Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I have a fitness function $f(x,y)$, which I am sampling at discrete $x$ and $y$ in order to minimize $f$. In addition to the location of the minimum, I would like to give an appropriate measure of confidence or quality of the determined location, so that I can detect if the minimum is rather wide, or if $f$ is non-convex.

Without making further assumptions about $f$, what would be an appropriate measure of quality?

share|improve this question
    
What method are you using to find the minimum? Or are you just sampling the function at many points and finding the minimum of this list? –  icurays1 Jan 25 '13 at 15:17
    
Indeed I'm sampling the function. –  Hendrik Jan 25 '13 at 15:19
    
I should add I'm sampling the function in a rectangular grid of $(x,y)$ values. –  Hendrik Jan 25 '13 at 15:20
    
Without further assumptions about $f$, you can say very little. It might be a rapidly oscillating function that you have undersampled, like $\sin(100x)$. –  Rahul Jan 27 '13 at 1:02
    
Okay, what if we exclude undersampling and assume that the function is steady? –  Hendrik Jan 27 '13 at 10:32

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.