Summary: Appendix D
Analysis of CD Learning:
Auxiliary Derivations
The appendix oers some of the auxiliary derivations supporting the result
(1.33) for the second and fourth moments hx 2
i i and hx 4
i i of the i th recon
struction of the visible variable x i for the xed initial point x 0 [see section
1.4.3].
To express hx 2
i i through the initial data point x 0 we make use of the
recurrent relation (1.30):
8 > <
> :
z i = x i + u i ; i 0
x j = z j 1 + v j ; j 1:
(D.1)
From (D.1) we can easily see that
z 0 = x 0 + u 0 (D.2)
x 1 = x 0 2 + u 0 + v 1 (D.3)
