Any advice on modelling a variable with combined prohibiting and promoting effects?

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charlie
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Any advice on modelling a variable with combined prohibiting and promoting effects?

Post by charlie » Wed Oct 03, 2018 8:15 pm

The case is like this: to evaluate a program that selects a fixed number of items for quality from a batch of them. Two parent variables - one for the stringency of the selection (X), one for the overall quality of the batch (Y). The resultant variable is the quality of the selected ones (Z).

The complication here is apparently that Y has both prohibiting and promoting effects: when Y is very poor approaching to nil (i.e. the entire batch is bad), it prohibits the effect of selection, but when Y is very good approaching to perfect (i.e. the entire batch is good) it makes the selection very easy and eventually redundant.

How should this be modelled, through a combination of different gates?

Anyone's advice is highly appreciated.

Charlie

charlie
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Re: Any advice on modelling a variable with combined prohibiting and promoting effects?

Post by charlie » Wed Oct 03, 2018 10:45 pm

Neither noisy-or or noisy-and applies. I used a noisy-adder the moment but don't feel fully satisfied.

marek [BayesFusion]
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Re: Any advice on modelling a variable with combined prohibiting and promoting effects?

Post by marek [BayesFusion] » Fri Oct 05, 2018 2:48 pm

If you have only two parents and one child, why not entering the parameters of the conditional probability distributions manually? Going through this exercise will clarify the issues for you. Canonical gates are meant to save you time and lead to fewer parameters in the model through additional independences. This becomes valuable when the number of parents is large. Please remember that in order to achieve savings, they have to simplify reality. So, if you have just two parents, perhaps entering the parameters manually may be the best way to go. Incidentally, I find the Noisy-Adder and the Noisy-Average gates not too intuitive myself.
I hope this helps,

Marek

charlie
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Re: Any advice on modelling a variable with combined prohibiting and promoting effects?

Post by charlie » Thu Nov 08, 2018 6:13 pm

You're certainly right, Marek. But in real situations there are often more than 2 parents and more than 2 status for each node. But a more important reason is of course I love to have the logicality taste in the model instead of a kind of "random" guess during knowledge elicitation.

I truly believe to include a few more types of logical gates, at least a Nosiy-MIN, will help unleash the power of GeNIe to the fullest. It seems to me interestingly that the two major types of application of Bayesian network sit just opposite to each other in terms of data demand (could be a naive view): machine learning applies to where a large quantity of data exist while knowledge building applies to where little data is available. In my case I often work in the latter.

It usually takes me three steps to do the knowledge elicitation: map out the causal relationships of the variables (including identifying the variables for a question in study), determine the logical interaction of parent variables for every child variable, and assign probabilities (including determining status).

I just wish to say your research on canonical gates and the philosophy around that is really a beauty of science.
Charles

marek [BayesFusion]
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Re: Any advice on modelling a variable with combined prohibiting and promoting effects?

Post by marek [BayesFusion] » Sat Nov 17, 2018 2:10 am

Thank you for your kind words. I just wanted to remark that the Noisy-Max gate in GeNIe allows you to create both OR and AND gates. To create an AND gate, just negate the parents (by changing the order of their states) and negate the child (by changing the order of its states). It is just a simple application of DeMorgan's laws. We will at some point provide an intuitive interface to the Noisy-AND gate but at this point you will have to organize it yourself. I hope this helps,

Marek

charlie
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Re: Any advice on modelling a variable with combined prohibiting and promoting effects?

Post by charlie » Sat Nov 17, 2018 3:09 pm

Yes I understand how to get a NoisyMIn negating the NoisyMAX but don't know how to deal with the distinguished state after that. The original distinguished state of the parent variable is no longer the distinguished state after negation (changing the order) and the top state is now forced to become distinguished state and set the value of {0,0...0,1} (across the child variable's states). This apparently does not represent the real situation I want to model.

In passing may I ask why to force the last state of parent variable to {0,0,...0,1} across the child variable's states in a noisyMAX node?

marek [BayesFusion]
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Re: Any advice on modelling a variable with combined prohibiting and promoting effects?

Post by marek [BayesFusion] » Tue Nov 20, 2018 3:07 am

I have to confess that I get confused here myself and have to always think hard before creating a Noisy-AND/MIN node. This means that our idea years ago to implement just one type of node for both OR and AND interactions was not that great -- what is theoretically simple, may be hard for a human modeler. We are going to fix this by introducing a Noisy-AND/MIN node (which under the hood will be a Noisy-OR/MAX). It is already on our TO DO list.

You are right that when nodes are negated, the distinguished state is what normally would be an active state in Noisy-OR/MAX. The real source of confusion, however, is the meaning of the parameters. Please look at the attached model -- node Accident is a Noisy-MIN node implemented by means of a Noisy-MAX. All three nodes are negated and the distinguished states are Accident, Failure, and Error. Probability 0.9 in the column Equipment Failure/NoFailure denotes the probability of NoAccident when the node Equipment Failure is in state NoFailure and all the other nodes are in their distinguished states (i.e., they are in the states that actually influence Accident). The parameter 0.9 describes the ability that the absence of a given single cause is able to cause the absence of the effect. Does this make sense? Please look at the effective CPT for this node. If you have a hard time with this, do not worry to much -- you are not alone :-).
I hope it will help,

Marek
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charlie
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Re: Any advice on modelling a variable with combined prohibiting and promoting effects?

