def rectifier(mean, var):
"""Return the mean and variance of a Gaussian distributed random variable,
described by its mean and variacne, after passing it through a rectified
linear unit.
Parameters
----------
mean : Theano variable
Theano variable of the shape ``s``.
var : Theano variable
Theano variable of the shape ``s``.
Returns
-------
mean_ : Theano variable
Theano variable of the shape ``r``.
var_ : Theano variable
Theano variable of the shape ``r``.
"""
std = T.sqrt(var)
ratio = mean / (std + epsilon)
mean_ = normal.cdf(ratio) * mean + normal.pdf(ratio) * std
A = mean * std * normal.pdf(ratio)
B = (mean ** 2 + std ** 2) * normal.cdf(ratio)
exp_of_squared = A + B
var_ = exp_of_squared - mean_ ** 2
return mean_, var_
def rectifier(mean, var):
std = T.sqrt(var)
ratio = mean / (std + epsilon)
mean_ = normal.cdf(ratio) * mean + normal.pdf(ratio) * std
A = mean * std * normal.pdf(ratio)
B = (mean ** 2 + std ** 2) * normal.cdf(ratio)
exp_of_squared = A + B
var_ = exp_of_squared - mean_ ** 2
return mean_, var_