Influence diagram and hierarchical MAU nodes

The front end.
Post Reply
Pavlacky
Posts: 5
Joined: Mon Nov 18, 2013 9:33 pm

Influence diagram and hierarchical MAU nodes

Post by Pavlacky »

Dear GeNie,

I am building an influence diagram that has multiple hierarchical MAU nodes and a single decision node with 10 policies.

The utility nodes at the base the MAU nodes contain variables (range = 1 -1,000) that are irrelevant to the decision.

The MAU nodes contain functions of the utility modes (range 0 - 1) and I want the terminal MAU nodes to represent the Objective Functions over which the policies will be evaluated.

It appears the policy evaluation is being optimized over the base utility nodes containing values between 1 and 1,000 as well as the MAU nodes with values ranging between 0 and 1.

I experimented with scaling the values in the utility nodes to small numbers (1 x 10^-4), and then back-transforming the values in the function, but I was uncertain about the validity of this approach.

Do you have advice for constructing a series of hierarchical MAU nodes where the objective function reflects the terminal MAU nodes?

What do you think about re-scaling the values in the utility nodes to very small numbers; is there a better solution?

Any help you can provide will be greatly appreciated.

With Thanks,

David
shooltz[BayesFusion]
Site Admin
Posts: 1417
Joined: Mon Nov 26, 2007 5:51 pm

Re: Influence diagram and hierarchical MAU nodes

Post by shooltz[BayesFusion] »

Can you post your model here?
Pavlacky
Posts: 5
Joined: Mon Nov 18, 2013 9:33 pm

Re: Influence diagram and hierarchical MAU nodes

Post by Pavlacky »

Hi Shooltz,

I attached a copy of the model and I look forward to your advice.

I want to set evidence for the green nodes in a decision support tool.

With thanks,

David
Attachments
Clayey_Green_River_and_Great_Divide_Basins_Copy.xdsl
BN and influence diagram
(118.64 KiB) Downloaded 533 times
shooltz[BayesFusion]
Site Admin
Posts: 1417
Joined: Mon Nov 26, 2007 5:51 pm

Re: Influence diagram and hierarchical MAU nodes

Post by shooltz[BayesFusion] »

You have four terminal nodes:

Song bird gain
Forage production gain
Forage production gain 2
GRSG gain
(There's also 'GRSG core value', but it's not connected to the main network segment)

To perform policy evaluation in influence diagrams, GeNIe needs a single terminal. For the models structured like yours, the program adds temporary ALU node, then connects the terminal nodes with the temporary using weights=1. The evaluated policy you can see in 'Management decison' after inference is equal to the expected utility of this temporary node.
Pavlacky
Posts: 5
Joined: Mon Nov 18, 2013 9:33 pm

Re: Influence diagram and hierarchical MAU nodes

Post by Pavlacky »

Hello Shooltz,

Thanks for your explanation and for getting back to me so soon.

The node "Forage production gain 2" was mistakenly included in the previously attached model (Clayey_Green_River_and_Great_Divide_Basins_Copy.xdsl).

I attached a new model that better reflects the intended structure (Clayey_Green_River_and_Great_Divide_Basins_Copy_2.xdsl). As suggested in your reply, I connected the GRSG core node and connected the three terminal MAU nodes into a single terminal MAU node.

The "Song bird gain", "GRSG gain" and "Forage production gain" MAU nodes represent the three objectives of the decision problem.

As I mentioned in my previous post, the MAU nodes are functions of values in the basal utility nodes, but the values in the basal utility nodes are of no consequence to the decision problem. It is important to the decision problem that the values in the basal utility nodes are not considered when evaluating the policies.

However, when I run the model, policy evaluation appears to be influenced by the values in the basal utility nodes (range 1 - 1,000). When I re-scale the values in the basal utility nodes to very small numbers (10^-4) , policy evaluation appears to be primarily driven by the values in the MAU nodes (range 0 -1). I want policy evaluation to reflect the objectives represented by the MAU nodes, and I do not want the values housed in the utility nodes to influence the policy evaluation.

My questions are:

1) Is policy evaluation conditioned on the values in the basal utility nodes and propagated through the MAU nodes?

2) If so, does re-scaling the values in the basal utility nodes to small numbers reduce the influence of the utility nodes on the policy evaluation?

3) Can you recommend another way of structuring the model to reduce the influence of values in the basal utility nodes on the policy evaluation?

Your insight is much appreciated.

Kind Regards,

David
Attachments
Clayey_Green_River_and_Great_Divide_Basins_Copy_2.xdsl
Influence diagram 2
(118.52 KiB) Downloaded 409 times
shooltz[BayesFusion]
Site Admin
Posts: 1417
Joined: Mon Nov 26, 2007 5:51 pm

Re: Influence diagram and hierarchical MAU nodes

Post by shooltz[BayesFusion] »

As I mentioned in my previous post, the MAU nodes are functions of values in the basal utility nodes, but the values in the basal utility nodes are of no consequence to the decision problem. It is important to the decision problem that the values in the basal utility nodes are not considered when evaluating the policies.
I'm sorry, but that's not possible. The MAU/ALU values are derived directly from the utility nodes by simple forward propagation, therefore policy evaluation is a function of both utility and MAU/ALU definitions.
Pavlacky
Posts: 5
Joined: Mon Nov 18, 2013 9:33 pm

Re: Influence diagram and hierarchical MAU nodes

Post by Pavlacky »

Hi Shooltz,

Thank you for the information.

What do you think about my solution of re-scaling the values in the utility nodes to very small numbers (10^-4)? Would this reduce the influence of the values in the utility nodes on the policy evaluation?

You input is much appreciated,

Kind Regards,

David
shooltz[BayesFusion]
Site Admin
Posts: 1417
Joined: Mon Nov 26, 2007 5:51 pm

Re: Influence diagram and hierarchical MAU nodes

Post by shooltz[BayesFusion] »

What do you think about my solution of re-scaling the values in the utility nodes to very small numbers (10^-4)? Would this reduce the influence of the values in the utility nodes on the policy evaluation?
The uniform scaling will not change much. The inference algorithm for influence diagram works by creating a temporary Bayesian network based on the original diagram:

- decision nodes are converted to CPTs with uniform distribution
- utility nodes are converted to CPTs with distribution based on their utilities by normalizing these values into [0..1] range
- MAU/ALU are removed

In the next step the BN is updated multiple times, each update for a unique combination of decision states being set as evidence in nodes converted to CPT. The posteriors of the converted utility nodes are read, scaled back to their original utility ranges and recorded in the influence diagram.

Finally, the expected utilities in influence diagram are propagated forward into MAU/ALU nodes. The values from the terminal utility is also copied into decision nodes.

As you can see, the nontrivial calculations (the BN part) are based on normalized expected utility values of utility nodes (and probabilities of the chance nodes in the influence diagram).
marek [BayesFusion]
Site Admin
Posts: 430
Joined: Tue Dec 11, 2007 4:24 pm

Re: Influence diagram and hierarchical MAU nodes

Post by marek [BayesFusion] »

David,

I have looked at your model from the point of view of decision-analytic modeling. The model that you have constructed says quite clearly that all utility nodes take part in the calculation of the expected utility for the decisions. GeNIe performs correct calculation. I suspect that you intended something else but it is hard for me to figure out what. If you want to talk briefly about this, I will be glad to.
Cheers,

Marek
Post Reply