## Monday, May 11, 2015

### Tensor train

One of probable approaches to build graphical models with categorical variables is tensor decomposition:
At this moment I'm thinking over possibility to build this into GB-train, since trained model for each event provides sequence of binary visible variables. In principle, this may be written in quite simple way. Provided, that $x_i$ is boolean variable corresponding to $i$th cut in the tree (in the train, to be more precise).
For instance, one can write partition function as $$Z = A_1[x_1, y] A_2[x_2, y] \dots A_n[x_n, y]$$ or as $$Z = A_1[x_1] B_1[y] A_2[x_2] B_2[y] \dots A_n[x_n] B_n[y]$$