bayespy.inference.vmp.nodes.gaussian.GaussianDistribution.compute_moments_and_cgf

GaussianDistribution.compute_moments_and_cgf(phi, mask=True)[source]

Compute the moments and g(\phi).

\overline{\mathbf{u}}  (\boldsymbol{\phi})
&=
\left[ \begin{matrix}
  - \frac{1}{2} \boldsymbol{\phi}^{-1}_2 \boldsymbol{\phi}_1
  \\
  \frac{1}{4} \boldsymbol{\phi}^{-1}_2 \boldsymbol{\phi}_1
  \boldsymbol{\phi}^{\mathrm{T}}_1 \boldsymbol{\phi}^{-1}_2
  - \frac{1}{2} \boldsymbol{\phi}^{-1}_2
\end{matrix} \right]
\\
g_{\boldsymbol{\phi}} (\boldsymbol{\phi})
&=
\frac{1}{4} \boldsymbol{\phi}^{\mathrm{T}}_1 \boldsymbol{\phi}^{-1}_2
\boldsymbol{\phi}_1
+ \frac{1}{2} \log | -2 \boldsymbol{\phi}_2 |