third_person

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third_person [2024/12/25 12:34] – [How to translate third-person into first-person?] pedroortegathird_person [2024/12/25 12:40] (current) – [Why does this happen?] pedroortega
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 This implies that P(Y|X) will predict well what will happen when the demonstrator chooses X, but it won't predict what will happen when the learner chooses X. This last prediction differs because the learner's choice---even when imitating---are based on their own subjective information state, which is ignorant about the unobserved intention θ, and thus unable to implement the necessary causal dependency between X and θ the same way the demonstrator did. This implies that P(Y|X) will predict well what will happen when the demonstrator chooses X, but it won't predict what will happen when the learner chooses X. This last prediction differs because the learner's choice---even when imitating---are based on their own subjective information state, which is ignorant about the unobserved intention θ, and thus unable to implement the necessary causal dependency between X and θ the same way the demonstrator did.
  
-==== Why does this happen? ====+==== The math: why does this happen? ====
  
 To understand what will happen when we substitute the demonstrator by the learner, we need P(Y|do(X)), i.e. the distribution over Y when X is chosen independently, also known as the effect Y under the //intervention X// in causal lingo.  To understand what will happen when we substitute the demonstrator by the learner, we need P(Y|do(X)), i.e. the distribution over Y when X is chosen independently, also known as the effect Y under the //intervention X// in causal lingo. 
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