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Linear Regression

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"""
Linear regression is the most basic type of regression commonly used for
predictive analysis. The idea is pretty simple: we have a dataset and we have
features associated with it. Features should be chosen very cautiously
as they determine how much our model will be able to make future predictions.
We try to set the weight of these features, over many iterations, so that they best
fit our dataset. In this particular code, I had used a CSGO dataset (ADR vs
Rating). We try to best fit a line through dataset and estimate the parameters.
"""
import numpy as np
import requests


def collect_dataset():
    """Collect dataset of CSGO
    The dataset contains ADR vs Rating of a Player
    :return : dataset obtained from the link, as matrix
    """
    response = requests.get(
        "https://raw.githubusercontent.com/yashLadha/"
        + "The_Math_of_Intelligence/master/Week1/ADRvs"
        + "Rating.csv"
    )
    lines = response.text.splitlines()
    data = []
    for item in lines:
        item = item.split(",")
        data.append(item)
    data.pop(0)  # This is for removing the labels from the list
    dataset = np.matrix(data)
    return dataset


def run_steep_gradient_descent(data_x, data_y, len_data, alpha, theta):
    """Run steep gradient descent and updates the Feature vector accordingly_
    :param data_x   : contains the dataset
    :param data_y   : contains the output associated with each data-entry
    :param len_data : length of the data_
    :param alpha    : Learning rate of the model
    :param theta    : Feature vector (weight's for our model)
    ;param return    : Updated Feature's, using
                       curr_features - alpha_ * gradient(w.r.t. feature)
    """
    n = len_data

    prod = np.dot(theta, data_x.transpose())
    prod -= data_y.transpose()
    sum_grad = np.dot(prod, data_x)
    theta = theta - (alpha / n) * sum_grad
    return theta


def sum_of_square_error(data_x, data_y, len_data, theta):
    """Return sum of square error for error calculation
    :param data_x    : contains our dataset
    :param data_y    : contains the output (result vector)
    :param len_data  : len of the dataset
    :param theta     : contains the feature vector
    :return          : sum of square error computed from given feature's
    """
    prod = np.dot(theta, data_x.transpose())
    prod -= data_y.transpose()
    sum_elem = np.sum(np.square(prod))
    error = sum_elem / (2 * len_data)
    return error


def run_linear_regression(data_x, data_y):
    """Implement Linear regression over the dataset
    :param data_x  : contains our dataset
    :param data_y  : contains the output (result vector)
    :return        : feature for line of best fit (Feature vector)
    """
    iterations = 100000
    alpha = 0.0001550

    no_features = data_x.shape[1]
    len_data = data_x.shape[0] - 1

    theta = np.zeros((1, no_features))

    for i in range(0, iterations):
        theta = run_steep_gradient_descent(data_x, data_y, len_data, alpha, theta)
        error = sum_of_square_error(data_x, data_y, len_data, theta)
        print("At Iteration %d - Error is %.5f " % (i + 1, error))

    return theta


def main():
    """Driver function"""
    data = collect_dataset()

    len_data = data.shape[0]
    data_x = np.c_[np.ones(len_data), data[:, :-1]].astype(float)
    data_y = data[:, -1].astype(float)

    theta = run_linear_regression(data_x, data_y)
    len_result = theta.shape[1]
    print("Resultant Feature vector : ")
    for i in range(0, len_result):
        print("%.5f" % (theta[0, i]))


if __name__ == "__main__":
    main()
Acerca de este algoritmo
import tensorflow as tf

The default version of TensorFlow in Colab will soon switch to TensorFlow 2.x.
We recommend you upgrade now or ensure your notebook will continue to use TensorFlow 1.x via the %tensorflow_version 1.x magic: more info.

# creating a node 
hello = tf.constant("hello , tensor")
# creating object
sess = tf.Session()

print(sess.run(hello))
b'hello , tensor'
# basic operation

# in normal python we write a = 2
# but in tensorflow

a = tf.constant(2)
b = tf.constant(3)

with tf.Session() as sess:
  print("addition of number ", sess.run(a+b))
  print("multiplication of number ", sess.run(a*b))
addition of number  5
multiplication of number  6
# but while using function we have to create placeholder which does define the data type
x = tf.placeholder(tf.int32)
y = tf.placeholder(tf.int32)

add = tf.add(x,y)
multi = tf.multiply(x,y)

# Launch the default graph.
with tf.Session() as sess:
  print("Addition of number : ", sess.run(add , feed_dict={x:2,y:3}))
  print("Multiply of number : ", sess.run(multi , feed_dict={x:2,y:3}))
Addition of number :  5
Multiply of number :  6
# matrix multiplication

#1x2
matrix1 = tf.constant([[3., 3.]])

