[PyTorch]Linear, Ridge, Lasso, ElasticNet implementation-코드 미완성

1. Linear Regression Numpy Implementation

from sklearn.datasets import make_regression
import matplotlib.pyplot as plt
import numpy as np

X, y= make_regression(n_samples=100, n_features=1, noise=0.4, bias=50)

def plotLine(theta0, theta1, X, y):
    max_x = np.max(X) + 100
    min_x = np.min(X) - 100


    xplot = np.linspace(min_x, max_x, 1000)
    yplot = theta0 + theta1 * xplot



    plt.plot(xplot, yplot, color='#58b970', label='Regression Line')

    plt.scatter(X,y)
    plt.axis([-10, 10, 0, 200])
    plt.show()

def hypothesis(theta0, theta1, x):
    return theta0 + (theta1*x) 

def cost(theta0, theta1, X, y):
    costValue = 0 
    for (xi, yi) in zip(X, y):
        costValue += 0.5 * ((hypothesis(theta0, theta1, xi) - yi)**2)
    return costValue

def derivatives(theta0, theta1, X, y):
    dtheta0 = 0
    dtheta1 = 0
    for (xi, yi) in zip(X, y):
        dtheta0 += hypothesis(theta0, theta1, xi) - yi
        dtheta1 += (hypothesis(theta0, theta1, xi) - yi)*xi

    dtheta0 /= len(X)
    dtheta1 /= len(X)

    return dtheta0, dtheta1

def updateParameters(theta0, theta1, X, y, alpha):
    dtheta0, dtheta1 = derivatives(theta0, theta1, X, y)
    theta0 = theta0 - (alpha * dtheta0)
    theta1 = theta1 - (alpha * dtheta1)

    return theta0, theta1

def LinearRegression(X, y):
    theta0 = np.random.rand()
    theta1 = np.random.rand()
    
    for i in range(0, 1000):
        if i % 100 == 0:
            plotLine(theta0, theta1, X, y)
            print(cost(theta0, theta1, X, y))
        theta0, theta1 = updateParameters(theta0, theta1, X, y, 0.005)

LinearRegression(X, y)

[302493.21138417]

[110433.00362617]

[40402.32548701]

[14812.95164304]

[5443.97939662]

[2007.39956265]

[744.68382217]

[279.98276534]

[108.71444941]

[45.5075413]

2. Ridge Regression Numpy Implementation

def hypothesis(theta0, theta1, x):
    return theta0 + (theta1*x) 

def Ridge_cost(theta0, theta1, X, y):
    costValue = 0 
    for (xi, yi) in zip(X, y):
        costValue += 0.5 * ((hypothesis(theta0, theta1, xi) - yi)**2)
    costValue += 


    return costValue

def Ridge_derivatives(theta0, theta1, X, y):
    dtheta0 = 0
    dtheta1 = 0
    for (xi, yi) in zip(X, y):
        dtheta0 += hypothesis(theta0, theta1, xi) - yi
        dtheta1 += (hypothesis(theta0, theta1, xi) - yi)*xi

    dtheta0 /= len(X)
    dtheta1 /= len(X)

    return dtheta0, dtheta1

def updateParameters(theta0, theta1, X, y, alpha):
    dtheta0, dtheta1 = Ridge_derivatives(theta0, theta1, X, y)
    theta0 = theta0 - (alpha * dtheta0)
    theta1 = theta1 - (alpha * dtheta1)

    return theta0, theta1

def RidgeRegression(X, y):
    theta0 = np.random.rand()
    theta1 = np.random.rand()
    
    for i in range(0, 1000):
        if i % 100 == 0:
            plotLine(theta0, theta1, X, y)
            print(Ridge_cost(theta0, theta1, X, y))
        theta0, theta1 = updateParameters(theta0, theta1, X, y, 0.005)

RidgeRegression(X, y)

[305493.70822568]

[111556.2529174]

[40822.75853898]

[14970.2999332]

[5502.86073888]

[2029.43132433]

[752.92674748]

[283.06650969]

[109.86801957]

[45.93904217]

3. Lasso Regression Numpy Implementation

def hypothesis(theta0, theta1, x):
    return theta0 + (theta1*x) 

def Lasso_cost(theta0, theta1, X, y):
    costValue = 0 
    for (xi, yi) in zip(X, y):
        costValue += 0.5 * ((hypothesis(theta0, theta1, xi) - yi)**2)
    return costValue

def Lasso_derivatives(theta0, theta1, X, y):
    dtheta0 = 0
    dtheta1 = 0
    for (xi, yi) in zip(X, y):
        dtheta0 += hypothesis(theta0, theta1, xi) - yi
        dtheta1 += (hypothesis(theta0, theta1, xi) - yi)*xi

    dtheta0 /= len(X)
    dtheta1 /= len(X)

    return dtheta0, dtheta1

def updateParameters(theta0, theta1, X, y, alpha):
    dtheta0, dtheta1 = Lasso_derivatives(theta0, theta1, X, y)
    theta0 = theta0 - (alpha * dtheta0)
    theta1 = theta1 - (alpha * dtheta1)

    return theta0, theta1

def LassoRegression(X, y):
    theta0 = np.random.rand()
    theta1 = np.random.rand()
    
    for i in range(0, 1000):
        if i % 100 == 0:
            plotLine(theta0, theta1, X, y)
            print(Lasso_cost(theta0, theta1, X, y))
        theta0, theta1 = updateParameters(theta0, theta1, X, y, 0.005)

LassoRegression(X, y)

[307794.36779767]

[112448.67312985]

[41167.18687274]

[15102.67157781]

[5553.55296535]

[2048.78522037]

[760.29670989]

[285.86670904]

[110.92988827]

[46.34103812]

4. ElasticNet Numpy Implementation (HW1)

def hypothesis(theta0, theta1, x):
    return theta0 + (theta1*x) 

def EN_cost(theta0, theta1, X, y):
    costValue = 0 
    for (xi, yi) in zip(X, y):
        costValue += 0.5 * ((hypothesis(theta0, theta1, xi) - yi)**2)
    return costValue

def EN_derivatives(theta0, theta1, X, y):
    dtheta0 = 0
    dtheta1 = 0
    for (xi, yi) in zip(X, y):
        dtheta0 += hypothesis(theta0, theta1, xi) - yi
        dtheta1 += (hypothesis(theta0, theta1, xi) - yi)*xi

    dtheta0 /= len(X)
    dtheta1 /= len(X)

    return dtheta0, dtheta1

def updateParameters(theta0, theta1, X, y, alpha):
    dtheta0, dtheta1 = EN_derivatives(theta0, theta1, X, y)
    theta0 = theta0 - (alpha * dtheta0)
    theta1 = theta1 - (alpha * dtheta1)

    return theta0, theta1

def ENRegression(X, y):
    theta0 = np.random.rand()
    theta1 = np.random.rand()
    
    for i in range(0, 1000):
        if i % 100 == 0:
            plotLine(theta0, theta1, X, y)
            print(EN_cost(theta0, theta1, X, y))
        theta0, theta1 = updateParameters(theta0, theta1, X, y, 0.005)

ENRegression(X, y)

[306402.60804692]

[111852.97684341]

[40919.30139496]

[15001.58623]

[5512.95154434]

[2032.66741257]

[753.95738261]

[283.39195684]

[109.96969251]

[45.97037289]