Home > Reasoning with causality > Uses of Bayes Nets in causality: Modeling type and token causal relevance

Uses of Bayes Nets in causality: Modeling type and token causal relevance

This is post 6 in a sequence exploring formalisations of causality entitled “Reasoning with causality”. This post continues to summarise the paper “Causal Reasoning with Causal Models”.

The previous post in the sequence is Is a causal interpretation of Bayes Nets fundamental?

Causal Relevance, as opposed to causal role, is simply interested in whether there is a causal relationship between a cause and an effect, not whether the cause increases or decreases the chance of the effect. “Causal Reasoning with Causal Models” attempts to find a way of capturing and formalizing causal relevance.

Type causal relevance

Type causality looks at relationships between general categories – does smoking cause cancer. Token causality looks at a specific instance – did smoking cause cancer in this patient.

In relation to capturing type causal relevance, the first act seems to be to look at the relationship under intervention. If we change the amount someone in general smokes, does this change their chance of getting cancer? If so, smoking is causally relevant to cancer. Unfortunately, it’s not this simple. Imagine the following case: Taking the pill increases the chance of getting thrombosis but decreases the chance of getting pregnant. Getting pregnant increases the chances of getting thrombosis. Further, imagine that these two effects balance perfectly: So whatever dosage of pill you take, the increased chance of getting thrombosis due to this is directly countered by the decreased chance of getting pregnancy caused thrombosis. However, we still want to say that the pill is causally relevant thrombosis.

The problem with the above scenario is that we want to consider the component causal effects rather than the net causal effects. This is achieved by looking at each path from a cause to an effect one at a time (and blocking the other paths while doing so). If there is a probabilistic dependence between any of the paths then the factor is causally relevant. So, if we block the path from the pill via decreased chance of pregnancy then there is plainly a probabilistic dependence between the pill and thrombosis via the other path.

Token causal relevance: First attempt

Extending this account to token causality is a little harder. Imagine a hiker walking up a hill when a boulder is dislodged. They duck and so survive. If the boulder had not fallen, they also would have survived. In terms of type causality, this sort of event can cause death so we want to see the boulder falling as causally relevant to survival. This is achieved with the analysis above. However, from a token perspective, this boulder fall was not causally relevant.

A possible criteria: A is causally relevant to B if for all paths from A to B there is a probabilistic dependence between A and B if the other paths are set at their observed file.

So in the boulder example, if we set the value of the variable duck to true then the boulder falling is not causally relevant to survival – just as we were hoping.

However, this criteria doesn’t solve all problems of this type: Imagine Suzy throws a rock at a bottle and a second late Billy does the same. Suzy’s rock breaks the bottle but there’s no probabalistic dependence because if she didn’t throw a rock the bottle would still have been broken (by Billy). This doesn’t change if we set the other paths to their observed value (ie. we set Billy throwing to true) But we do want her throw to have token causal relevance to the bottle breaking.

Token causal relevance: A solution

This can be solved if we have a more complex criteria for token causal relevance:

1.)     The causal model is correctly constructed – I won’t go into all the details here but this means the model must meet certain criteria (like all variables must be intervenable)

2.)     The context should be fixed according to observation (so fix the value of Billy throwing to true)

3.)     All paths from cause to effect must meet certain criteria including that they must be type causally relevant (there is some value of the variable which will induce a probabalistic dependence with other paths blocked). Other paths should be removed.

Now we check, without blocking other pathways from the cause to the effect, whether there is a probabalistic dependence.

So in the above example we construct the model as per 1:

We now fix the context so both Suzy throwing and Billy throwing are set to true. Now with the context of Suzy Throwing being set to true, there is no longer a probabalistic dependence between Billy throws and bottle breaks. So we remove the path.

Now the probabalistic dependence is clear. The same solution can also be used to solve a variety of scenarios which I haven’t had the space to go into here.

Thus we have a solution for how to formalise both type and token causal relevance.

The next post is Probabilistic causality

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  2. December 14, 2011 at 3:14 pm

    Matt Englett
    Great article on Matt Englett, keep up the good work by posting excellent content. awesome site

  1. October 15, 2010 at 11:16 am

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