def _log_cdf(self, x):
loc, scale, low, high = self._loc_scale_low_high()
std_low, std_high = self._standardized_low_and_high(
low=low, high=high, loc=loc, scale=scale)
return (_log_sub_exp(
special_math.log_ndtr(
(x - loc) / scale), special_math.log_ndtr(std_low)) -
self._log_normalizer(std_low=std_low, std_high=std_high))
def _mean(self):
loc, scale, low, high = self._loc_scale_low_high()
std_low, std_high = self._standardized_low_and_high(
loc=loc, scale=scale, low=low, high=high)
lse, sign = _log_sub_exp(_normal_log_pdf(std_low),
_normal_log_pdf(std_high),
return_sign=True)
return loc + scale * sign * tf.math.exp(
lse - self._log_normalizer(std_low=std_low, std_high=std_high))
def _normal_cdf_log_difference(x, y):
"""Computes log(ndtr(x) - ndtr(y)) assuming that x >= y."""
# When x >= y >= 0, we will return log(ndtr(-y) - ndtr(-x))
# because ndtr does not have a good precision for large positive x, y.
is_y_positive = y >= 0
x_hat = tf.where(is_y_positive, -y, x)
y_hat = tf.where(is_y_positive, -x, y)
return _log_sub_exp(special_math.log_ndtr(x_hat),
special_math.log_ndtr(y_hat))
def _log_normalizer(self,
loc=None,
scale=None,
low=None,
high=None,
std_low=None,
std_high=None):
if std_low is None or std_high is None:
std_low, std_high = self._standardized_low_and_high(
loc=loc, scale=scale, low=low, high=high)
return _log_sub_exp(
special_math.log_ndtr(std_high), special_math.log_ndtr(std_low))
def _log_normalizer(self,
loc=None,
scale=None,
low=None,
high=None,
std_low=None,
std_high=None):
if std_low is None or std_high is None:
std_low, std_high = self._standardized_low_and_high(loc=loc,
scale=scale,
low=low,
high=high)
return _log_sub_exp(_log_cauchy_cdf(std_high),
_log_cauchy_cdf(std_low))
def _variance(self):
loc, scale, low, high = self._loc_scale_low_high()
std_low, std_high = self._standardized_low_and_high(
loc=loc, scale=scale, low=low, high=high)
log_normalizer = self._log_normalizer(std_low=std_low, std_high=std_high)
var = (
tf.square(scale) *
(1. +
(std_low * _normal_pdf(std_low) - std_high * _normal_pdf(std_high)) /
tf.exp(log_normalizer) -
tf.exp(2. * (
_log_sub_exp( # ignore sign because result gets squared
_normal_log_pdf(std_low), _normal_log_pdf(std_high))
- log_normalizer))))
return var
