Community and Crime

This is a real dataset of per capita violent crime, with demographic data comprising 128 attributes from 1994 counties in the US.

The original dataset can be found here: http://archive.ics.uci.edu/ml/datasets/Communities+and+Crime

The target variables (per capita violent crime) are normalized to lie in a [0, 1] range. We preprocessed this dataset to exclude attributes with missing values.

# Author: Vinicius Marques <vini.type@gmail.com>
# License: MIT

Imports

import matplotlib.pyplot as plt
from sklearn.model_selection import train_test_split
from pyglmnet import GLM, GLMCV, datasets

Download and preprocess data files

X, y = datasets.fetch_community_crime_data()
n_samples, n_features = X.shape

Out:

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Split the data into training and test sets

X_train, X_test, y_train, y_test = \
    train_test_split(X, y, test_size=0.33, random_state=0)

Fit a binomial distributed GLM with elastic net regularization

# use the default value for reg_lambda
glm = GLMCV(distr='binomial', alpha=0.05, score_metric='pseudo_R2', cv=3,
            tol=1e-4)

# fit model
glm.fit(X_train, y_train)

# score the test set prediction
y_test_hat = glm.predict_proba(X_test)
print("test set pseudo $R^2$ = %f" % glm.score(X_test, y_test))

Out:

test set pseudo $R^2$ = 0.161891

Now use GridSearchCV to compare

import numpy as np # noqa
from sklearn.model_selection import GridSearchCV # noqa
from sklearn.model_selection import KFold # noqa

cv = KFold(3)

reg_lambda = np.logspace(np.log(0.5), np.log(0.01), 10,
                         base=np.exp(1))
param_grid = [{'reg_lambda': reg_lambda}]

glm = GLM(distr='binomial', alpha=0.05, score_metric='pseudo_R2',
          learning_rate=0.1, tol=1e-4, verbose=True)
glmcv = GridSearchCV(glm, param_grid, cv=cv)
glmcv.fit(X_train, y_train)

print("test set pseudo $R^2$ = %f" % glmcv.score(X_test, y_test))

Out:

/Users/mainak/Documents/github_repos/pyglmnet/pyglmnet/pyglmnet.py:864: UserWarning: Reached max number of iterations without convergence.
  "Reached max number of iterations without convergence.")
/Users/mainak/Documents/github_repos/pyglmnet/pyglmnet/pyglmnet.py:864: UserWarning: Reached max number of iterations without convergence.
  "Reached max number of iterations without convergence.")
/Users/mainak/Documents/github_repos/pyglmnet/pyglmnet/pyglmnet.py:864: UserWarning: Reached max number of iterations without convergence.
  "Reached max number of iterations without convergence.")
/Users/mainak/Documents/github_repos/pyglmnet/pyglmnet/pyglmnet.py:864: UserWarning: Reached max number of iterations without convergence.
  "Reached max number of iterations without convergence.")
/Users/mainak/Documents/github_repos/pyglmnet/pyglmnet/pyglmnet.py:864: UserWarning: Reached max number of iterations without convergence.
  "Reached max number of iterations without convergence.")
/Users/mainak/Documents/github_repos/pyglmnet/pyglmnet/pyglmnet.py:864: UserWarning: Reached max number of iterations without convergence.
  "Reached max number of iterations without convergence.")
/Users/mainak/Documents/github_repos/pyglmnet/pyglmnet/pyglmnet.py:864: UserWarning: Reached max number of iterations without convergence.
  "Reached max number of iterations without convergence.")
/Users/mainak/Documents/github_repos/pyglmnet/pyglmnet/pyglmnet.py:864: UserWarning: Reached max number of iterations without convergence.
  "Reached max number of iterations without convergence.")
/Users/mainak/Documents/github_repos/pyglmnet/pyglmnet/pyglmnet.py:864: UserWarning: Reached max number of iterations without convergence.
  "Reached max number of iterations without convergence.")
/Users/mainak/Documents/github_repos/pyglmnet/pyglmnet/pyglmnet.py:864: UserWarning: Reached max number of iterations without convergence.
  "Reached max number of iterations without convergence.")
/Users/mainak/Documents/github_repos/pyglmnet/pyglmnet/pyglmnet.py:864: UserWarning: Reached max number of iterations without convergence.
  "Reached max number of iterations without convergence.")
/Users/mainak/Documents/github_repos/pyglmnet/pyglmnet/pyglmnet.py:864: UserWarning: Reached max number of iterations without convergence.
  "Reached max number of iterations without convergence.")
/Users/mainak/Documents/github_repos/pyglmnet/pyglmnet/pyglmnet.py:864: UserWarning: Reached max number of iterations without convergence.
  "Reached max number of iterations without convergence.")
/Users/mainak/Documents/github_repos/pyglmnet/pyglmnet/pyglmnet.py:864: UserWarning: Reached max number of iterations without convergence.
  "Reached max number of iterations without convergence.")
/Users/mainak/Documents/github_repos/pyglmnet/pyglmnet/pyglmnet.py:864: UserWarning: Reached max number of iterations without convergence.
  "Reached max number of iterations without convergence.")
/Users/mainak/Documents/github_repos/pyglmnet/pyglmnet/pyglmnet.py:864: UserWarning: Reached max number of iterations without convergence.
  "Reached max number of iterations without convergence.")
test set pseudo $R^2$ = 0.153298

Plot the true and predicted test set target values

plt.plot(y_test[:50], 'ko-')
plt.plot(y_test_hat[:50], 'ro-')
plt.legend(['true', 'pred'], frameon=False)
plt.xlabel('Counties')
plt.ylabel('Per capita violent crime')

plt.tick_params(axis='y', right='off')
plt.tick_params(axis='x', top='off')
ax = plt.gca()
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)
plt.show()

Out:

/Users/mainak/Documents/github_repos/pyglmnet/examples/plot_community_crime.py:90: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure.
  plt.show()