Category: Machine Learning, Deep Learning & Artificial Intelligence

import math;

def sigmoid(x):
  return 1 / (1 + math.exp(-x))

import math;

def tanh(x):
  return (math.exp(x) - math.exp(-x)) / (math.exp(x) + math.exp(-x))

import math;

def relu(x):
    return max(0,x)

import math;

def leaky_relu(x):
    return max(0.1*x,x)

# Plain implementation

import numpy as np
y_hat = np.array([0.000, 0.166, 0.333])
y_true = np.array([0.000, 0.254, 0.998])

print("d is: " + str(["%.8f" % elem for elem in y_hat]))
print("p is: " + str(["%.8f" % elem for elem in y_true]))

def mae(predictions, targets):
    total_error = 0
    for yp, yt in zip(predictions, targets):
        total_error += abs(yp - yt)
    print("Total error is:",total_error)
    mae = total_error/len(predictions)
    print("Mean absolute error is:",mae)
    return mae

# Usage : mae(predictions, targets)

# Implementation using numpy
import numpy as np
y_hat = np.array([0.000, 0.166, 0.333])
y_true = np.array([0.000, 0.254, 0.998])

print("d is: " + str(["%.8f" % elem for elem in y_hat]))
print("p is: " + str(["%.8f" % elem for elem in y_true]))

def mae_np(predictions, targets):
    return np.mean(np.abs(predictions-targets))

mae_val = mae_np(y_hat, y_true)
print ("mae error is: " + str(mae_val))

# Plain implementation

import numpy as np

y_hat = np.array([0.000, 0.166, 0.333])
y_true = np.array([0.000, 0.254, 0.998])

def rmse(predictions, targets):
    total_error = 0
    for yt, yp in zip(targets, predictions):
        total_error += (yt-yp)**2
    print("Total Squared Error:",total_error)
    mse = total_error/len(y_true)
    print("Mean Squared Error:",mse)
    return mse

print("d is: " + str(["%.8f" % elem for elem in y_hat]))
print("p is: " + str(["%.8f" % elem for elem in y_true]))

rmse_val = rmse(y_hat, y_true)
print("rms error is: " + str(rmse_val))

# Implementation using numpy

import numpy as np

y_hat = np.array([0.000, 0.166, 0.333])
y_true = np.array([0.000, 0.254, 0.998])

def rmse(predictions, targets):
    return np.mean(np.square(targets-predictions))

print("d is: " + str(["%.8f" % elem for elem in y_hat]))
print("p is: " + str(["%.8f" % elem for elem in y_true]))

rmse_val = rmse(y_hat, y_true)
print("rms error is: " + str(rmse_val))

import numpy as np

y_predicted = np.array([[0.25,0.25,0.25,0.25],[0.01,0.01,0.01,0.96]])
y_true = np.array([[0,0,0,1],[0,0,0,1]])

def cross_entropy(predictions, targets, epsilon=1e-10):
    predictions = np.clip(predictions, epsilon, 1. - epsilon)
    N = predictions.shape[0]
    ce_loss = -np.sum(np.sum(targets * np.log(predictions + 1e-5)))/N
    return ce_loss
cross_entropy_loss = cross_entropy(predictions, targets)
print ("Cross entropy loss is: " + str(cross_entropy_loss))

# OR

def log_loss(predictions, targets, epsilon=1e-10):
    predicted_new = [max(i,epsilon) for i in predictions]
    predicted_new = [min(i,1-epsilon) for i in predicted_new]
    predicted_new = np.array(predicted_new)
    return -np.mean(targets*np.log(predicted_new)+(1-y_true)*np.log(1-predicted_new))

# Single Feature
import numpy as np
import matplotlib.pyplot as plt

%matplotlib inline

def gradient_descent(x, y, epochs = 10000, loss_thresold = 0.5, rate = 0.01):
    w1 = bias = 0
    n = len(x)
    plt.scatter(x, y, color='red', marker='+', linewidth='5')
    for i in range(epochs):
        y_predicted = (w1 * x)+ bias
        plt.plot(x, y_predicted, color='green')
        md = -(2/n)*sum(x*(y-y_predicted))
        yd = -(2/n)*sum(y-y_predicted)
        w1 = w1 - rate * md
        bias = bias - rate * yd
        print ("m {}, b {}, cost {} iteration {}".format(m_curr,b_curr,cost, i))

