def check_cost_function(lmd):
"""
Gradient checking for collaborative filtering
"""
# Create small problem
x_t = np.random.rand(4, 3)
theta_t = np.random.rand(5, 3)
# Zap out most entries
Y = np.dot(x_t, theta_t.T) # 4x5
Y[np.random.rand(Y.shape[0], Y.shape[1]) > 0.5] = 0
R = np.zeros(Y.shape)
R[Y != 0] = 1
# Run Gradient Checking
x = np.random.randn(x_t.shape[0], x_t.shape[1])
theta = np.random.randn(theta_t.shape[0], theta_t.shape[1])
num_users = Y.shape[1] #5
num_movies = Y.shape[0] #4
num_features = theta_t.shape[1] #3
def cost_func(p):
return cofi_cost_function(p, Y, R, num_users, num_movies, num_features,
lmd)
numgrad = compute_numerial_gradient(
cost_func, np.concatenate((x.flatten(), theta.flatten())))
cost, grad = cofi_cost_function(
np.concatenate((x.flatten(), theta.flatten())), Y, R, num_users,
num_movies, num_features, lmd)
print(np.c_[numgrad, grad])
print('The above two columns you get should be very similar.\n'
'(Left-Your Numerical Gradient, Right-Analytical Gradient')
diff = np.linalg.norm(numgrad - grad) / np.linalg.norm(numgrad + grad)
print('If you backpropagation implementation is correct, then\n'
'the relative difference will be small (less than 1e-9).\n'
'Relative Difference: {:0.3e}'.format(diff))
theta = data['Theta']
num_users = data['num_users']
num_movies = data['num_movies']
num_features = data['num_features']
# Reduce the data set size so that this runs faster
num_users = 4
num_movies = 5
num_features = 3
X = X[0:num_movies, 0:num_features]
theta = theta[0:num_users, 0:num_features]
Y = Y[0:num_movies, 0:num_users]
R = R[0:num_movies, 0:num_users]
# Evaluate cost function
cost = ccf.cofi_cost_function(np.concatenate((X.flatten(), theta.flatten())),
Y, R, num_users, num_movies, num_features, 0)
grad = ccf.cofi_gred_function(np.concatenate((X.flatten(), theta.flatten())),
Y, R, num_users, num_movies, num_features, 0)
print('Cost at loaded parameters: {:0.2f}\n(this value should be about 22.22)'.
format(cost))
input('Program paused. Press ENTER to continue')
# ===================== Part 3: Collaborative Filtering Gradient =====================
# Once your cost function matches up with ours, you should now implement
# the collaborative filtering gradient function. Specifically, you should
# complete the code in cofiCostFunction.py to return the grad argument.
#
print('Checking gradients (without regularization) ...')
def cost_func(p):
return ccf.cofi_cost_function(p, Y, R, num_users, num_movies,
num_features, lmd)
def grad_func(p):
return cofi_cost_function(p, Ynorm, R, num_users, num_movies, num_features,
lmd)[1]
def cost_func(p):
cost_tmp = ccf.cofi_cost_function(p, Y, R, num_users, num_movies,
num_features, lmd)
gred_tmp = ccf.cofi_gred_function(p, Y, R, num_users, num_movies,
num_features, lmd)
return cost_tmp, gred_tmp
