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Tag: Reverted |
Tag: Reverted |
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Line 91:
We can use this to find the other probabilities:
: <math>
\begin{align}
\Pr(Y_i=1) &= \frac{e^{\boldsymbol\beta_1 \cdot \mathbf{X}_i}}{1 + \sum_{j=1, j\neq 1}^{K} e^{\boldsymbol\beta_j \cdot \mathbf{X}_i}} \\
Line 103:
where the the summation runs from <math>1</math> to <math>K</math>, but excluding the term with the index of the probability being computed, or generally:
:<math>
\begin{align}
\Pr(Y_i=k) = \frac{e^{\boldsymbol\beta_{K-1} \cdot \mathbf{X}_i}}{1 + \sum_{j=1, j\neq k}^{K} e^{\boldsymbol\beta_j \cdot \mathbf{X}_i}}
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