پیاده‌سازی رگرسیون چندجمله‌ ای با پایتون از پایه

# Importing libraries

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import numpy as np

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import pandas as pd

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from sklearn.model_selection import train_test_split

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import matplotlib.pyplot as plt

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from sklearn.linear_model import LinearRegression

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# driver code

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def main() :

    # Create dataset

    X = np.array( [ [1], [2], [3], [4], [5], [6], [7] ] )

    Y = np.array( [ 45000, 50000, 60000, 80000, 110000, 150000, 200000 ] )

    # Model training

    model = LinearRegression()

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    model.fit( X, Y )

    # Prediction

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    Y_pred = model.predict( X )

    # Visualization 

    plt.scatter( X, Y, color = 'blue' )

    plt.plot( X, Y_pred, color = 'orange' )

    plt.title( 'X vs Y' )

    plt.xlabel( 'X' )

    plt.ylabel( 'Y' )

    plt.show()

if __name__ == "__main__" : 

    main()

# Importing libraries

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import numpy as np

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import math

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import matplotlib.pyplot as plt

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# Univariate Polynomial Regression

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class PolynomailRegression() :

    def __init__( self, degree, learning_rate, iterations ) :

        self.degree = degree

        self.learning_rate = learning_rate

        self.iterations = iterations

    # function to transform X

    def transform( self, X ) :

        # initialize X_transform

        X_transform = np.ones( ( self.m, 1 ) )

        j = 0

        for j in range( self.degree + 1 ) :

            if j != 0 :

                x_pow = np.power( X, j )

                # append x_pow to X_transform

                X_transform = np.append( X_transform, x_pow.reshape( -1, 1 ), axis = 1 )

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        return X_transform 

    # function to normalize X_transform

    def normalize( self, X ) :

        X[:, 1:] = ( X[:, 1:] - np.mean( X[:, 1:], axis = 0 ) ) / np.std( X[:, 1:], axis = 0 )

        return X

    # model training

    def fit( self, X, Y ) :

        self.X = X

        self.Y = Y

        self.m, self.n = self.X.shape

        # weight initialization

        self.W = np.zeros( self.degree + 1 )

        # transform X for polynomial h( x ) = w0 * x^0 + w1 * x^1 + w2 * x^2 + ........+ wn * x^n

        X_transform = self.transform( self.X )

        # normalize X_transform

        X_normalize = self.normalize( X_transform )

        # gradient descent learning

        for i in range( self.iterations ) :

            h = self.predict( self.X )

            error = h - self.Y

            # update weights 

            self.W = self.W - self.learning_rate * ( 1 / self.m ) * np.dot( X_normalize.T, error ) 

        return self

    # predict 

    def predict( self, X ) :

        # transform X for polynomial h( x ) = w0 * x^0 + w1 * x^1 + w2 * x^2 + ........+ wn * x^n

        X_transform = self.transform( X )

        X_normalize = self.normalize( X_transform )

        return np.dot( X_transform, self.W )

# Driver code    

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def main() : 

    # Create dataset

    X = np.array( [ [1], [2], [3], [4], [5], [6], [7] ] )

    Y = np.array( [ 45000, 50000, 60000, 80000, 110000, 150000, 200000 ] )

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    # model training

    model = PolynomailRegression( degree = 2, learning_rate = 0.01, iterations = 500 )

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    model.fit( X, Y )

    # Prediction on training set

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    Y_pred = model.predict( X )

    # Visualization 

    plt.scatter( X, Y, color = 'blue' )

    plt.plot( X, Y_pred, color = 'orange' )

    plt.title( 'X vs Y' )

    plt.xlabel( 'X' )

    plt.ylabel( 'Y' )

    plt.show()

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if __name__ == "__main__" : 

    main()