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Example on regression using python.
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| You are provided with 2 different data-sets- TrainingSet.mat and TestSet.mat. In this | |
| task, you are required to build a regression function and evaluate its performance on the | |
| testing set. | |
| (i) Learn the weights of a polynomial regressor by adopting a three-fold cross validation | |
| strategy on the data-set TrainingSet.mat. You may consider orders of polynomial | |
| between one to nine . Accordingly, select the order of polynomial(M ) that gives the | |
| lowest average error. | |
| (ii) Using the order(M ) obtained from (i), test the regression function on the Test- | |
| Set.mat and calculate the mean square error. |
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| import numpy as np; | |
| import matplotlib.pyplot as plt; | |
| import scipy.io; | |
| mat_file = scipy.io.loadmat('TrainingSet.mat'); | |
| train_x = mat_file['train_x'][0]; | |
| train_y = mat_file['train_y'][0]; | |
| plt.plot(train_x, train_y, 'ro'); | |
| # function to calculate weights | |
| def func_weights(arg_phi, arg_t): | |
| arg_phi_t = np.matrix.transpose(arg_phi); | |
| temp = np.dot(arg_phi_t, arg_phi); | |
| temp = np.linalg.pinv(temp); | |
| temp = np.dot(temp, arg_phi_t); | |
| return np.dot(temp, arg_t); | |
| # function to calculate Root Mean Square Error | |
| def func_error(arg_weights, arg_phi, arg_t): | |
| y = np.dot(arg_phi, arg_weights); | |
| y = y-arg_t; | |
| ans = 0; | |
| for i in y: | |
| ans += i*i; | |
| ans /= arg_t.size; | |
| return ans**0.5; | |
| # used to run multiple iterations of main() function to get frequencies | |
| # of order at which minimum order is attained. | |
| def find_freq(): | |
| freq = np.zeros(10); | |
| for i in range(500): | |
| freq[main()] += 1; | |
| print freq; | |
| # function to calculate Mean Square Error on test data | |
| def error_on_test(arg_weights): | |
| mat_file = scipy.io.loadmat('TestSet.mat'); | |
| test_x = mat_file['xtest'][0]; | |
| test_y = mat_file['ytest'][0]; | |
| y = np.zeros(test_x.size); | |
| for i in range(test_x.size): | |
| y = 0; | |
| for j in range(arg_weights.size): | |
| y += arg_weights[0][j]*(test_x[i]**j); | |
| y = y-test_y; | |
| ans=0; | |
| for i in y: | |
| ans += i*i; | |
| ans /= test_x.size; | |
| print "Mean Square Error on test data is : " + str(ans); | |
| # main function. | |
| def main(): | |
| # randomly split the training data into 3 parts. | |
| index = np.arange(train_x.size-1); | |
| np.random.shuffle(index); | |
| index = np.split(index, 3); | |
| error = np.zeros((3, 10)); | |
| for i in range(3): | |
| for order in range(10): | |
| phi = np.zeros((2*index[i].size, order+1)); | |
| for j in range(200): | |
| for k in range(order+1): | |
| phi[j][k] = train_x[index[i][j]]**k; | |
| for j in range(200, 400): | |
| for k in range(order+1): | |
| phi[j][k] = train_x[index[(i+1)%3][j-200]]**k; | |
| phi = np.zeros((index[i].size, order+1)); | |
| for j in range(200): | |
| for k in range(order+1): | |
| phi[j][k] = train_x[index[(i+2)%3][j]]**k; | |
| t = np.zeros((index[0].size, 1)); | |
| for j in range(200): | |
| t[j][0] = train_y[index[i][j]]; | |
| weights = func_weights(phi, t); | |
| error[i][order] = func_error(weights, phi, t); | |
| if i == 0 and order == 6: | |
| weights_1 = np.matrix.transpose(weights); | |
| elif i == 1 and order == 6: | |
| weights_2 = np.matrix.transpose(weights); | |
| elif i == 2 and order == 6: | |
| weights_3 = np.matrix.transpose(weights); | |
| avg_weights = (weights_1+weights_2+weights_3)/3; | |
| print "Weights for a 6 degree polynomial: " + str(avg_weights); | |
| avg_error = np.zeros(10); | |
| for i in range(10): | |
| avg_error[i] = (error[0][i]+error[1][i]+error[2][i])/3; | |
| # print avg_error; | |
| min_error_order = np.argmin(avg_error); | |
| # print "Minimum error is achieved for order: " + str(min_error_order); | |
| ## Finding Mean Square Error on test data. | |
| error_on_test(avg_weights); | |
| ## Plotting the data points and regression function using training data. | |
| poly = np.zeros(train_x.size); | |
| for i in range(train_x.size): | |
| poly[i] = 0; | |
| for j in range(avg_weights.size): | |
| poly[i] += avg_weights[0][j]*(train_x[i]**j); | |
| plt.plot(train_x, poly); | |
| plt.show(); | |
| return min_error_order; | |
| if __name__ == "__main__": | |
| main(); | |
| #find_freq(); |
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| 74dc e794 bd4a 4c88 89ba 2392 56b6 9f38 | |
| 58a6 7969 e851 d65c 7e3e 17e7 aa28 c6c3 | |
| 6f27 8f47 7c5a c4c7 f022 cb53 b517 f898 | |
| c935 f169 8be5 638d 61a1 fec7 b91c 7584 | |
| ee56 b861 2d81 9e7b 6fae e552 482c 0e3e | |
| 4c3b aa42 a94e 7aa6 572a e342 6282 e305 | |
| 79e9 2a02 0bbd ba5b 397e 043e b47f 7854 | |
| db84 526d 3754 cc0e 37a2 5407 ed2e 5b9f | |
| 3b45 a092 e180 74dc 1102 9bba 72cb 9ea6 | |
| 0af0 6ed7 de9b 9501 7c8c 113e 636d e0c1 | |
| c155 1b43 7def 3ce2 604e de27 439e df2c | |
| 2aa8 fe6b aa60 c2c4 7776 0529 3be8 0cbc | |
| b4ce eff2 c0db 69ac dedc 6137 f37c 0ad5 | |
| 64ef 3835 978f a389 58f1 79cf f661 dc1b | |
| 1cda 15e0 d58d 8eaa 41ae 49b7 3ea2 766b | |
| 594d 02fb 3cfc 0fb3 893f 21 |
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