bayespy.inference.vmp.nodes.gaussian.GaussianDistribution¶

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

Class for the VMP formulas of Gaussian variables.

Currently, supports only vector variables.

Notes

Message passing equations:

$\mathbf{x} &\sim \mathcal{N}(\boldsymbol{\mu}, \mathbf{\Lambda}),$

$\mathbf{x},\boldsymbol{\mu} \in \mathbb{R}^{D}, \quad \mathbf{\Lambda} \in \mathbb{R}^{D \times D}, \quad \mathbf{\Lambda} \text{ symmetric positive definite}$

$\log\mathcal{N}( \mathbf{x} | \boldsymbol{\mu}, \mathbf{\Lambda} ) &= - \frac{1}{2} \mathbf{x}^{\mathrm{T}} \mathbf{\Lambda} \mathbf{x} + \mathbf{x}^{\mathrm{T}} \mathbf{\Lambda} \boldsymbol{\mu} - \frac{1}{2} \boldsymbol{\mu}^{\mathrm{T}} \mathbf{\Lambda} \boldsymbol{\mu} + \frac{1}{2} \log |\mathbf{\Lambda}| - \frac{D}{2} \log (2\pi)$

__init__(shape)[source]¶: Initialize self. See help(type(self)) for accurate signature.

Methods

`__init__`(shape)	Initialize self.
`compute_cgf_from_parents`(u_mu_Lambda)	Compute $\mathrm{E}_{q(p)}[g(p)]$
`compute_fixed_moments_and_f`(x[, 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[, mask])	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.