Last updated 3 years ago
Was this helpful?
If Ξ΄k(x)\delta_k(x)Ξ΄kβ(x)is linear, then DDD is also linear.
E(Ykβ£X=x)=P(Gβ£X)E(Y_k|X=x)=P(G|X)E(Ykββ£X=x)=P(Gβ£X) When we estimate this with XTΞ²X^T\betaXTΞ², the range can be out of range 0 to 1.
minβ‘BΞ£β£β£yiβ[(1,xiT)B]Tβ£β£2\min_{\mathbf{B}} \Sigma||y_i-[(1,x_i^T)\mathbf{B}]^T||^2minBβΞ£β£β£yiββ[(1,xiTβ)B]Tβ£β£2
G^(x)=argmaxkβgf^k(x)βG^(x)=argminkβ£β£f^(x)βtkβ£β£2\hat{G}(x)=argmax_{k \in g}\hat{f}_k(x) \rightarrow \hat{G}(x)=argmin_{k}||\hat{f}(x)-t_k||^2G^(x)=argmaxkβgβf^βkβ(x)βG^(x)=argminkββ£β£f^β(x)βtkββ£β£2
βkG^(x)=1\sum_k\hat{G}(x)=1βkβG^(x)=1
