import numpy as np
import tensorflow as tf
from .. import config
from ..distribution import Distribution
def _normal_logp(X, mu, sigma):
return (
tf.log(1 / (tf.constant(np.sqrt(2 * np.pi), dtype=config.dtype) * sigma)) -
(X - mu)**2 / (tf.constant(2, dtype=config.dtype) * sigma**2)
)
def _normal_cdf(lim, mu, sigma):
return 0.5 * tf.erfc((mu - lim) / (tf.constant(np.sqrt(2), config.dtype) * sigma))
@Distribution
def Normal(mu, sigma, name=None):
# TODO(chrisburr) Just use NormalN?
X = tf.placeholder(config.dtype, name=name)
Distribution.logp = _normal_logp(X, mu, sigma)
def integral(lower, upper):
upper_integrand = tf.cond(
tf.is_inf(tf.cast(upper, config.dtype)),
lambda: tf.constant(1, dtype=config.dtype),
lambda: _normal_cdf(upper, mu, sigma)
)
lower_integrand = tf.cond(
tf.is_inf(tf.cast(lower, config.dtype)),
lambda: tf.constant(0, dtype=config.dtype),
lambda: _normal_cdf(lower, mu, sigma)
)
return upper_integrand - lower_integrand
Distribution.integral = integral
return X
# @Distribution
# def NormalN(mus, sigmas, name=None):
# X = tf.placeholder(config.dtype, name=name)
# logps = [_normal_logp(X, mu, sigma) for mu, sigma in zip(mus, sigmas)]
# def cdf(lim):
# raise NotImplementedError
# Distribution.logp = sum(logps)
# Distribution.integral = lambda lower, upper: cdf(upper) - cdf(lower)
# return X
