手写批量线性回归算法：在Python3中梯度下降方法实现模型训练

python3linearregr.py — datarandom.csv — learningRate 0.0001 — threshold 0.0001

iteration_number,weight0,weight1,weight2,...,weightN,sum_of_squared_errors

import argparse # to read inputs from command lineimport csv # to read the input data set fileimport numpy as np # to work with the data set

# initialise argument parser and read argumentsfrom command line with the respective flags and then call the main() functionif __name__ == '__main__':
    parser = argparse.ArgumentParser()
    parser.add_argument("-d", "--data", help="Data File")
    parser.add_argument("-l", "--learningRate", help="Learning Rate")
    parser.add_argument("-t", "--threshold", help="Threshold")
    main()

defmain():
    args = parser.parse_args()
    file, learningRate, threshold = args.data, float(
        args.learningRate), float(args.threshold) # save respective command line inputs into variables# read csv file and the last column is the target output and is separated from the input (X) as Ywith open(file) as csvFile:
        reader = csv.reader(csvFile, delimiter=',')
        X = []
        Y = []
        for row in reader:
            X.append([1.0] + row[:-1])
            Y.append([row[-1]])

    # Convert data points into float and initialise weight vector with 0s.
    n = len(X)
    X = np.array(X).astype(float)
    Y = np.array(Y).astype(float)
    W = np.zeros(X.shape[1]).astype(float)
    # this matrix is transposed to match the necessary matrix dimensions for calculating dot product
    W = W.reshape(X.shape[1], 1).round(4)

    # Calculate the predicted output value
    f_x = calculatePredicatedValue(X, W)

    # Calculate the initial SSE
    sse_old = calculateSSE(Y, f_x)

    outputFile = 'solution_' + \
                 'learningRate_' + str(learningRate) + '_threshold_' \
                 + str(threshold) + '.csv''''
        Output file is opened in writing mode and the data is written in the format mentioned in the post. After the
        first values are written, the gradient and updated weights are calculated using the calculateGradient function.
        An iteration variable is maintained to keep track on the number of times the batch linear regression is executed
        before it falls below the threshold value. In the infinite while loop, the predicted output value is calculated
        again and new SSE value is calculated. If the absolute difference between the older(SSE from previous iteration)
        and newer(SSE from current iteration) SSE is greater than the threshold value, then above process is repeated.
        The iteration is incremented by 1 and the current SSE is stored into previous SSE. If the absolute difference
        between the older(SSE from previous iteration) and newer(SSE from current iteration) SSE falls below the
        threshold value, the loop breaks and the last output values are written to the file.
    '''with open(outputFile, 'w', newline='') as csvFile:
        writer = csv.writer(csvFile, delimiter=',', quoting=csv.QUOTE_NONE, escapechar='')
        writer.writerow([*[0], *["{0:.4f}".format(val) for val in W.T[0]], *["{0:.4f}".format(sse_old)]])

        gradient, W = calculateGradient(W, X, Y, f_x, learningRate)

        iteration = 1whileTrue:
            f_x = calculatePredicatedValue(X, W)
            sse_new = calculateSSE(Y, f_x)

            if abs(sse_new - sse_old) > threshold:
                writer.writerow([*[iteration], *["{0:.4f}".format(val) for val in W.T[0]], *["{0:.4f}".format(sse_new)]])
                gradient, W = calculateGradient(W, X, Y, f_x, learningRate)
                iteration += 1
                sse_old = sse_new
            else:
                break
        writer.writerow([*[iteration], *["{0:.4f}".format(val) for val in W.T[0]], *["{0:.4f}".format(sse_new)]])
    print("Output File Name: " + outputFile

