Ex. 4.9

Ex. 4.9

Write a computer program to perform a quadratic discriminant analysis by fitting a separate Gaussian model per class. Try it out on the vowel data, and compute the misclassification error for the test data. The data can be found in the book website www-stat.stanford.edu/ElemStatLearn.

Soln. 4.9

The misclassification error for the test data is 52.8% in our simulation. See code below.

Code 
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from sklearn.discriminant_analysis import QuadraticDiscriminantAnalysis
import pathlib
import numpy as np
import pandas as pd

# get relative data folder
PATH = pathlib.Path(__file__).resolve().parents[1]
DATA_PATH = PATH.joinpath("data").resolve()

# train data
train = pd.read_csv(DATA_PATH.joinpath("vowel_train.csv"), header=0)

y_train = pd.DataFrame(train['y'])
y_train = y_train.to_numpy()
y_train = np.reshape(y_train, (1, len(y_train))).ravel()

x_train = pd.DataFrame(train[['x.1', 'x.2', 'x.3', 'x.4', 'x.5', 'x.6', 'x.7', 'x.8', 'x.9', 'x.10']])
x_train = x_train.to_numpy()

# test data
test = pd.read_csv(DATA_PATH.joinpath("vowel_test.csv"), header=0)
y_test = pd.DataFrame(test['y'])
y_test = y_test.to_numpy()
y_test = np.reshape(y_test, (1, len(y_test))).ravel()

x_test = pd.DataFrame(test[['x.1', 'x.2', 'x.3', 'x.4', 'x.5', 'x.6', 'x.7', 'x.8', 'x.9', 'x.10']])
x_test = x_test.to_numpy()


# a utility function to calculate error rate
# of predictions
def getErrorRate(a, b):
    if a.size != b.size:
        raise ValueError('Expect input arrays have equal size, a has {}, b has {}'.
                        format(a.size, b.size))

    if a.size == 0:
        raise ValueError('Expect non-empty input arrays')

    return np.sum(a != b) / a.size


# run
clf = QuadraticDiscriminantAnalysis()
clf.fit(x_train, y_train)
y_predict = clf.predict(x_test)
errorRate = getErrorRate(y_predict, y_test)

print(errorRate)