Inference in Dynamic Bayesian Network (continued)

For the past 2 weeks I have spent some time understanding the algorithmic implementation for inference and implementing it. Today I will be talking about the junction tree algorithm for inference in Dynamic Bayesian Networks.

For processing the algorithm, here are the following steps

1) Initialization :- This requires constructing the two initial junction trees J1 and Jt.

1. J1 is the junction tree created from the initial timeslice. is the junction tree created from the timeslice 1 of the 2TBN(2 - timeslice bayesian network).Jt is the junction tree created from the timeslice 2 of the 2TBN. Time counter is initialized to 0. Also, let the interface nodes(denoted by I1, I2 for the timeslices 1 and 2 respectively ) be those nodes whose children are there in the first timeslice.
2. If the queries are performed on the initial timeslice. Then the results can be output by the standard VariableElimination procedure where we could have the model having the timeslice 1 of the bayesian network as the base for inference.
3. For evidence, if the current time in the evidence is 0, then the evidence should be applied to the initial static bayesian network. Otherwise, it has to be applied to the second timeslice of the 2-TBN.
4. For creating the junction tree J1, the procedure as follows:-
1. Moralize the initial static bayesian network.
2. Add the edges from the interface nodes so as to make I1 a clique.
3. Rest of the procedure is the same as it was before. The above step is the only difference.
5. For the junction tree Jt, a similar procedure is followed, where there is a clique formed for I2 as well.

2) Inference procedure:- In this procedure, the clique potential from the interface nodes is passed onto the interface clique. (similar to the message passing algorithm). 

The time counter is incremented accordingly.

So basically the junction tree Jt` seems some sort of the engine where the in-clique is where the values are supplied and the out-clique is where the values are obtained, given the e

The variables in the query are taken out as always at each step, and the evidence is applied also.

The best part about this procedure, that this method eliminates entanglement and only the out-clique potential is required for inference. 

The implementation is still in progress.