aeppl provides tools for a[e]PPL written in Aesara.

# Features#

• Convert graphs containing Aesara RandomVariables into joint log-probability graphs

• Transforms for RandomVariables that map constrained support spaces to unconstrained spaces (e.g. the extended real numbers), and a rewrite that automatically applies these transformations throughout a graph

• Tools for traversing and transforming graphs containing RandomVariables

• RandomVariable-aware pretty printing and LaTeX output

# Examples#

Using aeppl, one can create a joint log-probability graph from a graph containing Aesara RandomVariables:

import aesara
from aesara import tensor as at

from aeppl import joint_logprob, pprint

# A simple scale mixture model
S_rv = at.random.invgamma(0.5, 0.5)
Y_rv = at.random.normal(0.0, at.sqrt(S_rv))

# Compute the joint log-probability
y = at.scalar("y")
s = at.scalar("s")
logprob = joint_logprob({Y_rv: y, S_rv: s})


Log-probability graphs are standard Aesara graphs, so we can compute values with them:

logprob_fn = aesara.function([y, s], logprob)

logprob_fn(-0.5, 1.0)
# array(-2.46287705)


Graphs can also be pretty printed:

from aeppl import pprint, latex_pprint

# Print the original graph
print(pprint(Y_rv))
# b ~ invgamma(0.5, 0.5) in R, a ~ N(0.0, sqrt(b)**2) in R
# a

print(latex_pprint(Y_rv))
# \begin{equation}
#   \begin{gathered}
#     b \sim \operatorname{invgamma}\left(0.5, 0.5\right)\,  \in \mathbb{R}
#     \\
#     a \sim \operatorname{N}\left(0.0, {\sqrt{b}}^{2}\right)\,  \in \mathbb{R}
#   \end{gathered}
#   \\
#   a
# \end{equation}

# Simplify the graph so that it's easier to read
from aesara.graph.opt_utils import optimize_graph
from aesara.tensor.basic_opt import topo_constant_folding

logprob = optimize_graph(logprob, custom_opt=topo_constant_folding)

print(pprint(logprob))
# s in R, y in R
# (switch(s >= 0.0,
#         ((-0.9189385175704956 +
#           switch(s == 0, -inf, (-1.5 * log(s)))) - (0.5 / s)),
#         -inf) +
#  ((-0.9189385332046727 + (-0.5 * ((y / sqrt(s)) ** 2))) - log(sqrt(s))))


Joint log-probabilities can be computed for some terms that are derived from RandomVariables, as well:

# Create a switching model from a Bernoulli distributed index
Z_rv = at.random.normal([-100, 100], 1.0, name="Z")
I_rv = at.random.bernoulli(0.5, name="I")

M_rv = Z_rv[I_rv]
M_rv.name = "M"

z = at.vector("z")
i = at.lscalar("i")
m = at.scalar("m")
# Compute the joint log-probability for the mixture
logprob = joint_logprob({M_rv: m, Z_rv: z, I_rv: i})

logprob = optimize_graph(logprob, custom_opt=topo_constant_folding)

print(pprint(logprob))
# i in Z, m in R, a in Z
# (switch((0 <= i and i <= 1), -0.6931472, -inf) +
#  ((-0.9189385332046727 + (-0.5 * (((m - [-100  100][a]) / [1. 1.][a]) ** 2))) -
#   log([1. 1.][a])))


# Installation#

The latest release of aeppl can be installed from PyPI using pip:

pip install aeppl


The current development branch of aeppl can be installed from GitHub, also using pip:

pip install git+https://github.com/aesara-devs/aeppl