preds = model.predict(img_processed)
top_pred_idx = tf.argmax(preds[0])
print("Predicted:", top_pred_idx, xception.decode_predictions(preds, top=1)[0])

# 5. Get the gradients of the last layer for the predicted label
grads = get_gradients(img_processed, top_pred_idx=top_pred_idx)

# 6. Get the integrated gradients
igrads = random_baseline_integrated_gradients(
    np.copy(orig_img), top_pred_idx=top_pred_idx, num_steps=50, num_runs=2
)

# 7. Process the gradients and plot
vis = GradVisualizer()
vis.visualize(
    image=orig_img,
    gradients=grads[0].numpy(),
    integrated_gradients=igrads.numpy(),
    clip_above_percentile=99,
    clip_below_percentile=0,
)

vis.visualize(
    image=orig_img,
    gradients=grads[0].numpy(),
    integrated_gradients=igrads.numpy(),
    clip_above_percentile=95,
    clip_below_percentile=28,
    morphological_cleanup=True,
    outlines=True,
)
 1/1 ━━━━━━━━━━━━━━━━━━━━ 5s 5s/step

WARNING: All log messages before absl::InitializeLog() is called are written to STDERR
I0000 00:00:1699486705.534012   86541 device_compiler.h:187] Compiled cluster using XLA!  This line is logged at most once for the lifetime of the process.

Predicted: tf.Tensor(386, shape=(), dtype=int64) [('n02504458', 'African_elephant', 0.8871446)]

png

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