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"""
Testing for Theil-Sen module (sklearn.linear_model.theil_sen)
"""
# Author: Florian Wilhelm <florian.wilhelm@gmail.com>
# License: BSD 3 clause
from __future__ import division, print_function, absolute_import
import os
import sys
from contextlib import contextmanager
import numpy as np
from numpy.testing import assert_array_equal, assert_array_less
from numpy.testing import assert_array_almost_equal, assert_warns
from scipy.linalg import norm
from scipy.optimize import fmin_bfgs
from sklearn.exceptions import ConvergenceWarning
from sklearn.linear_model import LinearRegression, TheilSenRegressor
from sklearn.linear_model.theil_sen import _spatial_median, _breakdown_point
from sklearn.linear_model.theil_sen import _modified_weiszfeld_step
from sklearn.utils.testing import (
assert_almost_equal, assert_greater, assert_less, assert_raises,
)
@contextmanager
def no_stdout_stderr():
old_stdout = sys.stdout
old_stderr = sys.stderr
with open(os.devnull, 'w') as devnull:
sys.stdout = devnull
sys.stderr = devnull
yield
devnull.flush()
sys.stdout = old_stdout
sys.stderr = old_stderr
def gen_toy_problem_1d(intercept=True):
random_state = np.random.RandomState(0)
# Linear model y = 3*x + N(2, 0.1**2)
w = 3.
if intercept:
c = 2.
n_samples = 50
else:
c = 0.1
n_samples = 100
x = random_state.normal(size=n_samples)
noise = 0.1 * random_state.normal(size=n_samples)
y = w * x + c + noise
# Add some outliers
if intercept:
x[42], y[42] = (-2, 4)
x[43], y[43] = (-2.5, 8)
x[33], y[33] = (2.5, 1)
x[49], y[49] = (2.1, 2)
else:
x[42], y[42] = (-2, 4)
x[43], y[43] = (-2.5, 8)
x[53], y[53] = (2.5, 1)
x[60], y[60] = (2.1, 2)
x[72], y[72] = (1.8, -7)
return x[:, np.newaxis], y, w, c
def gen_toy_problem_2d():
random_state = np.random.RandomState(0)
n_samples = 100
# Linear model y = 5*x_1 + 10*x_2 + N(1, 0.1**2)
X = random_state.normal(size=(n_samples, 2))
w = np.array([5., 10.])
c = 1.
noise = 0.1 * random_state.normal(size=n_samples)
y = np.dot(X, w) + c + noise
# Add some outliers
n_outliers = n_samples // 10
ix = random_state.randint(0, n_samples, size=n_outliers)
y[ix] = 50 * random_state.normal(size=n_outliers)
return X, y, w, c
def gen_toy_problem_4d():
random_state = np.random.RandomState(0)
n_samples = 10000
# Linear model y = 5*x_1 + 10*x_2 + 42*x_3 + 7*x_4 + N(1, 0.1**2)
X = random_state.normal(size=(n_samples, 4))
w = np.array([5., 10., 42., 7.])
c = 1.
noise = 0.1 * random_state.normal(size=n_samples)
y = np.dot(X, w) + c + noise
# Add some outliers
n_outliers = n_samples // 10
ix = random_state.randint(0, n_samples, size=n_outliers)
y[ix] = 50 * random_state.normal(size=n_outliers)
return X, y, w, c
def test_modweiszfeld_step_1d():
X = np.array([1., 2., 3.]).reshape(3, 1)
# Check startvalue is element of X and solution
median = 2.
new_y = _modified_weiszfeld_step(X, median)
assert_array_almost_equal(new_y, median)
# Check startvalue is not the solution
y = 2.5
new_y = _modified_weiszfeld_step(X, y)
assert_array_less(median, new_y)
assert_array_less(new_y, y)
# Check startvalue is not the solution but element of X
y = 3.
new_y = _modified_weiszfeld_step(X, y)
assert_array_less(median, new_y)
assert_array_less(new_y, y)
# Check that a single vector is identity
X = np.array([1., 2., 3.]).reshape(1, 3)
y = X[0, ]
new_y = _modified_weiszfeld_step(X, y)
assert_array_equal(y, new_y)
def test_modweiszfeld_step_2d():
X = np.array([0., 0., 1., 1., 0., 1.]).reshape(3, 2)
y = np.array([0.5, 0.5])
# Check first two iterations
new_y = _modified_weiszfeld_step(X, y)
assert_array_almost_equal(new_y, np.array([1 / 3, 2 / 3]))
new_y = _modified_weiszfeld_step(X, new_y)
assert_array_almost_equal(new_y, np.array([0.2792408, 0.7207592]))
# Check fix point
y = np.array([0.21132505, 0.78867497])
new_y = _modified_weiszfeld_step(X, y)
assert_array_almost_equal(new_y, y)
def test_spatial_median_1d():
X = np.array([1., 2., 3.]).reshape(3, 1)
true_median = 2.
