bayespy.inference.vmp.nodes.gaussian.GaussianWishartDistribution¶

class bayespy.inference.vmp.nodes.gaussian.GaussianWishartDistribution[source]¶

Class for the VMP formulas of Gaussian-Wishart variables.

Currently, supports only vector variables.

$\log p(\mathbf{x}, \mathbf{\Lambda} | \boldsymbol{\mu}, \alpha, n, \mathbf{V}) =& - \frac{1}{2} \alpha \mathbf{x}^T \mathbf{\Lambda} \mathbf{x} + \frac{1}{2} \alpha \mathbf{x}^T \mathbf{\Lambda} \boldsymbol{\mu} + \frac{1}{2} \alpha \boldsymbol{\mu}^T \mathbf{\Lambda} \mathbf{x} - \frac{1}{2} \alpha \boldsymbol{\mu}^T \mathbf{\Lambda} \boldsymbol{\mu} + \frac{1}{2} \log|\mathbf{\Lambda}| + \frac{D}{2} \log\alpha - \frac{D}{2} \log(2\pi) \\ & - \frac{1}{2} \mathrm{tr}(\mathbf{V}\mathbf{\Lambda}) + \frac{n-d-1}{2} \log|\mathbf{\Lambda}| - \frac{nd}{2}\log 2 - \frac{n}{2} \log|\mathbf{V}| - \log\Gamma_d(\frac{n}{2})$

Posterior approximation:

$\log q(\mathbf{x}, \mathbf{\Lambda}) =& \mathbf{x}^T \mathbf{\Lambda} \boldsymbol{\phi}_1 + \phi_2 \mathbf{x}^T \mathbf{\Lambda} \mathbf{x} + \mathrm{tr}(\mathbf{\Lambda} \mathbf{\Phi}_3) + \phi_4 \log|\mathbf{\Lambda}| + g(\boldsymbol{\phi}_1, \phi_2, \mathbf{\Phi}_3, \phi_4) + f(\mathbf{x}, \mathbf{\Lambda})$

__init__($self, /, *args, **kwargs)¶: Initialize self. See help(type(self)) for accurate signature.

Methods

`compute_cgf_from_parents`(u_mu_alpha, u_n, u_V)	Compute $\mathrm{E}_{q(p)}[g(p)]$
`compute_fixed_moments_and_f`(x, Lambda[, 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_alpha, u_n, u_V)	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`(*params[, plates])	Draw a random sample from the distribution.