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Analysis of CD Learning: Auxiliary Derivations

Summary: Appendix D
Analysis of CD Learning:
Auxiliary Derivations
The appendix o ers 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
 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:
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)


Source: Agakov, Felix - Institute for Adaptive and Neural Computation, School of Informatics, University of Edinburgh


Collections: Computer Technologies and Information Sciences