bayespy.inference.vmp.nodes.gaussian.GaussianGammaDistribution.compute_message_to_parent

GaussianGammaDistribution.compute_message_to_parent(parent, index, u, u_mu_Lambda, u_a, u_b)[source]

Compute the message to a parent node.

  • Parent (\boldsymbol{\mu}, \mathbf{\Lambda})

    Moments:

    \begin{bmatrix} \mathbf{\Lambda}\boldsymbol{\mu} \\ \boldsymbol{\mu}^T\mathbf{\Lambda}\boldsymbol{\mu} \\ \mathbf{\Lambda} \\ \log|\mathbf{\Lambda}| \end{bmatrix}

    Message:

    \begin{bmatrix} \langle \tau \mathbf{x} \rangle \\ - \frac{1}{2} \langle \tau \rangle \\ - \frac{1}{2} \langle \tau \mathbf{xx}^T \rangle \\ \frac{1}{2} \end{bmatrix}

  • Parent a:

    Moments:

    \begin{bmatrix} a \\ \log \Gamma(a) \end{bmatrix}

    Message:

    \begin{bmatrix} \langle \log\tau \rangle + \langle \log b \rangle \\ -1 \end{bmatrix}

  • Parent b:

    Moments:

    \begin{bmatrix} b \\ \log b \end{bmatrix}

    Message:

    \begin{bmatrix} - \langle \tau \rangle \\ \langle a \rangle \end{bmatrix}