# Create another Constant that produces a 2x1 matrix.
matrix2 = tf.constant([[2.],[2.]])

# Create a Matmul op that takes 'matrix1' and 'matrix2' as inputs.
# The returned value, 'product', represents the result of the matrix
# multiplication.
product = tf.matmul(matrix1, matrix2)

with tf.Session() as sess:
    result = sess.run(product)
    print(result)
[[12.]]

Let's dive into linear regression

# import library
import tensorflow as tf
import numpy as np
import matplotlib.pyplot as plt
# just use to make graph looks nicer
%config InlineBackend.figure_format = 'svg'

linear regression using tensorflow

# y = f(x)
# we have set of input and set of output based on input dataset
# what we have to find out is f(x) which will be the relation between x and y (i.e input and output)

we need to learn the relationship between them that is called a hypothesis.

In case of Linear regression, the hypothesis is a straight line, i.e, h(x) = wx + b Where w is a vector called Weights and b is a scalar called Bias. The Weights and Bias are called the parameters of the model.

All we need to do is estimate the value of w and b from the given set of data such that the resultant hypothesis produces the least cost J which is defined by the following cost function

image.png

where m is the number of data points in the given dataset. This cost function is also called Mean Squared Error.

# let's start coding

learning_rate = 0.01
epochs = 200

n_sample= 30
# now take a random points

train_x = np.linspace(0,20,n_sample)
# y = mx + c + noise
train_y = 3*train_x + 4*np.random.randn(n_sample)
# let's plot a graph
plt.plot(train_x, train_y)
plt.show()
# Hmmm i don't like lines
# lets make points

plt.plot(train_x, train_y , 'o')
plt.show()
# bit nicer

# lets check difference between lines 
# with noise and without noise
plt.plot(train_x, train_y , 'o')
plt.plot(train_x, 3*train_x)

plt.show()

# define variable 

X = tf.placeholder(tf.float32)
Y = tf.placeholder(tf.float32)

# only written single value
w = tf.Variable(np.random.randn() , name = 'weight')
b = tf.Variable(np.random.randn() , name = 'bias')
print(b.value())
Tensor("bias_4/read:0", shape=(), dtype=float32)
  # pred = x*w + b
  prediction = tf.add(tf.multiply(X, w) ,b)
# to minimize the cost
cost = tf.reduce_sum((prediction-Y)**2 / (2*n_sample))
# define optimizer

optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(cost)
# initalize all are parameters
init = tf.global_variables_initializer()
with tf.Session() as sess:
  sess.run(init)
  # number of procedure will be decided by epoch
  for epoch in range(epochs):
    for x, y in zip(train_x , train_y):
      sess.run(optimizer , feed_dict={X:x , Y:y})
      
      # let us see output
    if (epoch%20) == 0:
      c = sess.run(cost, feed_dict={X:train_x ,Y:train_y})
      W = sess.run(w)
      B = sess.run(b)
      print("cost:{} w:{} b:{}".format(c ,W, B))
      # we see that cost minimizing
      #print(f'epoch:{epoch:04d} c={cost:.4f} W={W:.4f} B={B:.4f}')
  weight = sess.run(w)
  bias = sess.run(b)   
  plt.plot(train_x , train_y ,'o')
  plt.plot(train_x ,weight * train_x + bias)
  plt.show()
cost:54.30986404418945 w:2.182626247406006 b:0.5245328545570374
cost:8.714800834655762 w:2.99739408493042 b:0.586540699005127
cost:8.714640617370605 w:2.9978182315826416 b:0.5799477100372314
cost:8.714499473571777 w:2.9982216358184814 b:0.5736895799636841
cost:8.714378356933594 w:2.9986038208007812 b:0.5677502751350403
cost:8.71426773071289 w:2.998966693878174 b:0.5621128678321838
cost:8.714173316955566 w:2.9993114471435547 b:0.5567613840103149
cost:8.714091300964355 w:2.999638319015503 b:0.5516825914382935
cost:8.714018821716309 w:2.9999492168426514 b:0.546862006187439
cost:8.713956832885742 w:3.000243902206421 b:0.5422860980033875

this will be predicted result