_, median = _spatial_median(X)
assert_array_almost_equal(median, true_median)
# Test larger problem and for exact solution in 1d case
random_state = np.random.RandomState(0)
X = random_state.randint(100, size=(1000, 1))
true_median = np.median(X.ravel())
_, median = _spatial_median(X)
assert_array_equal(median, true_median)
def test_spatial_median_2d():
X = np.array([0., 0., 1., 1., 0., 1.]).reshape(3, 2)
_, median = _spatial_median(X, max_iter=100, tol=1.e-6)
def cost_func(y):
dists = np.array([norm(x - y) for x in X])
return np.sum(dists)
# Check if median is solution of the Fermat-Weber location problem
fermat_weber = fmin_bfgs(cost_func, median, disp=False)
assert_array_almost_equal(median, fermat_weber)
# Check when maximum iteration is exceeded a warning is emitted
assert_warns(ConvergenceWarning, _spatial_median, X, max_iter=30, tol=0.)
def test_theil_sen_1d():
X, y, w, c = gen_toy_problem_1d()
# Check that Least Squares fails
lstq = LinearRegression().fit(X, y)
assert_greater(np.abs(lstq.coef_ - w), 0.9)
# Check that Theil-Sen works
theil_sen = TheilSenRegressor(random_state=0).fit(X, y)
assert_array_almost_equal(theil_sen.coef_, w, 1)
assert_array_almost_equal(theil_sen.intercept_, c, 1)
def test_theil_sen_1d_no_intercept():
X, y, w, c = gen_toy_problem_1d(intercept=False)
# Check that Least Squares fails
lstq = LinearRegression(fit_intercept=False).fit(X, y)
assert_greater(np.abs(lstq.coef_ - w - c), 0.5)
# Check that Theil-Sen works
theil_sen = TheilSenRegressor(fit_intercept=False,
random_state=0).fit(X, y)
assert_array_almost_equal(theil_sen.coef_, w + c, 1)
assert_almost_equal(theil_sen.intercept_, 0.)
def test_theil_sen_2d():
X, y, w, c = gen_toy_problem_2d()
# Check that Least Squares fails
lstq = LinearRegression().fit(X, y)
assert_greater(norm(lstq.coef_ - w), 1.0)
# Check that Theil-Sen works
theil_sen = TheilSenRegressor(max_subpopulation=1e3,
random_state=0).fit(X, y)
assert_array_almost_equal(theil_sen.coef_, w, 1)
assert_array_almost_equal(theil_sen.intercept_, c, 1)
def test_calc_breakdown_point():
bp = _breakdown_point(1e10, 2)
assert_less(np.abs(bp - 1 + 1 / (np.sqrt(2))), 1.e-6)
def test_checksubparams_negative_subpopulation():
X, y, w, c = gen_toy_problem_1d()
theil_sen = TheilSenRegressor(max_subpopulation=-1, random_state=0)
assert_raises(ValueError, theil_sen.fit, X, y)
def test_checksubparams_too_few_subsamples():
X, y, w, c = gen_toy_problem_1d()
theil_sen = TheilSenRegressor(n_subsamples=1, random_state=0)
assert_raises(ValueError, theil_sen.fit, X, y)
def test_checksubparams_too_many_subsamples():
X, y, w, c = gen_toy_problem_1d()
theil_sen = TheilSenRegressor(n_subsamples=101, random_state=0)
assert_raises(ValueError, theil_sen.fit, X, y)
def test_checksubparams_n_subsamples_if_less_samples_than_features():
random_state = np.random.RandomState(0)
n_samples, n_features = 10, 20
X = random_state.normal(size=(n_samples, n_features))
y = random_state.normal(size=n_samples)
theil_sen = TheilSenRegressor(n_subsamples=9, random_state=0)
assert_raises(ValueError, theil_sen.fit, X, y)
def test_subpopulation():
X, y, w, c = gen_toy_problem_4d()
theil_sen = TheilSenRegressor(max_subpopulation=250,
random_state=0).fit(X, y)
assert_array_almost_equal(theil_sen.coef_, w, 1)
assert_array_almost_equal(theil_sen.intercept_, c, 1)
def test_subsamples():
X, y, w, c = gen_toy_problem_4d()
theil_sen = TheilSenRegressor(n_subsamples=X.shape[0],
random_state=0).fit(X, y)
lstq = LinearRegression().fit(X, y)
# Check for exact the same results as Least Squares
assert_array_almost_equal(theil_sen.coef_, lstq.coef_, 9)
def test_verbosity():
X, y, w, c = gen_toy_problem_1d()
# Check that Theil-Sen can be verbose
with no_stdout_stderr():
TheilSenRegressor(verbose=True, random_state=0).fit(X, y)
TheilSenRegressor(verbose=True,
max_subpopulation=10,
random_state=0).fit(X, y)
def test_theil_sen_parallel():
X, y, w, c = gen_toy_problem_2d()
# Check that Least Squares fails
lstq = LinearRegression().fit(X, y)
assert_greater(norm(lstq.coef_ - w), 1.0)
# Check that Theil-Sen works
theil_sen = TheilSenRegressor(n_jobs=-1,
random_state=0,
max_subpopulation=2e3).fit(X, y)
assert_array_almost_equal(theil_sen.coef_, w, 1)
assert_array_almost_equal(theil_sen.intercept_, c, 1)
def test_less_samples_than_features():
random_state = np.random.RandomState(0)
n_samples, n_features = 10, 20
X = random_state.normal(size=(n_samples, n_features))
y = random_state.normal(size=n_samples)
# Check that Theil-Sen falls back to Least Squares if fit_intercept=False
theil_sen = TheilSenRegressor(fit_intercept=False,
random_state=0).fit(X, y)
lstq = LinearRegression(fit_intercept=False).fit(X, y)
assert_array_almost_equal(theil_sen.coef_, lstq.coef_, 12)
# Check fit_intercept=True case. This will not be equal to the Least
# Squares solution since the intercept is calculated differently.
theil_sen = TheilSenRegressor(fit_intercept=True, random_state=0).fit(X, y)
y_pred = theil_sen.predict(X)
assert_array_almost_equal(y_pred, y, 12)
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