class bayespy.inference.vmp.nodes.gaussian.GaussianGammaDistribution(shape)[source]

Class for the VMP formulas of Gaussian-Gamma-ISO variables.

Currently, supports only vector variables.

Log pdf of the prior:

\log p(\mathbf{x}, \tau | \boldsymbol{\mu}, \mathbf{\Lambda}, a, b) =&
- \frac{1}{2} \tau \mathbf{x}^T \mathbf{\Lambda} \mathbf{x}
+ \frac{1}{2} \tau \mathbf{x}^T \mathbf{\Lambda} \boldsymbol{\mu}
+ \frac{1}{2} \tau \boldsymbol{\mu}^T \mathbf{\Lambda} \mathbf{x}
- \frac{1}{2} \tau \boldsymbol{\mu}^T \mathbf{\Lambda} \boldsymbol{\mu}
+ \frac{1}{2} \log|\mathbf{\Lambda}|
+ \frac{D}{2} \log\tau
- \frac{D}{2} \log(2\pi)
\\ &
- b \tau
+ a \log\tau
- \log\tau
+ a \log b
- \log \Gamma(a)

Log pdf of the posterior approximation:

\log q(\mathbf{x}, \tau) =&
\tau \mathbf{x}^T \boldsymbol{\phi}_1
+ \tau \mathbf{x}^T \mathbf{\Phi}_2 \mathbf{x}
+ \tau \phi_3
+ \log\tau \phi_4
+ g(\boldsymbol{\phi}_1, \mathbf{\Phi}_2, \phi_3, \phi_4)
+ f(x, \tau)


Initialize self. See help(type(self)) for accurate signature.


__init__(shape) Initialize self.
compute_cgf_from_parents(u_mu_Lambda, u_a, u_b) Compute \mathrm{E}_{q(p)}[g(p)]
compute_fixed_moments_and_f(x_alpha[, mask]) Compute the moments and f(x) for a fixed value.
compute_gradient(g, u, phi) Compute the standard gradient with respect to the natural parameters.
compute_logpdf(u, phi, g, f, ndims) Compute E[log p(X)] given E[u], E[phi], E[g] and E[f].
compute_message_to_parent(parent, index, u, …) Compute the message to a parent node.
compute_moments_and_cgf(phi[, mask]) Compute the moments and g(\phi).
compute_phi_from_parents(u_mu_Lambda, u_a, u_b) Compute the natural parameter vector given parent moments.
compute_weights_to_parent(index, weights) Maps the mask to the plates of a parent.
plates_from_parent(index, plates) Resolve the plate mapping from a parent.
plates_to_parent(index, plates) Resolves the plate mapping to a parent.
random(*phi[, plates]) Draw a random sample from the distribution.