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 $q(\mathbf{V})$ :

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