import tensorflow as tf

import numpy as np

from sklearn.linear_model import LogisticRegression

from sklearn import preprocessing

# Read x and y

x_data = np.loadtxt("ex4x.dat").astype(np.float32)

y_data = np.loadtxt("ex4y.dat").astype(np.float32)

scaler = preprocessing.StandardScaler().fit(x_data)

x_data_standard = scaler.transform(x_data)

# We evaluate the x and y by sklearn to get a sense of the coefficients.

reg = LogisticRegression(C=999999999, solver="newton-cg")  # Set C as a large positive number to minimize the regularization effect

reg.fit(x_data, y_data)

print ("Coefficients of sklearn: K=%s, b=%f" % (reg.coef_, reg.intercept_))

# Now we use tensorflow to get similar results.

W = tf.Variable(tf.zeros([2, 1]))

b = tf.Variable(tf.zeros([1, 1]))

y = 1 / (1 + tf.exp(-tf.matmul(x_data_standard, W) + b))

loss = tf.reduce_mean(- y_data.reshape(-1, 1) *  tf.log(y) - (1 - y_data.reshape(-1, 1)) * tf.log(1 - y))

optimizer = tf.train.GradientDescentOptimizer(1.3)

train = optimizer.minimize(loss)

init = tf.initialize_all_variables()

sess = tf.Session()

sess.run(init)

for step in range(100):

    sess.run(train)

    if step % 10 == 0:

        print (step, sess.run(W).flatten(), sess.run(b).flatten())

print ("Coefficients of tensorflow (input should be standardized): K=%s, b=%s" % (sess.run(W).flatten(), sess.run(b).flatten()))

print ("Coefficients of tensorflow (raw input): K=%s, b=%s" % (sess.run(W).flatten() / scaler.scale_, sess.run(b).flatten() - np.dot(scaler.mean_ / scaler.scale_, sess.run(W))))

# Problem solved and we are happy. But...

# I'd like to implement the logistic regression from a multi-class viewpoint instead of binary.

# In machine learning domain, it is called softmax regression

# In economic and statistics domain, it is called multinomial logit (MNL) model, proposed by Daniel McFadden, who shared the 2000  Nobel Memorial Prize in Economic Sciences.

print ("------------------------------------------------")

print ("We solve this binary classification problem again from the viewpoint of multinomial classification")

print ("------------------------------------------------")

# As a tradition, sklearn first

reg = LogisticRegression(C=9999999999, solver="newton-cg", multi_class="multinomial")

reg.fit(x_data, y_data)

print ("Coefficients of sklearn: K=%s, b=%f" % (reg.coef_, reg.intercept_))

print ("A little bit difference at first glance. What about multiply them with 2?")

# Then try tensorflow

W = tf.Variable(tf.zeros([2, 2]))  # first 2 is feature number, second 2 is class number

b = tf.Variable(tf.zeros([1, 2]))

V = tf.matmul(x_data_standard, W) + b

y = tf.nn.softmax(V)  # tensorflow provide a utility function to calculate the probability of observer n choose alternative i, you can replace it with `y = tf.exp(V) / tf.reduce_sum(tf.exp(V), keep_dims=True, reduction_indices=[1])`

# Encode the y label in one-hot manner

lb = preprocessing.LabelBinarizer()

lb.fit(y_data)

y_data_trans = lb.transform(y_data)

y_data_trans = np.concatenate((1 - y_data_trans, y_data_trans), axis=1)  # Only necessary for binary class

loss = tf.reduce_mean(-tf.reduce_sum(y_data_trans * tf.log(y), reduction_indices=[1]))

optimizer = tf.train.GradientDescentOptimizer(1.3)

train = optimizer.minimize(loss)

init = tf.initialize_all_variables()

sess = tf.Session()

sess.run(init)

for step in range(100):

    sess.run(train)

    if step % 10 == 0:

        print (step, sess.run(W).flatten(), sess.run(b).flatten())

print ("Coefficients of tensorflow (input should be standardized): K=%s, b=%s" % (sess.run(W).flatten(), sess.run(b).flatten()))

print ("Coefficients of tensorflow (raw input): K=%s, b=%s" % ((sess.run(W) / scaler.scale_).flatten(),  sess.run(b).flatten() - np.dot(scaler.mean_ / scaler.scale_, sess.run(W))))