# Usage
x = np.array([1,2,3,4,5])
y = np.array([5,7,9,11,13])
gradient_descent(x, y, 500)

---

# Multiple Feature
def gradient_descent(x1, x2, y, epochs = 10000, loss_thresold = 0.5, rate = 0.01):
    w1 = w2 = bias = 1
    rate = 0.5
    n = len(x1)
    for i in range(epochs):
        weighted_sum = (w1 * x1) + (w2 * x2) + bias
        y_predicted = sigmoid_numpy(weighted_sum)
        loss = log_loss(y_predicted, y)

        w1d = (1/n)*np.dot(np.transpose(x1),(y_predicted-y)) 
        w2d = (1/n)*np.dot(np.transpose(x2),(y_predicted-y)) 

        bias_d = np.mean(y_predicted-y)
        w1 = w1 - rate * w1d
        w2 = w2 - rate * w2d
        bias = bias - rate * bias_d

        print (f'Epoch:{i}, w1:{w1}, w2:{w2}, bias:{bias}, loss:{loss}')

        if loss<=loss_thresold:
            break

    return w1, w2, bias

# Usage
gradient_descent(
    X_train_scaled['age'],
    X_train_scaled['affordibility'],
    y_train,
    1000, 
    0.4631
)

# custom neural network class

class myNN:

    def __init__(self):
        self.w1 = 1 
        self.w2 = 1
        self.bias = 0
    
    def sigmoid_numpy(self, X):
        import numpy as np;
        return 1/(1+np.exp(-X))

    def log_loss(self, y_true, y_predicted):
        import numpy as np;
        epsilon = 1e-15
        y_predicted_new = [max(i,epsilon) for i in y_predicted]
        y_predicted_new = [min(i,1-epsilon) for i in y_predicted_new]
        y_predicted_new = np.array(y_predicted_new)
        return -np.mean(y_true*np.log(y_predicted_new)+(1-y_true)*np.log(1-y_predicted_new))
    
    def fit(self, X, y, epochs, loss_thresold):
        self.w1, self.w2, self.bias = self.gradient_descent(X['age'],X['affordibility'],y, epochs, loss_thresold)
        print(f"Final weights and bias: w1: {self.w1}, w2: {self.w2}, bias: {self.bias}")
    
    def predict(self, X_test):
        weighted_sum = self.w1*X_test['age'] + self.w2*X_test['affordibility'] + self.bias
        return self.sigmoid_numpy(weighted_sum)

    def gradient_descent(self, age,affordability, y_true, epochs, loss_thresold):
        import numpy as np;
        w1 = w2 = 1
        bias = 0
        rate = 0.5
        n = len(age)
        for i in range(epochs):
            weighted_sum = w1 * age + w2 * affordability + bias
            y_predicted = self.sigmoid_numpy(weighted_sum)
            loss = self.log_loss.log_loss(y_true, y_predicted)
            
            w1d = (1/n)*np.dot(np.transpose(age),(y_predicted-y_true)) 
            w2d = (1/n)*np.dot(np.transpose(affordability),(y_predicted-y_true)) 

            bias_d = np.mean(y_predicted-y_true)
            w1 = w1 - rate * w1d
            w2 = w2 - rate * w2d
            bias = bias - rate * bias_d
            
            if i%50==0:
                print (f'Epoch:{i}, w1:{w1}, w2:{w2}, bias:{bias}, loss:{loss}')
            
            if loss<=loss_thresold:
                print (f'Epoch:{i}, w1:{w1}, w2:{w2}, bias:{bias}, loss:{loss}')
                break

        return w1, w2, bias
  

# Usage
customModel = myNN()
customModel.fit(X_train_scaled, y_train, epochs=8000, loss_thresold=0.4631)

# Usage
customModel = myNN()
customModel.fit(
        X_train_scaled, 
        y_train,
        epochs=8000,
        loss_thresold=0.4631
)

def batch_gradient_descent(X, y_true, epochs, learning_rate = 0.01):

