bayespy.inference.vmp.nodes.gaussian.GaussianWishartDistribution.compute_message_to_parent

GaussianWishartDistribution.compute_message_to_parent(parent, index, u, u_mu_alpha, u_n, u_V)[source]

Compute the message to a parent node.

For parent q(\boldsymbol{\mu}, \alpha):

\alpha \boldsymbol{\mu}^T \mathbf{m}_1
\Rightarrow &
\mathbf{m}_1 = \langle \mathbf{\Lambda x} \rangle
\\
\alpha \boldsymbol{\mu}^T \mathbf{M}_2 \boldsymbol{\mu}
\Rightarrow &
\mathbf{M}_2 = - \frac{1}{2} \langle \mathbf{\Lambda} \rangle
\\
\alpha m_3
\Rightarrow &
m_3 = - \frac{1}{2} \langle \mathbf{x}^T \mathbf{\Lambda} \mathbf{x} \rangle
\\
m_4 \log \alpha
\Rightarrow &
m_4 = \frac{d}{2}

For parent q(\mathbf{V}):

\mathbf{M}_1 &= \frac{\partial \langle \log p \rangle}{\partial
\langle \mathbf{V} \rangle} = -\frac{1}{2} \langle \mathbf{\Lambda} \rangle
\\
\mathbf{M}_2 &= \frac{\partial \langle \log p \rangle}{\partial \langle \log|\mathbf{V}| \rangle}
= ...