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.

squeeze(axis)

Squeeze a plate axis from the distribution