A particular cost function

[Christos Dimitrakakis]

I have a sequence of observations (x(1), x(2), ...,)

There is a set of functions f_i, such that

y_i(t) = f_i(x(t-N),...,x(t-1))

I have the MSE cost function:

C = \sum_t \sum_i (p_i(t) (y_i(t)-x(t)))^2 (1)

which I try to minimise by gradient descent.. If p_i(t) is independent on
the input x, or is directly dependent on the input (ala mixtures of
experts) then things are very simple, but actually:

p_i(t+1) = a p_i(t) + (1-a) \frac {\exp(e_i^2(t+1))} (2)
{\sum_j \exp(e_j^2(t+1))}

where e_i(t) = y_i(t) - x(t).

In that case , what is the derivative of C with respect to y_i?


Cheers, Christos

--
Christos Dimitrakakis