Timeline for Levenberg-Marquadt near the minima for non-zero-residual problems
Current License: CC BY-SA 3.0
4 events
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| Sep 5, 2012 at 17:59 | comment | added | Brian Borchers | This is confusing- are you minimizing a sum of squares or are you using some other objective (such as the Huber measure)? If you're not minimizing a sum of squares than LM isn't appropriate in the first place. Assuming that you are doing nonlinear least squares, and assuming that you have a reasonable assessment of the uncertainty in the measurements (e.g. $y_{i}$ is known with uncertainty $\sigma_{i}$, then you should normalize by $c(x)=\sum ((f_{i}(x)-y_{i})/\sigma_{i})^{2}$. You should also scale the parameters $x$ so that they're all of similar magnitude. | |
| Sep 5, 2012 at 16:31 | comment | added | Alex Flint | @BrianBorchers. Thanks, yes that is definitely something I should be doing. I'm aware of scaling issues but unsure precisely how to scale my problem given that I'm using a robust error function. What is the relevant quantity to normalize in general? | |
| Sep 4, 2012 at 4:19 | comment | added | Brian Borchers | By the way, it's easy to compute the gradient of $c(x)$ given $J$ and the values of $f_{i}(x)-y_{i}$. You should always check that the gradient is reasonably small as part of your termination criteria. | |
| Sep 4, 2012 at 0:33 | history | answered | Brian Borchers | CC BY-SA 3.0 |