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from __future__ import division
import numpy as np
from scipy.sparse import csr_matrix
from sklearn.utils import check_random_state
from sklearn.utils.testing import (assert_array_equal, assert_almost_equal,
assert_false, assert_raises, assert_equal,
assert_greater)
from sklearn.feature_selection.mutual_info_ import (
mutual_info_regression, mutual_info_classif, _compute_mi)
def test_compute_mi_dd():
# In discrete case computations are straightforward and can be done
# by hand on given vectors.
x = np.array([0, 1, 1, 0, 0])
y = np.array([1, 0, 0, 0, 1])
H_x = H_y = -(3/5) * np.log(3/5) - (2/5) * np.log(2/5)
H_xy = -1/5 * np.log(1/5) - 2/5 * np.log(2/5) - 2/5 * np.log(2/5)
I_xy = H_x + H_y - H_xy
assert_almost_equal(_compute_mi(x, y, True, True), I_xy)
def test_compute_mi_cc():
# For two continuous variables a good approach is to test on bivariate
# normal distribution, where mutual information is known.
# Mean of the distribution, irrelevant for mutual information.
mean = np.zeros(2)
# Setup covariance matrix with correlation coeff. equal 0.5.
sigma_1 = 1
sigma_2 = 10
corr = 0.5
cov = np.array([
[sigma_1**2, corr * sigma_1 * sigma_2],
[corr * sigma_1 * sigma_2, sigma_2**2]
])
# True theoretical mutual information.
I_theory = (np.log(sigma_1) + np.log(sigma_2) -
0.5 * np.log(np.linalg.det(cov)))
rng = check_random_state(0)
Z = rng.multivariate_normal(mean, cov, size=1000)
x, y = Z[:, 0], Z[:, 1]
# Theory and computed values won't be very close, assert that the
# first figures after decimal point match.
for n_neighbors in [3, 5, 7]:
I_computed = _compute_mi(x, y, False, False, n_neighbors)
assert_almost_equal(I_computed, I_theory, 1)
def test_compute_mi_cd():
# To test define a joint distribution as follows:
# p(x, y) = p(x) p(y | x)
# X ~ Bernoulli(p)
# (Y | x = 0) ~ Uniform(-1, 1)
# (Y | x = 1) ~ Uniform(0, 2)
# Use the following formula for mutual information:
# I(X; Y) = H(Y) - H(Y | X)
# Two entropies can be computed by hand:
# H(Y) = -(1-p)/2 * ln((1-p)/2) - p/2*log(p/2) - 1/2*log(1/2)
# H(Y | X) = ln(2)
# Now we need to implement sampling from out distribution, which is
# done easily using conditional distribution logic.
n_samples = 1000
rng = check_random_state(0)
for p in [0.3, 0.5, 0.7]:
x = rng.uniform(size=n_samples) > p
y = np.empty(n_samples)
mask = x == 0
y[mask] = rng.uniform(-1, 1, size=np.sum(mask))
y[~mask] = rng.uniform(0, 2, size=np.sum(~mask))
I_theory = -0.5 * ((1 - p) * np.log(0.5 * (1 - p)) +
p * np.log(0.5 * p) + np.log(0.5)) - np.log(2)
# Assert the same tolerance.
for n_neighbors in [3, 5, 7]:
I_computed = _compute_mi(x, y, True, False, n_neighbors)
assert_almost_equal(I_computed, I_theory, 1)
def test_compute_mi_cd_unique_label():
# Test that adding unique label doesn't change MI.
n_samples = 100
x = np.random.uniform(size=n_samples) > 0.5
y = np.empty(n_samples)
mask = x == 0
y[mask] = np.random.uniform(-1, 1, size=np.sum(mask))
y[~mask] = np.random.uniform(0, 2, size=np.sum(~mask))
mi_1 = _compute_mi(x, y, True, False)
x = np.hstack((x, 2))
y = np.hstack((y, 10))
mi_2 = _compute_mi(x, y, True, False)
assert_equal(mi_1, mi_2)
# We are going test that feature ordering by MI matches our expectations.
def test_mutual_info_classif_discrete():
X = np.array([[0, 0, 0],
[1, 1, 0],
[2, 0, 1],
[2, 0, 1],
[2, 0, 1]])
y = np.array([0, 1, 2, 2, 1])
# Here X[:, 0] is the most informative feature, and X[:, 1] is weakly
# informative.
mi = mutual_info_classif(X, y, discrete_features=True)
assert_array_equal(np.argsort(-mi), np.array([0, 2, 1]))
def test_mutual_info_regression():
# We generate sample from multivariate normal distribution, using
# transformation from initially uncorrelated variables. The zero
# variables after transformation is selected as the target vector,
# it has the strongest correlation with the variable 2, and
# the weakest correlation with the variable 1.
T = np.array([
[1, 0.5, 2, 1],
[0, 1, 0.1, 0.0],
[0, 0.1, 1, 0.1],
[0, 0.1, 0.1, 1]
])
cov = T.dot(T.T)
mean = np.zeros(4)
rng = check_random_state(0)
Z = rng.multivariate_normal(mean, cov, size=1000)
X = Z[:, 1:]
y = Z[:, 0]
mi = mutual_info_regression(X, y, random_state=0)
assert_array_equal(np.argsort(-mi), np.array([1, 2, 0]))
def test_mutual_info_classif_mixed():
# Here the target is discrete and there are two continuous and one
# discrete feature. The idea of this test is clear from the code.
rng = check_random_state(0)
X = rng.rand(1000, 3)
X[:, 1] += X[:, 0]
y = ((0.5 * X[:, 0] + X[:, 2]) > 0.5).astype(int)
X[:, 2] = X[:, 2] > 0.5
mi = mutual_info_classif(X, y, discrete_features=[2], n_neighbors=3,
random_state=0)
assert_array_equal(np.argsort(-mi), [2, 0, 1])
for n_neighbors in [5, 7, 9]:
mi_nn = mutual_info_classif(X, y, discrete_features=[2],
n_neighbors=n_neighbors, random_state=0)
# Check that the continuous values have an higher MI with greater
# n_neighbors
assert_greater(mi_nn[0], mi[0])
assert_greater(mi_nn[1], mi[1])
# The n_neighbors should not have any effect on the discrete value
# The MI should be the same
assert_equal(mi_nn[2], mi[2])
def test_mutual_info_options():
X = np.array([[0, 0, 0],
[1, 1, 0],
[2, 0, 1],
[2, 0, 1],
[2, 0, 1]], dtype=float)
y = np.array([0, 1, 2, 2, 1], dtype=float)
X_csr = csr_matrix(X)
for mutual_info in (mutual_info_regression, mutual_info_classif):
assert_raises(ValueError, mutual_info_regression, X_csr, y,
discrete_features=False)
mi_1 = mutual_info(X, y, discrete_features='auto', random_state=0)
mi_2 = mutual_info(X, y, discrete_features=False, random_state=0)
mi_3 = mutual_info(X_csr, y, discrete_features='auto',
random_state=0)
mi_4 = mutual_info(X_csr, y, discrete_features=True,
random_state=0)
assert_array_equal(mi_1, mi_2)
assert_array_equal(mi_3, mi_4)
assert_false(np.allclose(mi_1, mi_3))
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