XAI Functions

• ACTM Performer: CSU team;

• Author: Elizabeth A. Barnes (eabarnes@colostate.edu) and Antonios Mamalakis (amamalak@colostate.edu)

Here we provide a clean code snippet to implement XAI methods to explain AI models.

Specifically, we provide the code to compute the gradients and integrated gradients of a specific model output with respect to the corresponding input (local explanation).

To execute the snippet:

Step 1: Download the code in a Jupyter notebook format, using the corresponding option below.

Step 2: Integrate the snippet into your code and run it.

Step 3: Define the object “model” (i.e., the machine learning model that you want to explain) and call the XAI function you want to use.

#.............................................
# IMPORT STATEMENTS
#.............................................

#Handling data
import numpy as np

#machine learning package
import tensorflow as tf


#.............................................
# XAI functions
#.............................................

# Before calling these functions in your notebook, make sure you have defined the object "model".
# The "model" is the machine learning model (e.g., neural network) that you want to explain.

def get_gradients(inputs, top_pred_idx=None):
    """Computes the gradients of outputs w.r.t input image.

    Args:
        inputs: 2D/3D/4D matrix of samples
        top_pred_idx: (optional) Predicted label for the x_data
                      if classification problem. If regression,
                      do not include.

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

    with tf.GradientTape() as tape:
        tape.watch(inputs)

        # Run the forward pass of the layer and record operations
        # on GradientTape.
        preds = model(inputs, training=False)

        # For classification, grab the top class
        if top_pred_idx is not None:
            preds = preds[:, top_pred_idx]

    # Use the gradient tape to automatically retrieve
    # the gradients of the trainable variables with respect to the loss.
    grads = tape.gradient(preds, inputs)
    return grads

def get_integrated_gradients(inputs, baseline=None, num_steps=50, top_pred_idx=None):
    """Computes Integrated Gradients for a prediction.

    Args:
        inputs (ndarray): 2D/3D/4D matrix of samples
        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.
        top_pred_idx: (optional) Predicted label for the x_data
                      if classification problem. If regression,
                      do not include.

    Returns:
        Integrated gradients w.r.t input image
    """
    # If baseline is not provided, start with zeros
    # having same size as the input image.
    if baseline is None:
        input_size = np.shape(inputs)[1:]
        baseline = np.zeros(input_size).astype(np.float32)
    else:
        baseline = baseline.astype(np.float32)

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

    # 3. Get the gradients
    grads = []
    for i, x_data in enumerate(interpolated_inputs):
        grad = get_gradients(x_data, top_pred_idx=top_pred_idx)
        grads.append(grad)
    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 = (inputs - baseline) * avg_grads
    return integrated_grads

def random_baseline_integrated_gradients(inputs, num_steps=50, num_runs=5, top_pred_idx=None):
    """Generates a number of random baseline images.

    Args:
        inputs (ndarray): 2D/3D/4D matrix of samples
        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
        top_pred_idx: (optional) Predicted label for the x_data
                      if classification problem. If regression,
                      do not include.

    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.zeros(np.shape(inputs)[1:])
        for i in np.arange(0,np.shape(baseline)[0]):
            j = np.random.choice(np.arange(0,np.shape(inputs)[0]))
            baseline[i] = inputs[j,i]

        igrads = get_integrated_gradients(
            inputs=inputs,
            baseline=baseline,
            num_steps=num_steps,
            top_pred_idx=top_pred_idx)
        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)