Error Estimation and Stability Control NN
unixops
neural networks. Rather than traditional prediction and classification
as the broad scope of neural network applications ,looking at
optimization strategies that combine or utilize traditional
applications.
In context to this subject if we take a nonlinear prediction x+h(t) | x
(t) s.t. h() is a polynomial or quadratic criteria to predict a given x
(t+h) in a set x. Utilizing a neural network it is easy to estimate
any given x(t)+h(t) for a given history of x(t), s.t e(x) is an error
of h(x(t)). This provides us with two time series the prediction x+h
(t) and its error e(x). Most applications objective is to minimize the
error w.r.t. time.
If we add an additional estimation g(x) as an estimate of a given
error e(x) for each delay or approximation of x(t), s.t. g(1,x)=e(x)
of x+h(x(t+1)). 1) How do we organize our error approximations g(x)
for all h(x)? 2) Does their exist a function that describes g(x) say
g'(x), for a range of delays [x(t+1),x(t+2),..x(t+10)] s.t. g'(x) maps
to a feedback of h(x'), h('x)-h(x)<=0. And if this function can be
derived analytically is it safe to substitute g'(x) as a transfer
function of the error estimate e(x) for all x(t) | x? 3) What methods
or functions could be used to establish the stability of g(x) for a
given criteria of h(x)?
With respect to neural network implimentation x(t) and h(x) constitute
one network, where e(x) and g(x) and a secondary network. Here g(x) is
feedback into our first network at h(x').
And what is the goal of this? Using a NN to estimate x(t) and derive a
prediction of the error that holds for any given delay x+h(x(t+100))
given only x(t)+h(t=[1,2,...,10]) | x(t). Such an example may require
a 'comparator' function that minimizes e(x') and e(x) for both the
actual error estimate and the feedback function g('x) in h(x').
Any suggestions, comments, notes, or references to other works in
progress are welcome.
Sincerely yours,
Doug