qii.py

import random
import numpy
from scipy import stats

def sample_left():
    return random.uniform(0, 1000)

def sample_right():
    return random.uniform(0, 1000)

def get_observation():
    return (sample_left(), sample_right())

population = [get_observation() for i in range(100000)]

adversary_map = {}
for p in population:
    left = p[0]
    right = p[1]
    record = adversary_map.get(right, (0, 0))
    adversary_map[right] = (record[0] + left, record[1] + 1)

def get_score_adversarial(left, right):
    record = adversary_map.get(right)
    if record is None:
        return int(left)
    return int(record[0] / record[1])

def get_score(left, right):
    #### Even weight ####
    # return left * 0.5 + right * 0.5

    #### Biased right ####
    # return left * 0.25 + right * 0.75

    #### Adversarial behavior ####
    return get_score_adversarial(left, right)

def estimate_left_cause(p, samples=1000):
    right = p[1]
    real_score = get_score(p[0], right)
    sampled_scores = [get_score(sample_left(), right) for i in range(samples)]
    return real_score - numpy.mean(sampled_scores)

def estimate_right_cause(p, samples=1000):
    left = p[0]
    real_score = get_score(left, p[1])
    sampled_scores = [get_score(left, sample_right()) for i in range(samples)]
    return real_score - numpy.mean(sampled_scores)

example_person = random.choice(population)
left_cause = estimate_left_cause(example_person)
right_cause = estimate_right_cause(example_person)
print '==== Example person:', example_person, '===='
print 'left_cause:', left_cause
print 'right_cause:', right_cause
print

sample = random.sample(population, 1000)
mean_abs_left_cause = numpy.mean([abs(estimate_left_cause(p)) for p in sample])
mean_abs_right_cause = numpy.mean([abs(estimate_right_cause(p)) for p in sample])
print '==== Sample mean ===='
print 'mean_abs_left_cause:', mean_abs_left_cause
print 'mean_abs_right_cause:', mean_abs_right_cause
print

left = [p[0] for p in population]
right = [p[1] for p in population]
score = [get_score(p[0], p[1]) for p in population]
left_score_rvalue = stats.linregress(left, score)[2]
right_score_rvalue = stats.linregress(right, score)[2]
print '==== Summary stats ===='
print 'R^2_{left, score}: ', left_score_rvalue * left_score_rvalue
print 'R^2_{right, score}: ', right_score_rvalue * right_score_rvalue