Hi Gilles and Randy,
that sounds really interesting I'll try this out, both the sigmodial and
the scaling stuff!
I'm relative new to all this least squares things and I'm not a
mathematician so I need to learn a lot, so don't hesitate to point out
things that might seem obvious to the advanced user, that's really
welcome :-)
Am 08.06.21 um 15:23 schrieb Gilles Sadowski:
Hello.
Le mar. 8 juin 2021 à 08:14, Christoph Läubrich
<[email protected]> a écrit :
Hi Gilles,
I have used the the INFINITY approach for a while now and it works quite
good. I just recently found a problem where I got very bad fits after a
handful of iterations using the LevenbergMarquardtOptimizer.
The problem arises whenever there is a relative small range of valid
values for *one* parameter.
Too keep up with the Gausian example assume that the mean is only valid
in a small window, but norm and sigma are completely free.
My guess is, if in the data there are outlier that indicates a strong
maximum outside this range the optimizer try to go in that 'direction'
because I reject this solution it 'gives up' as it seems evident that
there is no better solution. This then can result in a gausian that is
very thin and a really bad fit (cost e.g about 1E4).
If I help the optimizer (e.g. by adjusting the initial guess of sigma)
it finds a much better solution (cost about 1E-9).
So what I would need to tell the Optimizer (not sure if this is possible
at all!) that not the *whole* solution is bad, but only the choice of
*one* variable so it could use larger increments for the other variables.
If you want to restrict the range of, say, the mean:
public class MyFunc implements ParametricUnivariateFunction {
private final Sigmoid meanTransform;
public MyFunc(double minMean, double maxMean) {
meanTransform = new Sigmoid(minMean, maxMean);
}
public double value(double x, double ... param) {
final double mu = meanTransform.value(param[1]); // param[1]
is the mean.
final double diff = x - mu;
final double norm = param[0]; // param[0] is the height.
final double s = param[2]; // param[2] is the standard deviation.
final double i2s2 = 1 / (2 * s * s);
return Gaussian.value(diff, norm, i2s2);
}
}
// ...
final MyFunc f = new MyFunc(min, max);
final double[] best = fitter.fit(f); // Perform fit.
final double bestMean = new Logit(min, max).value(best[1]);
HTH,
Gilles
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