bayespy.inference.vmp.nodes.multinomial.MultinomialDistribution.compute_gradient¶
- MultinomialDistribution.compute_gradient(g, u, phi)[source]¶
Compute the Euclidean gradient.
In order to compute the Euclidean gradient, we first need to derive the gradient of the moments with respect to the variational parameters:
Now we can make use of the chain rule. Given the Riemannian gradient
of the variational lower bound
with respect to the variational parameters
, put the above result to the derivative term and re-organize the terms to get the Euclidean gradient
:
Thus, the Euclidean gradient is:
See also
compute_moments_and_cgf
Computes the moments
given the variational parameters
.