Linear Model

• If $\delta_k(x)$is linear, then $D$ is also linear.

• $E(Y_k|X=x)=P(G|X)$ When we estimate this with $X^T\beta$, the range can be out of range 0 to 1.

• $\min_{\mathbf{B}} \Sigma||y_i-[(1,x_i^T)\mathbf{B}]^T||^2$

• $\hat{G}(x)=argmax_{k \in g}\hat{f}_k(x) \rightarrow \hat{G}(x)=argmin_{k}||\hat{f}(x)-t_k||^2$

• $\sum_k\hat{G}(x)=1$