Fisher Information Matrix

fim.py

import numpy as np
import tensorflow as tf

from sklearn.datasets import make_blobs

# Set random seed (for reproducibility)
np.random.seed(1000)

# Create dataset
nb_samples=2000
X, Y = make_blobs(n_samples=nb_samples, n_features=2, centers=2, cluster_std=1.1, random_state=2000)

# Transform the original dataset so to learn the bias as any other parameter
Xc = np.ones((nb_samples, X.shape[1] + 1), dtype=np.float32)
Yc = np.zeros((nb_samples, 1), dtype=np.float32)

Xc[:, 1:3] = X
Yc[:, 0] = Y

# Create Tensorflow graph
graph = tf.Graph()

with graph.as_default():
    Xi = tf.placeholder(tf.float32, Xc.shape)
    Yi = tf.placeholder(tf.float32, Yc.shape)
    
    # Weights (+ bias)
    W = tf.Variable(tf.random_normal([Xc.shape[1], 1], 0.0, 0.01))
    
    # Z = wx + b
    Z = tf.matmul(Xi, W)
    
    # Log-likelihood
    log_likelihood = tf.reduce_sum(tf.nn.sigmoid_cross_entropy_with_logits(logits=Z, labels=Yi))
    
    # Cost function (Log-likelihood + L2 penalty)
    cost = log_likelihood + 0.5*tf.norm(W, ord=2)
    
    trainer = tf.train.GradientDescentOptimizer(0.000025)
    training_step = trainer.minimize(cost)
    
    # Compute the FIM
    dW = tf.gradients(-log_likelihood, W)
    FIM = tf.matmul(tf.reshape(dW, (Xc.shape[1], 1)), tf.reshape(dW, (Xc.shape[1], 1)), transpose_b=True)
    
# Create Tensorflow session
session = tf.InteractiveSession(graph=graph)

# Initialize all variables
tf.global_variables_initializer().run()

# Run a training cycle
# The model is quite simple, however a check on the cost function should be performed
for _ in range(3500):
    _, _ = session.run([training_step, cost], feed_dict={Xi: Xc, Yi: Yc})
    
# Compute Fisher Information Matrix on MLE
fisher_information_matrix = session.run([FIM], feed_dict={Xi: Xc, Yi: Yc})

# Log-likelihood
log_likelihood = tf.reduce_sum(tf.nn.sigmoid_cross_entropy_with_logits(logits=Z, labels=Yi))

shouldn't it be a mean instead of a sum?