    number_of_features = X.shape[1]
    # numpy array with 1 row and columns equal to number of features. In 
    # our case number_of_features = 2 (area, bedroom)
    w = np.ones(shape=(number_of_features)) 
    b = 0
    total_samples = X.shape[0] # number of rows in X
    
    cost_list = []
    epoch_list = []
    
    for i in range(epochs):        
        y_predicted = np.dot(w, X.T) + b

        w_grad = -(2/total_samples)*(X.T.dot(y_true-y_predicted))
        b_grad = -(2/total_samples)*np.sum(y_true-y_predicted)
        
        w = w - learning_rate * w_grad
        b = b - learning_rate * b_grad
        
        cost = np.mean(np.square(y_true-y_predicted)) # MSE (Mean Squared Error)
        
        if i%10==0:
            cost_list.append(cost)
            epoch_list.append(i)
        
    return w, b, cost, cost_list, epoch_list

w, b, cost, cost_list, epoch_list = batch_gradient_descent(
    scaled_X,
    scaled_y.reshape(scaled_y.shape[0],),
    500
)
w, b, cost

def mini_batch_gradient_descent(X, y_true, epochs = 100, batch_size = 5, learning_rate = 0.01):
    
    number_of_features = X.shape[1]
    # numpy array with 1 row and columns equal to number of features. In 
    # our case number_of_features = 3 (area, bedroom and age)
    w = np.ones(shape=(number_of_features)) 
    b = 0
    total_samples = X.shape[0] # number of rows in X
    
    if batch_size > total_samples: # In this case mini batch becomes same as batch gradient descent
        batch_size = total_samples
        
    cost_list = []
    epoch_list = []
    
    num_batches = int(total_samples/batch_size)
    
    for i in range(epochs):    
        random_indices = np.random.permutation(total_samples)
        X_tmp = X[random_indices]
        y_tmp = y_true[random_indices]
        
        for j in range(0,total_samples,batch_size):
            Xj = X_tmp[j:j+batch_size]
            yj = y_tmp[j:j+batch_size]
            y_predicted = np.dot(w, Xj.T) + b
            
            w_grad = -(2/len(Xj))*(Xj.T.dot(yj-y_predicted))
            b_grad = -(2/len(Xj))*np.sum(yj-y_predicted)
            
            w = w - learning_rate * w_grad
            b = b - learning_rate * b_grad
                
            cost = np.mean(np.square(yj-y_predicted)) # MSE (Mean Squared Error)
        
        if i%10==0:
            cost_list.append(cost)
            epoch_list.append(i)
        
    return w, b, cost, cost_list, epoch_list

w, b, cost, cost_list, epoch_list = mini_batch_gradient_descent(
    scaled_X,
    scaled_y.reshape(scaled_y.shape[0],),
    epochs = 120,
    batch_size = 5
)
w, b, cost

def stochastic_gradient_descent(X, y_true, epochs, learning_rate = 0.01):
 
    number_of_features = X.shape[1]
    # numpy array with 1 row and columns equal to number of features. In 
    # our case number_of_features = 3 (area, bedroom and age)
    w = np.ones(shape=(number_of_features)) 
    b = 0
    total_samples = X.shape[0]
    
    cost_list = []
    epoch_list = []
    
    for i in range(epochs):    
        random_index = random.randint(0,total_samples-1) # random index from total samples
        sample_x = X[random_index]
        sample_y = y_true[random_index]
        
        y_predicted = np.dot(w, sample_x.T) + b
    
        w_grad = -(2/total_samples)*(sample_x.T.dot(sample_y-y_predicted))
        b_grad = -(2/total_samples)*(sample_y-y_predicted)
        
        w = w - learning_rate * w_grad
        b = b - learning_rate * b_grad
        
        cost = np.square(sample_y-y_predicted)
        
        if i%100==0: # at every 100th iteration record the cost and epoch value
            cost_list.append(cost)
            epoch_list.append(i)
        
    return w, b, cost, cost_list, epoch_list

w_sgd, b_sgd, cost_sgd, cost_list_sgd, epoch_list_sgd = SGD(
    scaled_X,
    scaled_y.reshape(scaled_y.shape[0],),
    10000
)
w_sgd, b_sgd, cost_sgd