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Categories and types of intervention

October 27, 2010 2 comments

This is post8 in a sequence exploring formalisations of causality entitled “Reasoning with causality”.

This post will summarise the paper Varieties of Causal Intervention and, by doing so, will explore what a causal intervention is. To start with, imagines a Bayes Net representing a causal process. So let’s say that cleaning your teeth and genes both effect the chances of dental decay but that the same genes also influence the chance that you’ll do your teeth:

Now image there’s a government policy being considered whereby police men would enforce tooth cleaning. To analyse the affects of this we would intervene on “Clean”, which we can think of as setting the value of the variable and ignoring the influence of any parents, and we would then observe the effects of the intervention on decay.

Intervention vs Observation

This concept of intervention is different to observation. Imagine, for example, that we observed someone cleaning their teeth. This may have a different effect to intervene to make them clean their teeth as it suggests they’re more likely to have certain genes and these genes also make it less likely that teeth will decay. Thus, in this case, the observation of tooth cleaning would have a stronger causal effect on decay than an intervention.

The important point is that the two concepts are different because intervention surgically removes the context of any parent nodes.

Make interventions complex

The simple view of interventions, expressed in most of the literature on the topic, is that they are deterministic, always achieve a desired effect and affect only one variable. However, interventions in the real world often fail to match these simplified assumptions. For example, an intervention to pressure someone to clean their teeth might fail. Or an intervention might affect multiple variables, rather than just one. And finally, an intervention may be indeterminstic and fail to set a variable to a specific value.

To model this, rather than simple changing the value of a variable in the system (setting clean to true, in the above example), the paper suggests introducing a new parent node for the variable which is introduced to change the variable to some particular target distribution and which is outside of the system. See below:

This intervention node will be binary (yes/no) but its interaction with other nodes is open so that the particular target distribution may not be achieved. Note that intervention variables can be parents of more than their target variable, allowing side effects to be modelled.

Types of intervention

An intervention then leads to a new probability distribution across its states in the targeted variable. The types of interventions possible are:

  1. An independent intervention where the results of the intervention do not depend on other parents of the variable. This changes the probability distribution of the target to that intended by the intervention. A dependent intervention would calculate the new probability distribution based on both this intended distribution and also based on the other parents. So imagine a gene therapy intervention that fixes that effects of bad genes on not cleaning teeth. To someone with bad genes this will decrease the chance of decay. For someone who already has the good genes, this will have no effect. This would be a dependent intervention.
  2. A deterministic intervention aims to achieve a specific effect. Say to force people to clean their teeth. That’s to say, it aims to set a variable to a specific value. It may still be complicated to model if the intervention is dependent. A stochastic intervention aims to leave the target variable with a distribution over more than one state.

Conclusion

Representing interventions as the introduction of a new parent node rather than as a surgical change of the value of a variable allows a wider range of types of intervention to be modelled.

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