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# 多分类逻辑回归模型

假设Y的取值集合是${1, 2, \cdots, K}$，则

$$
\begin{aligned}
P(Y=k|x) = \frac{\exp (w\_k \cdot x)}{1+\sum\_{k=1}^{K-1}exp(w\_k \cdot x)}  \\
P(Y=K) = \frac{1}{1+\sum\_{k=1}^{K-1}exp(w\_k \cdot x)}
\end{aligned}
$$

其中$x \in R^{n+1}$，$w\_k \in R^{n+1}$