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I saw these in a machine learning notes. and like to know the meaning of them? also the formula of them?

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welcome to SO! They are simply a notation for conditional probabilities. You often see them in Bayesian statistics.

How to interpret it:

For instance, your example $p(y|x;\theta)$ means what is the probability that you observe $y$, when $x$ and $\theta$ 'holds'. Usually, $x$ stands for some data and $\theta$ parameters of distribution, or a model. It can be the probability of observing something given the dataset $x$ and estimated linear regression coefficients $\theta = (\beta_0,\beta_1)$.

Have a look for instance at Wiki page

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  • $\begingroup$ Thanks, but it didn't say about p(x;y) , p(x|y,z) and p(x|y;z) $\endgroup$ Aug 22, 2017 at 12:36
  • $\begingroup$ that is just the notation of conditional probability, if not stated otherwise $\endgroup$
    – Jan Sila
    Aug 22, 2017 at 12:40
  • $\begingroup$ This is being automatically flagged as low quality, probably because it is so short. At present it is more of a comment than an answer by our standards. Can you expand on it? You can also turn it into a comment. $\endgroup$ Aug 22, 2017 at 13:52

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