Code logic for implementing mini-batch gradient descent algorithm using Python

Let theta = model parameters and max_iters = number of epochs. For itr=1,2,3,...,max_iters: For mini_batch(X_mini,y_mini):

Forward pass of batch X_mini:

1. Predict small batches

2. Use the current value of the parameter to calculate the prediction error (J(theta))

Post-transmission: Calculate the gradient (theta)=J(theta)wrt the partial derivative of theta

Update parameters: theta=theta–learning_rate*gradient(theta)

Code process for implementing gradient descent algorithm in Python

Step 1: Import dependencies, generate data for linear regression, and visualize it generated data. Take 8000 data examples, each example has 2 attribute features. These data samples are further divided into training set (X_train, y_train) and test set (X_test, y_test), with 7200 and 800 samples respectively.

import numpy as np
import matplotlib.pyplot as plt

mean=np.array([5.0,6.0])
cov=np.array([[1.0,0.95],[0.95,1.2]])
data=np.random.multivariate_normal(mean,cov,8000)

plt.scatter(data[:500,0],data[:500,1],marker='.')
plt.show()
data=np.hstack((np.ones((data.shape[0],1)),data))
split_factor=0.90
split=int(split_factor*data.shape[0])
X_train=data[:split,:-1]
y_train=data[:split,-1].reshape((-1,1))
X_test=data[split:,:-1]
y_test=data[split:,-1].reshape((-1,1))

print(& quot Number of examples in training set= % d & quot % (X_train.shape[0]))
print(& quot Number of examples in testing set= % d & quot % (X_test.shape[0]))

Number of examples in the training set = 7200 Number of examples in the test set = 800

Step 2:

Code to implement linear regression using mini-batch gradient descent . gradientDescent() is the main driving function, and other functions are auxiliary functions:

Prediction-hypothesis()

Calculate gradient-gradient()

Calculate error- —cost()

Create mini-batches —create_mini_batches()

Driver function initializes parameters, calculates the optimal parameter set for the model, and returns these parameters along with a list containing parameter updates error history.

def hypothesis(X,theta):
    return np.dot(X,theta)

def gradient(X,y,theta):
    h=hypothesis(X,theta)
    grad=np.dot(X.transpose(),(h-y))
    return grad

def cost(X,y,theta):
    h=hypothesis(X,theta)
    J=np.dot((h-y).transpose(),(h-y))
    J/=2
    return J[0]

def create_mini_batches(X,y,batch_size):
    mini_batches=[]
    data=np.hstack((X,y))
    np.random.shuffle(data)
    n_minibatches=data.shape[0]//batch_size
    i=0
    for i in range(n_minibatches+1):
        mini_batch=data[i*batch_size:(i+1)*batch_size,:]
        X_mini=mini_batch[:,:-1]
        Y_mini=mini_batch[:,-1].reshape((-1,1))
        mini_batches.append((X_mini,Y_mini))
    if data.shape[0]%batch_size!=0:
       mini_batch=data[i*batch_size:data.shape[0]]
       X_mini=mini_batch[:,:-1]
       Y_mini=mini_batch[:,-1].reshape((-1,1))
       mini_batches.append((X_mini,Y_mini))
    return mini_batches

def gradientDescent(X,y,learning_rate=0.001,batch_size=32):
    theta=np.zeros((X.shape[1],1))
    error_list=[]
    max_iters=3
    for itr in range(max_iters):
        mini_batches=create_mini_batches(X,y,batch_size)
        for mini_batch in mini_batches:
            X_mini,y_mini=mini_batch
            theta=theta-learning_rate*gradient(X_mini,y_mini,theta)
            error_list.append(cost(X_mini,y_mini,theta))
    return theta,error_list

Call the gradientDescent() function to calculate the model parameters (theta) and visualize the changes in the error function.

theta,error_list=gradientDescent(X_train,y_train)
print("Bias=",theta[0])
print("Coefficients=",theta[1:])

plt.plot(error_list)
plt.xlabel("Number of iterations")
plt.ylabel("Cost")
plt.show()

Deviation=[0.81830471]Coefficient=[[1.04586595]]

Step 3: Predict the test set and calculate the average absolute error in the prediction.

y_pred=hypothesis(X_test,theta)
plt.scatter(X_test[:,1],y_test[:,],marker='.')
plt.plot(X_test[:,1],y_pred,color='orange')
plt.show()

error=np.sum(np.abs(y_test-y_pred)/y_test.shape[0])
print(& quot Mean absolute error=&quot,error)

Mean absolute error=0.4366644295854125

The orange line represents the final hypothesis function: theta[0] theta[1]*X_test[:,1] theta[2]*X_test[ :,2]=0

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