bayespy.inference.vmp.nodes.gaussian.GaussianDistribution.compute_message_to_parent

GaussianDistribution.compute_message_to_parent(parent, index, u, u_mu_Lambda)[source]

Compute the message to a parent node.

\boldsymbol{\phi}_{\boldsymbol{\mu}} (\mathbf{x}, \mathbf{\Lambda}) &= \left[ \begin{matrix} \mathbf{\Lambda} \mathbf{x} \\ - \frac{1}{2} \mathbf{\Lambda} \end{matrix} \right] \\ \boldsymbol{\phi}_{\mathbf{\Lambda}} (\mathbf{x}, \boldsymbol{\mu}) &= \left[ \begin{matrix} - \frac{1}{2} \mathbf{xx}^{\mathrm{T}} + \frac{1}{2} \mathbf{x}\boldsymbol{\mu}^{\mathrm{T}} + \frac{1}{2} \boldsymbol{\mu}\mathbf{x}^{\mathrm{T}} - \frac{1}{2} \boldsymbol{\mu\mu}^{\mathrm{T}} \\ \frac{1}{2} \end{matrix} \right]