regression_svm.md

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Regression with SVM

%matplotlib inline
import matplotlib.pyplot as plt
import seaborn as sns
import pandas as pd
import numpy as np

from sklearn import svm, datasets, metrics, model_selection, preprocessing, pipeline

Load the data set

boston = datasets.load_boston()
print(boston.DESCR)

.. _boston_dataset:

Boston house prices dataset
---------------------------

**Data Set Characteristics:**  

    :Number of Instances: 506 

    :Number of Attributes: 13 numeric/categorical predictive. Median Value (attribute 14) is usually the target.

    :Attribute Information (in order):
        - CRIM     per capita crime rate by town
        - ZN       proportion of residential land zoned for lots over 25,000 sq.ft.
        - INDUS    proportion of non-retail business acres per town
        - CHAS     Charles River dummy variable (= 1 if tract bounds river; 0 otherwise)
        - NOX      nitric oxides concentration (parts per 10 million)
        - RM       average number of rooms per dwelling
        - AGE      proportion of owner-occupied units built prior to 1940
        - DIS      weighted distances to five Boston employment centres
        - RAD      index of accessibility to radial highways
        - TAX      full-value property-tax rate per $10,000
        - PTRATIO  pupil-teacher ratio by town
        - B        1000(Bk - 0.63)^2 where Bk is the proportion of blacks by town
        - LSTAT    % lower status of the population
        - MEDV     Median value of owner-occupied homes in $1000's

    :Missing Attribute Values: None

    :Creator: Harrison, D. and Rubinfeld, D.L.

This is a copy of UCI ML housing dataset.
https://archive.ics.uci.edu/ml/machine-learning-databases/housing/


This dataset was taken from the StatLib library which is maintained at Carnegie Mellon University.

The Boston house-price data of Harrison, D. and Rubinfeld, D.L. 'Hedonic
prices and the demand for clean air', J. Environ. Economics & Management,
vol.5, 81-102, 1978.   Used in Belsley, Kuh & Welsch, 'Regression diagnostics
...', Wiley, 1980.   N.B. Various transformations are used in the table on
pages 244-261 of the latter.

The Boston house-price data has been used in many machine learning papers that address regression
problems.   
     
.. topic:: References

   - Belsley, Kuh & Welsch, 'Regression diagnostics: Identifying Influential Data and Sources of Collinearity', Wiley, 1980. 244-261.
   - Quinlan,R. (1993). Combining Instance-Based and Model-Based Learning. In Proceedings on the Tenth International Conference of Machine Learning, 236-243, University of Massachusetts, Amherst. Morgan Kaufmann.

X = pd.DataFrame(boston.data, columns=boston.feature_names)
y = boston.target

X_train, X_test, y_train, y_test = model_selection.train_test_split(X, y, train_size=0.7)

print('train samples:', len(X_train))
print('test samples', len(X_test))

train samples: 354
test samples 152

df_train = pd.DataFrame(y_train, columns=['target'])
df_train['type'] = 'train'

df_test = pd.DataFrame(y_test, columns=['target'])
df_test['type'] = 'test'

df_set = df_train.append(df_test)

_ = sns.displot(df_set, x="target" ,hue="type", kind="kde", log_scale=False)

model = pipeline.make_pipeline(preprocessing.StandardScaler(), svm.SVR(C=1.0, epsilon=0.2))
model.fit(X_train, y_train)

Pipeline(steps=[('standardscaler', StandardScaler()),
                ('svr', SVR(epsilon=0.2))])

predicted = model.predict(X_test)

fig, ax = plt.subplots()
ax.scatter(y_test, predicted)

ax.set_xlabel('True Values')
ax.set_ylabel('Predicted')
_ = ax.plot([0, y.max()], [0, y.max()], ls='-', color='red')

residual = y_test - predicted

fig, ax = plt.subplots()
ax.scatter(y_test, residual)
ax.set_xlabel('y')
ax.set_ylabel('residual')

_ = plt.axhline(0, color='red', ls='--')

sns.displot(residual, kind="kde");

<seaborn.axisgrid.FacetGrid at 0x145de40a0>

print("r2 score: {}".format(metrics.r2_score(y_test, predicted)))
print("mse: {}".format(metrics.mean_squared_error(y_test, predicted)))
print("rmse: {}".format(np.sqrt(metrics.mean_squared_error(y_test, predicted))))
print("mae: {}".format(metrics.mean_absolute_error(y_test, predicted)))

r2 score: 0.5798174615037461
mse: 39.175048983419224
rmse: 6.258997442356022
mae: 3.7327256030498606