# dot product of X(input) and W(weights) as numpy matrices and returning the result which is the predicted outputdefcalculatePredicatedValue(X, W):
    f_x = np.dot(X, W)
    return f_x

defcalculateGradient(W, X, Y, f_x, learningRate):
    gradient = (Y - f_x) * X
    gradient = np.sum(gradient, axis=0)
    temp = np.array(learningRate * gradient).reshape(W.shape)
    W = W + temp
    return gradient, W

defcalculateSSE(Y, f_x):
    sse = np.sum(np.square(f_x - Y))
    return sse

import argparse
import csv
import numpy as np


defmain():
    args = parser.parse_args()
    file, learningRate, threshold = args.data, float(
        args.learningRate), float(args.threshold) # save respective command line inputs into variables# read csv file and the last column is the target output and is separated from the input (X) as Ywith open(file) as csvFile:
        reader = csv.reader(csvFile, delimiter=',')
        X = []
        Y = []
        for row in reader:
            X.append([1.0] + row[:-1])
            Y.append([row[-1]])

    # Convert data points into float and initialise weight vector with 0s.
    n = len(X)
    X = np.array(X).astype(float)
    Y = np.array(Y).astype(float)
    W = np.zeros(X.shape[1]).astype(float)
    # this matrix is transposed to match the necessary matrix dimensions for calculating dot product
    W = W.reshape(X.shape[1], 1).round(4)

    # Calculate the predicted output value
    f_x = calculatePredicatedValue(X, W)

    # Calculate the initial SSE
    sse_old = calculateSSE(Y, f_x)

    outputFile = 'solution_' + \
                 'learningRate_' + str(learningRate) + '_threshold_' \
                 + str(threshold) + '.csv''''
        Output file is opened in writing mode and the data is written in the format mentioned in the post. After the
        first values are written, the gradient and updated weights are calculated using the calculateGradient function.
        An iteration variable is maintained to keep track on the number of times the batch linear regression is executed
        before it falls below the threshold value. In the infinite while loop, the predicted output value is calculated
        again and new SSE value is calculated. If the absolute difference between the older(SSE from previous iteration)
        and newer(SSE from current iteration) SSE is greater than the threshold value, then above process is repeated.
        The iteration is incremented by 1 and the current SSE is stored into previous SSE. If the absolute difference
        between the older(SSE from previous iteration) and newer(SSE from current iteration) SSE falls below the
        threshold value, the loop breaks and the last output values are written to the file.
    '''with open(outputFile, 'w', newline='') as csvFile:
        writer = csv.writer(csvFile, delimiter=',', quoting=csv.QUOTE_NONE, escapechar='')
        writer.writerow([*[0], *["{0:.4f}".format(val) for val in W.T[0]], *["{0:.4f}".format(sse_old)]])

        gradient, W = calculateGradient(W, X, Y, f_x, learningRate)

        iteration = 1whileTrue:
            f_x = calculatePredicatedValue(X, W)
            sse_new = calculateSSE(Y, f_x)

            if abs(sse_new - sse_old) > threshold:
                writer.writerow([*[iteration], *["{0:.4f}".format(val) for val in W.T[0]], *["{0:.4f}".format(sse_new)]])
                gradient, W = calculateGradient(W, X, Y, f_x, learningRate)
                iteration += 1
                sse_old = sse_new
            else:
                break
        writer.writerow([*[iteration], *["{0:.4f}".format(val) for val in W.T[0]], *["{0:.4f}".format(sse_new)]])
    print("Output File Name: " + outputFile


defcalculateGradient(W, X, Y, f_x, learningRate):
    gradient = (Y - f_x) * X
    gradient = np.sum(gradient, axis=0)
    # gradient = np.array([float("{0:.4f}".format(val)) for val in gradient])
    temp = np.array(learningRate * gradient).reshape(W.shape)
    W = W + temp
    return gradient, W


defcalculateSSE(Y, f_x):
    sse = np.sum(np.square(f_x - Y))

    return sse


defcalculatePredicatedValue(X, W):
    f_x = np.dot(X, W)
    return f_x


if __name__ == '__main__':
    parser = argparse.ArgumentParser()
    parser.add_argument("-d", "--data", help="Data File")
    parser.add_argument("-l", "--learningRate", help="Learning Rate")
    parser.add_argument("-t", "--threshold", help="Threshold")
    main()