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--- third_person [2024/12/25 12:39] – [Why does this happen?] pedroortega
+++ third_person [2024/12/25 12:40] (current) – [Why does this happen?] pedroortega
@@ Line 38: / Line 38: @@
 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.
@@ Line 56: / Line 56: @@
 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 ====