Aside: Bayes nets which are representing decision problems are usually calledinfluence diagramsrather than Bayes nets. I think this convention is silly; why do we need a special term for that?
In influence diagrams, nodes have a type—uncertainty, decision, or objective. This gives you legibility, and makes it more obvious what sort of interventions are ‘in the spirit of the problem’ or ‘necessary to give a full solution.’ (It’s not obvious from the structure of the causal network that I should set ‘my action’ instead of ‘Omega’s prediction’ in Newcomb’s Problem; I need to read it off the labels. In an influence diagram, it’s obvious from the shape of the node.) This is a fairly small benefit, tho, and seems much less useful than the restriction on causal networks that the arrows imply causation.
[Edit] They also make it clearer how to do factorized decision-making with different states of local knowledge, especially when knowledge is downstream of earlier decisions you made; if you’re trying to reason about how a simple agent should deal with a simple situation, this isn’t that helpful, but if you’re trying to reason about many different corporate policies simultaneously, then something influence-diagram shaped might be better.
I guess, philosophically, I worry that giving the nodes special types like that pushes people toward thinking about agents as not-embedded-in-the-world, thinking things like “we need to extend Bayes nets to represent actions and utilities, because those are not normal variable nodes”. Not that memoryless cartesian environments are any better in that respect.
I guess, philosophically, I worry that giving the nodes special types like that pushes people toward thinking about agents as not-embedded-in-the-world, thinking things like “we need to extend Bayes nets to represent actions and utilities, because those are not normal variable nodes”. Not that memoryless cartesian environments are any better in that respect.
I see where this is coming from, but I think it might also go the opposite direction. For example, my current guess of how counterfactuals/counterlogicals ground out is the imagination process; I implicitly or explicitly think of different actions I could take (or different ways math could be), and somehow select from those actions (hypotheses / theories); the ‘magic’ is all happening in my imagination instead of ‘in the world’ (noting that, of course, my imagination is being physically instantiated). Less imaginative reactive processes (like thermostats ‘deciding’ whether to turn on the heater or not) don’t get this treatment, and are better considered as ‘just part of the environment’, and if we build an imaginative process out of unimaginative processes (certainly neurons are more like thermostats than they are like minds) then it’s clear the ‘magic’ comes from the arrangement of them rather than the individual units.
Which suggests how the type distinction might be natural; places where I see decision nodes are ones where I expect to think about what action to take next (or expect some other process to think about what action to take next), or think that it’s necessary to think about how that thinking will go.
I’m not sure which you’re addressing, but, note that I’m not objecting to the practice of illustrating variables with diamonds and boxes rather than only circles so that you can see at a glance where the choices and the utility are (although I don’t tend to use the convention myself). I’m objecting to the further implication that doing this makes it not a Bayes net.
I’m objecting to the further implication that doing this makes it not a Bayes net.
I mean, white horses are not horses, right? [Example non-troll interpretations of that are “the set ‘horses’ only contains horses, not sets” and “the two sets ‘white horses’ and ‘horses’ are distinct.” An example interpretation that is false is “for all members X of the set ‘white horses’, X is not a member of the set ‘horses’.”]
To be clear, I don’t think it’s all that important to use influence diagrams instead of causal diagrams for decision problems, but I do think it’s useful to have distinct and precise concepts (such that if it even becomes important to separate the two, we can).
What is it that you want out of them being Bayes nets?
I disagree. All the nodes in the network should be thought of as grounding out in imagination, in that it’s a world-model, not a world. Maybe I’m not seeing your point.
I would definitely like to see a graphical model that’s more capable of representing the way the world-model itself is recursively involved in decision-making.
One argument for calling an influence diagram a generalization of a bayes could be that the conditional probability table for the agent’s policy given observations is not given as part of the influence diagram, and instead must be solved for. But we can still think of this as a special case of a Bayes net, rather than a generalization, by thinking of an influence diagram as a special sort of Bayes net in which the decision nodes have to have conditional probability tables obeying some optimality notion (such as the CDT optimality notion, the EDT optimality notion, etc).
This constraint is not easily represented within the Bayes net itself, but instead imposed from outside. It would be nice to have a graphical model in which you could represent that kind of constraint naturally. But simply labelling things as decision nodes doesn’t do much. I would rather have a way of identifying something as agent-like based on the structure of the model for it. (To give a really bad version: suppose you allow directed cycles, rather than requiring DAGs, and you think of the “backwards causality” as agency. But, this is really bad, and I offer it only to illustrate the kind of thing I mean—allowing you to express the structure which gives rise to agency, rather than taking agency as a new primitive.)
All the nodes in the network should be thought of as grounding out in imagination, in that it’s a world-model, not a world. Maybe I’m not seeing your point.
