Mixtures

There are two ways to define mixtures in AePPL with Aesara constructs.

By creating an array of random variables and indexing it with a random variable:

import aesara.tensor as at

srng = at.random.RandomStream()

w_rv = srng.normal(-2, 1)
x_rv = srng.normal(0, 1)
y_rv = srng.normal(2, 1)
mix_rv = at.stack([w_rv, x_rv, y_rv])

p = at.vector('p')
i_rv = srng.categorical(p)
Z_rv = mix_rv[i_rv]

Using aesara.tensor.switch:

import aesara.tensor as at

srng = at.random.RandomStream()

x_rv = srng.normal(0, 1)
y_rv = srng.normal(2, 1)

p = at.scalar('p')
i_rv = srng.bernoulli(p)
Z_rv = at.switch(i_rv, x_rv, y_rv)

Rewrites

The following rewrites identify mixtures in Aesara graphs and replace them with MixtureRVs, which are then used to compute the model’s log-density.

aeppl.mixture.mixture_replace()

A NodeRewriter constructed from a function.

aeppl.mixture.switch_mixture_replace()

A NodeRewriter constructed from a function.

Log-density

class aeppl.mixture.logprob_MixtureRV(op, values, *inputs, name=None, **kwargs)

Parameters:

inputs (Union[TensorVariable, slice, None]) –