What is the meaning of $p(y|x;\theta)$ and $p(x;\theta)$ and $p(x,y|z)$?

Question

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

The answers to this question might be helpful. – Sven Hohenstein Aug 22 '17 at 12:40 — Sven Hohenstein, Aug 22 '17 at 12:40

Jan Sila · Answer 1 · 2017-08-22T14:05:03.187

2

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

edited Aug 22 '17 at 14:05

answered Aug 22 '17 at 11:56

Jan Sila

315

Thanks, but it didn't say about p(x;y) , p(x|y,z) and p(x|y;z) – user3486308 Aug 22 '17 at 12:36
that is just the notation of conditional probability, if not stated otherwise – Jan Sila Aug 22 '17 at 12:40
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. – gung - Reinstate Monica Aug 22 '17 at 13:52

What is the meaning of $p(y|x;\theta)$ and $p(x;\theta)$ and $p(x,y|z)$?

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