Can Continuous Nodes be Used in the Temporal Plate of a DBN?

[Andy123]

Hello all!

I hope all is well with you. I wanted to ask if it is possible and if GENIE supports having continuous/equation nodes in the temporal plate of a DBN? In all of the examples I have seen in the manual, it utilizes chance/deterministic nodes. I have been successful in building a DBN using chance nodes, but the necessary discretization of my input space is too coarse. For example, I am predicting temperature in a system given the previous temperature, mass flow rate, and pressure. I can build the DBN with chance nodes with outcomes of ["Low","Mid","High"] for all nodes and it will run to completion. But I would like to have more specific information of the temperature increasing as a numerical value instead of the probability of "High" increasing over time. I have tried increasing the number of outcomes to emulate a distribution, e.g. ["500-501","501-502",...], but this is not a scalable solution as the size of the CPTs would become an issue. I have built this model as a static BN with equation nodes, but am having trouble including the time domain. My end goal is to produce a model where I can provide evidence of the mass flow rate being 50 kg/s at time t=10 and this information can then be propagated throughout the network and throughout time to see how it impacts the temperature. Is this something that is possible in GENIE? If not, I am thinking SMILE with custom python routines may work? Before trying SMILE with python, I wanted to check if there was not already a way to do this in GENIE?

Thank you so much for your time and help!

Andy

[marek [BayesFusion]]

Hi Andy,

I'm afraid the link between DBNs and hybrid networks is still on our TO DO list. It is not something that will cause any serious theoretical problems, it is just that we haven't gotten to it. At the moment, unfortunately you will still need to use discrete variables. Doing things directly in SMILE will not help either, as you will need to provide your own algorithms in this case (SMILE algorithm for DBNs does not allow for continuous nodes). What could possibly help you is using continuous nodes in a static BN and discretizing the nodes to produce the CPTs that you need. I have played to that effect with systems of difference equations (an equivalent of DBNs in continuous domain). Please look at the two attached networks: One is used to produce tables for the other. I'm sure you will figure out what I have intended to do and how I have achieved it :-).
I hope this helps,

Marek

[Andy123]

Hello Marek,

Thank you so much for the quick reply and example input files, they were very helpful in understanding the concept of using a static BN with continuous nodes to build the DBN CPTs. To confirm, I wanted to ask if I understood how you built the CPTs correctly. As an example, if we want to fill the entry of R(0..10|R[t-1]=0..10,F[t-1]=0..10) in the DBN, in the static BN we could change the distribution of the F-1 and R-1 nodes to be Uniform(0,10) and record the number of samples that were between zero and ten divided by the total number of samples generated. Then we can do this for all combinations of R[t-1] and F[t-1] to fill in the rest of the table. Am I understanding the process correctly? Thank you so much again for your help!

Andy

[marek [BayesFusion]]

Hi Andy,

You are right -- this is the way GeNIe/SMILE generate the samples when deriving the CPTs in the discretized version of the nodes. I believe that there is a brief description of this process in GeNIe manual. Please also note that in my DBN model, the variables are numerical, even though they are interval based. This allows for calculating and displaying the mean as a function of time, something that one might want to see.
Cheers,

Marek

[Andy123]

Hi Marek,

Thank you very much for confirming and for responding so quickly. Everything now makes sense to me and I can move forward with this approach. Thank you so much again for all of your help. I really appreciate it!
Best,

Andy