My point is that my world model contains both ‘unimaginative things’ and ‘things like world models’, and it makes sense to separate those nodes (because the latter are typically functions of the former). Agreed that all of it is ‘in my head’, but it’s important that the ‘in my head’ realm contain the ‘in X’s head’ toolkit.
In influence diagrams, nodes have a type—uncertainty, decision, or objective. This gives you legibility, and makes it more obvious what sort of interventions are ‘in the spirit of the problem’ or ‘necessary to give a full solution.’ (It’s not obvious from the structure of the causal network that I should set ‘my action’ instead of ‘Omega’s prediction’ in Newcomb’s Problem; I need to read it off the labels. In an influence diagram, it’s obvious from the shape of the node.) This is a fairly small benefit, tho, and seems much less useful than the restriction on causal networks that the arrows imply causation.
[Edit] They also make it clearer how to do factorized decision-making with different states of local knowledge, especially when knowledge is downstream of earlier decisions you made; if you’re trying to reason about how a simple agent should deal with a simple situation, this isn’t that helpful, but if you’re trying to reason about many different corporate policies simultaneously, then something influence-diagram shaped might be better.
I guess, philosophically, I worry that giving the nodes special types like that pushes people toward thinking about agents as not-embedded-in-the-world, thinking things like “we need to extend Bayes nets to represent actions and utilities, because those are not normal variable nodes”. Not that memoryless cartesian environments are any better in that respect.
I see where this is coming from, but I think it might also go the opposite direction. For example, my current guess of how counterfactuals/counterlogicals ground out is the imagination process; I implicitly or explicitly think of different actions I could take (or different ways math could be), and somehow select from those actions (hypotheses / theories); the ‘magic’ is all happening in my imagination instead of ‘in the world’ (noting that, of course, my imagination is being physically instantiated). Less imaginative reactive processes (like thermostats ‘deciding’ whether to turn on the heater or not) don’t get this treatment, and are better considered as ‘just part of the environment’, and if we build an imaginative process out of unimaginative processes (certainly neurons are more like thermostats than they are like minds) then it’s clear the ‘magic’ comes from the arrangement of them rather than the individual units.
Which suggests how the type distinction might be natural; places where I see decision nodes are ones where I expect to think about what action to take next (or expect some other process to think about what action to take next), or think that it’s necessary to think about how that thinking will go.
I’m not sure which you’re addressing, but, note that I’m not objecting to the practice of illustrating variables with diamonds and boxes rather than only circles so that you can see at a glance where the choices and the utility are (although I don’t tend to use the convention myself). I’m objecting to the further implication that doing this makes it not a Bayes net.
I mean, white horses are not horses, right? [Example non-troll interpretations of that are “the set ‘horses’ only contains horses, not sets” and “the two sets ‘white horses’ and ‘horses’ are distinct.” An example interpretation that is false is “for all members X of the set ‘white horses’, X is not a member of the set ‘horses’.”]
To be clear, I don’t think it’s all that important to use influence diagrams instead of causal diagrams for decision problems, but I do think it’s useful to have distinct and precise concepts (such that if it even becomes important to separate the two, we can).
What is it that you want out of them being Bayes nets?
I disagree. All the nodes in the network should be thought of as grounding out in imagination, in that it’s a world-model, not a world. Maybe I’m not seeing your point.
I would definitely like to see a graphical model that’s more capable of representing the way the world-model itself is recursively involved in decision-making.
One argument for calling an influence diagram a generalization of a bayes could be that the conditional probability table for the agent’s policy given observations is not given as part of the influence diagram, and instead must be solved for. But we can still think of this as a special case of a Bayes net, rather than a generalization, by thinking of an influence diagram as a special sort of Bayes net in which the decision nodes have to have conditional probability tables obeying some optimality notion (such as the CDT optimality notion, the EDT optimality notion, etc).
This constraint is not easily represented within the Bayes net itself, but instead imposed from outside. It would be nice to have a graphical model in which you could represent that kind of constraint naturally. But simply labelling things as decision nodes doesn’t do much. I would rather have a way of identifying something as agent-like based on the structure of the model for it. (To give a really bad version: suppose you allow directed cycles, rather than requiring DAGs, and you think of the “backwards causality” as agency. But, this is really bad, and I offer it only to illustrate the kind of thing I mean—allowing you to express the structure which gives rise to agency, rather than taking agency as a new primitive.)
My point is that my world model contains both ‘unimaginative things’ and ‘things like world models’, and it makes sense to separate those nodes (because the latter are typically functions of the former). Agreed that all of it is ‘in my head’, but it’s important that the ‘in my head’ realm contain the ‘in X’s head’ toolkit.