【导读】集成梯度是一种用于将分类模型的预测归因于其输入特征的技术。这是一种模型可解释性技术:它来可视化输入要素和模型预测之间的关系。
原文链接:
https://keras.io/examples/vision/integrated_gradients/
介绍
集成梯度是在计算预测输出相对于输入特征的梯度时的变体。要计算集成梯度,我们需要执行以下步骤:
1. 识别输入和输出。在我们的例子中,输入是图像,输出是模型的最后一层(具有softmax激活的Dense层)。
2.在对特定数据点进行预测时,计算哪些特征对神经网络很重要。为了识别这些特征,我们需要选择一个基线输入。基线输入可以是黑色图像(所有像素值均设置为零)或随机噪声。基线输入的形状需要与我们的输入图像相同,例如(299,299,3)。
3. 在给定的步骤数内插基线。步数表示对于给定的输入图像,我们需要进行梯度近似的步骤。步骤数是一个超参数。作者建议使用20到1000步之间的任何步长。
4. 预处理这些插值图像并进行正向传递。
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。
设置
import numpy as np
import matplotlib.pyplot as plt
from scipy import ndimage
from IPython.display import Image
import tensorflow as tf
from tensorflow import keras
from tensorflow.keras import layers
from tensorflow.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))
显示图片
集成梯度算法
def get_img_array(img_path, size=(299, 299)):
# `img` is a PIL image of size 299x299
img = keras.preprocessing.image.load_img(img_path, target_size=size)
# `array` is a float32 Numpy array of shape (299, 299, 3)
array = keras.preprocessing.image.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 usiing 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)
可视化梯度与集成梯度
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.measurements.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()
预测
# 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])
", 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(
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,
)