Path: blob/master/examples/vision/ipynb/integrated_gradients.ipynb
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Kernel: Python 3
Model interpretability with Integrated Gradients
Author: A_K_Nain
Date created: 2020/06/02
Last modified: 2020/06/02
Description: How to obtain integrated gradients for a classification model.
Integrated Gradients
Integrated Gradients is a technique for attributing a classification model's prediction to its input features. It is a model interpretability technique: you can use it to visualize the relationship between input features and model predictions.
Integrated Gradients is a variation on computing the gradient of the prediction output with regard to features of the input. To compute integrated gradients, we need to perform the following steps:
Identify the input and the output. In our case, the input is an image and the output is the last layer of our model (dense layer with softmax activation).
Compute which features are important to a neural network when making a prediction on a particular data point. To identify these features, we need to choose a baseline input. A baseline input can be a black image (all pixel values set to zero) or random noise. The shape of the baseline input needs to be the same as our input image, e.g. (299, 299, 3).
Interpolate the baseline for a given number of steps. The number of steps represents the steps we need in the gradient approximation for a given input image. The number of steps is a hyperparameter. The authors recommend using anywhere between 20 and 1000 steps.
Preprocess these interpolated images and do a forward pass.
Get the gradients for these interpolated images.
Approximate the gradients integral using the trapezoidal rule.
To read in-depth about integrated gradients and why this method works, consider reading this excellent article.
References:
Integrated Gradients original paper
Setup
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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))
Integrated Gradients algorithm
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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)
Helper class for visualizing gradients and integrated gradients
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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()
Let's test-drive it
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# 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, )