Placing the constant when defining a matrix in python - python-3.x

Question

Can someone explain to me why these seemingly same pieces of code yield different results in using my function on test data from a MNIST dataset('http://yann.lecun.com/exdb/mnist/')?
1
def fit_generative_model1(x,y):
k = 10 # labels 0,1,...,k-1
d = (x.shape)[1] # number of features
mu = np.zeros((k,d))
sigma = np.zeros((k,d,d))
pi = np.zeros(k)
for label in range(0,k):
c = 4000
indices = (y == label)
mu[label] = np.mean(x[indices,:], axis=0)
sigma[label] = np.cov(x[indices,:], rowvar=0, bias=1) + c*np.identity(784, dtype=float) # regularizing the matrix
return mu, sigma, pi
mu, sigma, pi = fit_generative_model1(train_data, train_labels)
2
def fit_generative_model2(x,y):
k = 10 # labels 0,1,...,k-1
d = (x.shape)[1] # number of features
mu = np.zeros((k,d))
sigma = np.zeros((k,d,d))
pi = np.zeros(k)
for label in range(0,k):
indices= (y==label)
mu[label]= np.mean(x[indices,:],axis=0)
sigma[label]= np.cov(x[indices,:], rowvar=0, bias=1) + 4000*np.eye(784) #Regularized
pi[label]= float(sum(indices))/float(len(y))
return mu, sigma, pi
mu, sigma, pi = fit_generative_model2(train_data, train_labels)
Next, making predictions on the test data.
# Compute log Pr(label|image) for each [test image,label] pair.
k = 10
score = np.zeros((len(test_labels),k))
for label in range(0,k):
rv = multivariate_normal(mean=mu[label], cov=sigma[label])
for i in range(0,len(test_labels)):
score[i,label] = np.log(pi[label]) + rv.logpdf(test_data[i,:])
predictions = np.argmax(score, axis=1)
# Finally, tally up score
errors = np.sum(predictions != test_labels)
print("Your model makes " + str(errors) + " errors out of 10000")
print("This is " + str(errors/100) + "% error rate")
#with model1 -??
Your model makes 9020 errors out of 10000
This is 90.2% error rate
#with model2 - all good.
Your model makes 431 errors out of 10000
This is 4.31% error rate
I am also struggling to make the loop to work for the best c.
for c in [20,2000, 4000]:
k = 10
score = np.zeros((len(test_labels),k))
for label in range(0,k):
rv = multivariate_normal(mean=mu[label], cov=sigma[label])
for i in range(0,len(test_labels)):
score[i,label] = np.log(pi[label]) + rv.logpdf(test_data[i,:])
predictions = np.argmax(score, axis=1)
errors = np.sum(predictions != test_labels)
print("Model with "+ str(c) + " has a " + str(errors/100) + " error rate")
Model with 20 has a 4.31 error rate
Model with 2000 has a 4.31 error rate
Model with 4000 has a 4.31 error rate