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#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""This module abstracts information measures."""
import abc
from enum import Enum
import numpy as np
from scipy.stats import chi2_contingency
from entropy import entropy
from sc import sc
class DMType(Enum):
NHST = 1 # Null Hypothesis Significance Testing
INFO = 2 # Information-theoretic
class DependenceMeasure(abc.ABC):
@property
@abc.abstractmethod
def type(self):
pass
@staticmethod
@abc.abstractmethod
def measure(seq1, seq2=None):
pass
class Entropy(DependenceMeasure):
type = DMType.INFO
def measure(seq1, seq2=None):
return entropy(seq1)
class StochasticComplexity(DependenceMeasure):
type = DMType.INFO
def measure(seq1, seq2=None):
return sc(seq1)
class ChiSquaredTest(DependenceMeasure):
type = DMType.NHST
@staticmethod
def contingency_table(seq1, seq2):
dom_seq1 = list(set(seq1))
dom_seq2 = list(set(seq2))
ndom_seq1 = len(dom_seq1)
ndom_seq2 = len(dom_seq2)
indices1 = dict(zip(dom_seq1, range(ndom_seq1)))
indices2 = dict(zip(dom_seq2, range(ndom_seq2)))
table = np.zeros((ndom_seq1, ndom_seq2))
for k, v1 in enumerate(seq1):
v2 = seq2[k]
i, j = indices1[v1], indices2[v2]
table[i, j] += 1
return table
@staticmethod
def nhst(seq1, seq2):
assert len(seq1) == len(seq2), "samples are not of the same size"
table = ChiSquaredTest.contingency_table(seq1, seq2)
chi2, p_value, _, _ = chi2_contingency(table, correction=True)
return chi2, p_value
@staticmethod
def measure(seq1, seq2=None):
chi2, p_value = ChiSquaredTest.nhst(seq1, seq2)
# we want to minimise the dependence between seq1 and seq2 in ANM
# that is, maximise the independence between seq1 and seq2 in ANM
# H0: seq1 and seq2 are independent
# H0 becomes true if p-value is greater than a threshold
# thus we want to maximise p-value, or minimise the negative of p-value
p_value *= -1
# as chi2 gets smaller, p-value increases (check the chi2 plot in wiki)
# if the p-value is too small, we reject H0 anyway
# in such a case, we want to minimise chi2
if p_value < 10 ** -16:
p_value = chi2
return p_value
if __name__ == "__main__":
print(ChiSquaredTest.measure(np.random.choice(
[1, 2, 3], 10), np.random.choice([1, 2], 10)))
print(Entropy.measure(np.random.choice([1, 2, 3], 10)))
print(StochasticComplexity.measure(np.random.choice([1, 2, 3], 10)))
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