Post by charlie » Tue Nov 20, 2018 5:47 am

Thanks Marek. It will be so merciful of you if a noisy-Min/And node is made available. I already studied the "accident" example in the user manual.

In terms of the meaning, I tried to explain to myself this way: noisy-Min node is to maximise the opportunity of realising the most strengthened state of the child variable so the distinguished states of the parent variables are at the opposite end - the most weakening end. For the same token, a noisy-Max node is to maximise the opportunity of realising the most weakened state of the child variable so the distinguished states of the parent variables are at the most strengthening end. That said a variable in the real world can only have one distinguished state, either the most strengthened or most distinguished end, and can hardly have both.

Charles

marek [BayesFusion]
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Re: Any advice on modelling a variable with combined prohibiting and promoting effects?

Post by marek [BayesFusion] » Tue Nov 20, 2018 12:49 pm

Agreed here -- when building an AND/MIN interaction by means of an OR/MAX gate, the distinguished states are a complete fiction, just to allow for the negations. In reality, there is one distinguished state and it is the one that has no influence.

Please look at the model that I have attached to my previous post -- your questions have prompted me to think about it again, change the parameters somewhat to make things more intuitive, and also modify the GeNIe manual a little. We are about to make a new major release of the program (there will be no separate Noisy-AND/MIN yet, I'm afraid).
Good luck!

Marek

charlie
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Re: Any advice on modelling a variable with combined prohibiting and promoting effects?

Post by charlie » Tue Nov 20, 2018 9:37 pm

I studied the model. The states of the model are binary which somewhat marred the issue. If the states are expanded to multiple e.g. No accident, Light injury, Serious injury, and Fatal for Accident node, and Serious, Medium, Light, Without for both Equipment Failure and Human Error nodes, the problem in relation to the distinguished state becomes more obvious. Here "Without", rather than "Serious", will be the "natural" distinguished state for Equipment Failure and Human Error as well, right? However, in that noisy-Min model, "Without" will be the top state and "Serious" will be the distinguished state.

I guess an easy fix as an interim is to remove the forced {0,0,...,0,1} setting for the distinguished state and allow user to specify probabilities in them.

With regards

Charles

charlie
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Re: Any advice on modelling a variable with combined prohibiting and promoting effects?

Post by charlie » Wed Nov 21, 2018 6:53 pm

At my end, I used this way to get around it - to add a pseudo state named e.g. "NotForUse" for the parent and child nodes, and let this state be the distinguished state for the parents and the bottom state for the child. Forced 1 will then fall at the bottom-right cell to release the real states for meaningful probability assignment.

Anyway I still don't understand why a dedicated distinguished state and the constraining of it is necessary.

Charles

marek [BayesFusion]
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Re: Any advice on modelling a variable with combined prohibiting and promoting effects?

Post by marek [BayesFusion] » Sat Dec 01, 2018 4:26 am

Anyway I still don't understand why a dedicated distinguished state and the constraining of it is necessary.
Noisy-MAX nodes need to have a distinguished state. A good starting point for understanding this is a technical report by Javier Diez and myself, available at http://www.ia.uned.es/~fjdiez/papers/canonical.html (we refer to it in the report as "neutral state" or "normality state").
I hope this helps,

Marek

charlie
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Re: Any advice on modelling a variable with combined prohibiting and promoting effects?

Post by charlie » Sat Dec 01, 2018 11:01 pm

Thanks Merek. As I said before probably in another thread I already studied your paper sometime ago. But I still don't quite get it for applying BN in a realworld setting why variables have to have a neutral state.
Cheers
Charles

marek [BayesFusion]
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Re: Any advice on modelling a variable with combined prohibiting and promoting effects?

Post by marek [BayesFusion] » Tue Dec 04, 2018 9:17 pm

There are two other papers that you may find useful in obtaining insight into the Noisy-OR/Noisy-MAX gates:

(1) The original paper by Max Henrion, where he introduces the Noisy-OR gate: Henrion, Max (1989). Some practical issues in constructing belief networks. Kanal, L.N., Levitt, T.S. & Lemmer, J.F. (eds.), Uncertainty in Artificial Intelligence 3. Elsevier Science Publishers B.V. (North Holland), pages 161-173.

(2) A paper by D. Heckerman, J. Breese. Causal Independence for Probability Assessment and Inference Using Bayesian Networks. IEEE Transactions on Systems, Man, and Cybernetics, 26:826-831, 1996

Both papers discuss the structure of of the Noisy-OR gate, its properties, and independences that they imply. I hope these help you with the intuition.

Marek

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