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Suppose that $X$ and $T$ are both random variables. Where $T$ is a label.
I just want to ask is tha finding probabilities on the label $P(T=t)$ or conditional probabilities $P(X=x|T=t)$ meaningful or necessary ?
Since, I never see an example that finding these probabilities yet and I am new to the term "label" here.

Thanks for answering !

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  • $\begingroup$ A pretty standard machine learning is classification, which involves finding the probability of the labels given a value of $X$ (the “features” or “predictors”). That could be why you don’t see what you describe, even if it is a perfectly reasonable probability (in some sense…the issue gets funky if your $X$ is a continuous variable). // That said, I do not totally know what question you’re trying to ask, just why the conditional probability tends to be talked about in the reverse order to what you posted? $\endgroup$
    – Dave
    Sep 24, 2021 at 22:48
  • $\begingroup$ Well, like right now I have only seen examples that finding out the value of $P(X=x)$, $P(T=t|X=x)$ and the joint probability $P(T=t, X=x)$ but I have never seen any examples to find the value of $P(T=t)$ and $P(X=x|T=t)$ when $T$ is a label. So, I am wondering if finding the probabilities like $P(T=t)$ and $P(X=x|T=t)$ when $T$ is a label are unmeaningful or unnecessary things to do ? $\endgroup$
    – xxxxxx
    Sep 24, 2021 at 23:29

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They're neither unmeaningful nor unnecessary. For example, Bayes classifier (or Naive Bayes more commonly) explicitly uses them. $P(T=t)$ is the prior probability of the label, and $P(X=x|T=t)$ is the conditional likelihood of the sample.

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  • $\begingroup$ @xxxxxx does this answer your question? $\endgroup$
    – gunes
    Sep 27, 2021 at 14:05

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