third_person

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third_person [2024/12/25 12:39] – [Why does this happen?] 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 $\theta$, and thus unable to implement the necessary causal dependency between $X$ and $\theta$ 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 $\theta$, and thus unable to implement the necessary causal dependency between $X$ and $\theta$ 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 $P(Y|\text{do}(X))$, 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 $P(Y|\text{do}(X))$, 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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 that is, without coupling terms (or, $R(x,\theta)=1$, meaning that no information is transmitted between $x$ and $\theta$). that is, without coupling terms (or, $R(x,\theta)=1$, meaning that no information is transmitted between $x$ and $\theta$).
  
-Simply stated, replacing the demonstrator by the learner changes the statistical relation between the random variables. 
 ==== Core mechanism of imitation ==== ==== Core mechanism of imitation ====
  
  • third_person.txt
  • Last modified: 2024/12/25 12:40
  • by pedroortega