《机器学习》推导

aE △w;=-17 E (t1-O 2 kEoutputs aE ae, ar net d OE anet. aw anet oed aEd oo ne Oo. Onet ae,a 1 ∑(k-0) k∈ outputs

j i j d j i j j d j i d x net E w net net E w E   =     =   ji d ji w E w    = −   → = − k outputs d k ok E w t 2 ( ) 2 1 ( ) j j net o     =   j d j d o E net E 2 ( ) 2 1   −   =   k outputs k k j j d t o o o E

E00 O(t1-o1) (t1-0)2=2(1-0) 2 Onet OE △wj 77 =7( ),(1-O,)x OE ae anet onet, keDownstream() anetk Onet ∑ anet aE, do ∑-k k∈ Downstrean(j anet k∈ Downstream) do anet ∑ onet ∑ k∈ Downstrean(j) ∈ Downstrean(j)

( ) ( ) 2( ) 2 1 ( ) 2 1 o 2 j j j j j j j j j j j d t o o t o t o t o o E = − −   − − = −   =   (1 ) ( ) j j j j j o o net netj net o = −   =    j j j j j i j i d j i t o o o x w E w = ( − ) (1− )    = −            = − −   = −     = −   = −     =   ( ) ( ) ( ) ( ) ( ) (1 ) k Downstream j k kj j j j j k Downstream j k kj k Downstream j j j j d k k Downstream j j k k k Downstream j j k k d j d w o o net o w net o o E net net net net net E net E    

)∑6w k∈ Downstrean(j =7o,x

j i j j i k Downstream j j j j k kj w x o o w     = = −   ( ) (1 )