I have 3 vectors (a,b and c), with 17 numeric elements in each.I am comparing these to another vector, d, (also 17 numeric elements) which is used as the gold-standard reference point.
Individually I can find how well each of the three vectors compare with d using mae:
meanAbsoluteErrorA = mae(d-a);
meanAbsoluteErrorB = mae(d-b);
meanAbsoluteErrorC = mae(d-c);
I was then wondering if I could combine and weight the three vectors a,b and c to reduce the error. e.g: if you took each to have an equal weighting:
meanAbsoluteErrorCombined = mae((1/3 * a) + (1/3 * b) + (1/3 * c) - d)
How could i optimise the choosing of the weights to get the smallest mae. I can't seem to work this using the optimisation tool. Is it possible to optimise an mae like this as I seem to be producing error after error and also can't seem to find a similar example online.
Effectively, I have the following optimisation problem:
Minimise f(alpha1,alpha2) = mae((alpha1*a) +(alpha2*b)+(alpha3*c) - d)
with alpha1+alpha2 + alpha3 = 1
Minimise f(alpha1,alpha2) = mae((alpha1*a) +(alpha2*b)+((1-alpha1-alpha2)*c) - d)
with alpha1, alpha2, alpha3>=0
Thanks in advance!