def log_normalization(self):
marginal = self.variables[0].value
message = self.messages[0].value
message_from_variable = marginal / message
mean = message_from_variable.mean
std = message_from_variable.stdev
z = (Gaussian.cumulative_to((self.epsilon - mean) / std) -
Gaussian.cumulative_to((-self.epsilon - mean) / std))
return -Gaussian.log_product_normalization(message_from_variable, message) + log(z)
def log_normalization(self):
marginal = self.variables[0].value
message = self.messages[0].value
message_from_variable = marginal / message
mean = message_from_variable.mean
std = message_from_variable.stdev
z = (Gaussian.cumulative_to(
(self.epsilon - mean) / std) - Gaussian.cumulative_to(
(-self.epsilon - mean) / std))
return -Gaussian.log_product_normalization(message_from_variable,
message) + log(z)
def w_within_margin(team_performance_difference, draw_margin):
team_performance_difference_abs = abs(team_performance_difference)
denominator = (Gaussian.cumulative_to(draw_margin - team_performance_difference_abs) -
Gaussian.cumulative_to(-draw_margin - team_performance_difference_abs))
if denominator < 2.222758749e-162:
return 1.0
vt = v_within_margin(team_performance_difference_abs, draw_margin)
return (vt ** 2 +
(
(draw_margin - team_performance_difference_abs) *
Gaussian.at(draw_margin - team_performance_difference_abs) -
(-draw_margin - team_performance_difference_abs) *
Gaussian.at(-draw_margin - team_performance_difference_abs)) / denominator)
def testCumulativeTo(self):
expected = 0.691462461274013
answer = Gaussian.cumulative_to(0.5)
self.assertAlmostEqual(
expected, answer, None,
"testCumulativeTo expected %.15f, got %.15f" % (expected, answer),
GaussianDistributionTest.ERROR_TOLERANCE)
def log_normalization(self):
marginal = self.variables[0].value
message = self.messages[0].value
message_from_variable = marginal / message
return (-Gaussian.log_product_normalization(message_from_variable, message) +
log(Gaussian.cumulative_to((message_from_variable.mean - self.epsilon) / message_from_variable.stdev)))
def v_within_margin(team_performance_difference, draw_margin):
team_performance_difference_abs = abs(team_performance_difference)
denominator = (
Gaussian.cumulative_to(draw_margin - team_performance_difference_abs) -
Gaussian.cumulative_to(-draw_margin - team_performance_difference_abs))
if denominator < 2.222758749e-162:
if team_performance_difference < 0.0:
return -team_performance_difference - draw_margin
return -team_performance_difference + draw_margin
numerator = (Gaussian.at(-draw_margin - team_performance_difference_abs) -
Gaussian.at(draw_margin - team_performance_difference_abs))
if team_performance_difference < 0.0:
return -numerator / denominator
return numerator / denominator
def w_exceeds_margin(team_performance_difference, draw_margin):
denominator = Gaussian.cumulative_to(team_performance_difference - draw_margin)
if denominator < 2.222758749e-162:
if team_performance_difference < 0.0:
return 1.0
return 0.0
v_win = v_exceeds_margin(team_performance_difference, draw_margin)
return v_win * (v_win + team_performance_difference - draw_margin)
def w_within_margin(team_performance_difference, draw_margin):
team_performance_difference_abs = abs(team_performance_difference)
denominator = (
Gaussian.cumulative_to(draw_margin - team_performance_difference_abs) -
Gaussian.cumulative_to(-draw_margin - team_performance_difference_abs))
if denominator < 2.222758749e-162:
return 1.0
vt = v_within_margin(team_performance_difference_abs, draw_margin)
return (vt**2 +
((draw_margin - team_performance_difference_abs) *
Gaussian.at(draw_margin - team_performance_difference_abs) -
(-draw_margin - team_performance_difference_abs) *
Gaussian.at(-draw_margin - team_performance_difference_abs)) /
denominator)
def v_within_margin(team_performance_difference, draw_margin):
team_performance_difference_abs = abs(team_performance_difference)
denominator = (
Gaussian.cumulative_to(draw_margin - team_performance_difference_abs) -
Gaussian.cumulative_to(-draw_margin - team_performance_difference_abs))
if denominator < 2.222758749e-162:
if team_performance_difference < 0.0:
return -team_performance_difference - draw_margin
return -team_performance_difference + draw_margin
numerator = (Gaussian.at(-draw_margin - team_performance_difference_abs) -
Gaussian.at(draw_margin - team_performance_difference_abs))
if team_performance_difference < 0.0:
return -numerator / denominator
return numerator / denominator
def w_exceeds_margin(team_performance_difference, draw_margin):
denominator = Gaussian.cumulative_to(team_performance_difference -
draw_margin)
if denominator < 2.222758749e-162:
if team_performance_difference < 0.0:
return 1.0
return 0.0
v_win = v_exceeds_margin(team_performance_difference, draw_margin)
return v_win * (v_win + team_performance_difference - draw_margin)
def log_normalization(self):
marginal = self.variables[0].value
message = self.messages[0].value
message_from_variable = marginal / message
return (
-Gaussian.log_product_normalization(message_from_variable, message)
+ log(
Gaussian.cumulative_to(
(message_from_variable.mean - self.epsilon) /
message_from_variable.stdev)))
def v_exceeds_margin(team_performance_difference, draw_margin):
denominator = Gaussian.cumulative_to(team_performance_difference - draw_margin)
if (denominator < 2.22275874e-162):
return -team_performance_difference + draw_margin
return Gaussian.at(team_performance_difference - draw_margin) / denominator
def testCumulativeTo(self):
expected = 0.691462461274013
answer = Gaussian.cumulative_to(0.5)
self.assertAlmostEqual(expected, answer, None,
"testCumulativeTo expected %.15f, got %.15f" % (expected, answer),
GaussianDistributionTest.ERROR_TOLERANCE)
def v_exceeds_margin(team_performance_difference, draw_margin):
denominator = Gaussian.cumulative_to(team_performance_difference -
draw_margin)
if (denominator < 2.22275874e-162):
return -team_performance_difference + draw_margin
return Gaussian.at(team_performance_difference - draw_margin) / denominator
