Table 2.

Summary of the EM algorithm for mixtures of Gaussians on vectors and tensors.

Numerical calculation of the symmetrized KL distance dK L,t(p(T|Θ1), p(T|Θ2))
Step 1	Generate N tensors T1,i according to p(T|Θ1)
	Generate N tensors T1,i according to p(T|Θ2)
Step 2	$\text{Compute}\frac{1}{N}{\sum }_{i=1}^N{g}_1\left({\mathbf{T}}_{1,i}\right),\text{where}g\left({\mathbf{T}}_{1,i}\right)=\text{log}\left(\frac{p({\mathbf{T}}_{1,i}\mid {ϴ}_1)}{p({\mathbf{T}}_{1,i}\mid {ϴ}_2)}\right)$
	$\text{Compute}\frac{1}{N}{\sum }_{i=1}^N{g}_2\left({\mathbf{T}}_{2,i}\right),\text{where}g\left({\mathbf{T}}_{2,i}\right)=\text{log}\left(\frac{p({\mathbf{T}}_{2,i}\mid {ϴ}_2)}{p({\mathbf{T}}_{2,i}\mid {ϴ}_1)}\right)$
Step 3	$\text{Calculate}{d}_{KL,t}(p(\mathbf{T}\mid {ϴ}_1),p(\mathbf{T}\mid {ϴ}_2))=\frac{1}{2}\left[\frac{1}{N}{\sum }_{i=1}^N{g}_1\left({\mathbf{T}}_{1,i}\right)+\frac{1}{N}{\sum }_{i=1}^N{g}_2\left({\mathbf{T}}_{2,i}\right)\right]$