Source code for mgcpy.independence_tests.hhg

```import numpy as np

from mgcpy.independence_tests.abstract_class import IndependenceTest
from mgcpy.independence_tests.utils.compute_distance_matrix import \
compute_distance

[docs]class HHG(IndependenceTest):
def __init__(self, compute_distance_matrix=None):
"""
:param compute_distance_matrix: a function to compute the pairwise distance matrix, given a data matrix
:type compute_distance_matrix: FunctionType or callable()
"""
IndependenceTest.__init__(self, compute_distance_matrix)
self.which_test = "hhg"

[docs]    def test_statistic(self, matrix_X, matrix_Y):
"""
Computes the HHG correlation measure between two datasets.

:param matrix_X: a [n*p] data matrix, a matrix with n samples in p dimensions
:type matrix_X: 2D `numpy.array`

:param matrix_Y: a [n*q] data matrix, a matrix with n samples in q dimensions
:type matrix_Y: 2D `numpy.array`

:param replication_factor: specifies the number of replications to use for
the permutation test. Defaults to 1000.
:type replication_factor: int

:return: returns a list of two items, that contains:

- :test_statistic_: test statistic
- :test_statistic_metadata_: (optional) a ``dict`` of metadata other than the p_value,
that the independence tests computes in the process
:rtype: float, dict

**Example:**

>>> import numpy as np
>>> from mgcpy.independence_tests.hhg import HHG

>>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045,
0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1)
>>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312,
1.35857623, -0.06729464, 0.16168344, -0.61048226, 0.41711113]).reshape(-1, 1)
>>> hhg = HHG()
>>> hhg_test_stat = hhg.test_statistic(X, Y)
"""
distance_matrix_X, distance_matrix_Y = compute_distance(matrix_X, matrix_Y, self.compute_distance_matrix)

n = distance_matrix_X.shape[0]
S = np.zeros((n, n))

for i in range(n):
for j in range(n):
if i != j:
tmp1 = distance_matrix_X[i, :] <= distance_matrix_X[i, j]
tmp2 = distance_matrix_Y[i, :] <= distance_matrix_Y[i, j]
t11 = np.sum(tmp1 * tmp2) - 2
t12 = np.sum(tmp1 * (1-tmp2))
t21 = np.sum((1-tmp1) * tmp2)
t22 = np.sum((1-tmp1) * (1-tmp2))
denom = (t11+t12) * (t21+t22) * (t11+t21) * (t12+t22)
if denom > 0:
S[i, j] = (n-2) * \
np.power((t12*t21 - t11*t22), 2) / denom
corr = np.sum(S)

# no metadata for HHG
self.test_statistic_ = corr

[docs]    def p_value(self, matrix_X=None, matrix_Y=None, replication_factor=1000):
"""
Tests independence between two datasets using HHG and permutation test.

:param matrix_X: a [n*p] data matrix, a matrix with n samples in p dimensions
:type matrix_X: 2D `numpy.array`

:param matrix_Y: a [n*q] data matrix, a matrix with n samples in q dimensions
:type matrix_Y: 2D `numpy.array`

:param replication_factor: specifies the number of replications to use for
the permutation test. Defaults to 1000.
:type replication_factor: int

:return: returns a list of two items, that contains:

- :p_value_: P-value
- :p_value_metadata_: (optional) a ``dict`` of metadata other than the p_value,
that the independence tests computes in the process
:rtype: float, dict

**Example:**

>>> import numpy as np
>>> from mgcpy.independence_tests.hhg import HHG

>>> X = np.array([0.07487683, -0.18073412, 0.37266440, 0.06074847, 0.76899045,
0.51862516, -0.13480764, -0.54368083, -0.73812644, 0.54910974]).reshape(-1, 1)
>>> Y = np.array([-1.31741173, -0.41634224, 2.24021815, 0.88317196, 2.00149312,
1.35857623, -0.06729464, 0.16168344, -0.61048226, 0.41711113]).reshape(-1, 1)
>>> hhg = HHG()
>>> hhg_p_value = hhg.p_value(X, Y)
"""
return super(HHG, self).p_value(matrix_X, matrix_Y)
```