I wrote some words in Roweis and my spectroscopic calibration document, mainly about modeling of spectral traces. Our current plans will lead (I'm pretty sure) to a non-linear fit, which doesn't worry me in terms of local optimization, but it does worry me in terms of convexity. I don't see any simple way to keep the problem we are trying to solve—a spectral reduction pipeline that learns its own calibration information as it goes—convex. That's not a drop-dead requirement, but it sure is nice to know that you are at a global optimum.
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