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While going through one of the answer I came across the following notation

$P( y_i =1 \mid \mathbf{x}_i ; \theta)$

I am not sure about its interpretation and how should it be read.

The exact usage can be found here

Now logistic regression says that the probability that class variable value $y_i =1$ , $i=1,2,...m$ can be modelled as follows

$$ P( y_i =1 \mid \mathbf{x}_i ; \theta) = h_{\theta}(\mathbf{x}_i) = \dfrac{1}{1+e^{(- \theta^T \mathbf{x}_i)}} $$

so $y_i = 1$ with probability $h_{\theta}(\mathbf{x}_i)$ and $y_i=0$ with probability $1-h_{\theta}(\mathbf{x}_i)$.

Lee David Chung Lin
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  • Welcome to MSE. Please edit and use [MathJax](https://math.meta.stackexchange.com/questions/5020) to properly format math expressions. – Lee David Chung Lin Feb 18 '20 at 09:01
  • It is just saying this is the conditional probability that $y_i=1$ given the parameter $\mathbf \theta$ and the values of the independent variables in $\mathbf x_i$ – Henry Feb 18 '20 at 09:11

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