psf and trace modeling

Roweis is not afraid of large numbers of parameters! He modeled the spectrograph output with a trace model that has more parameters than pixel rows, and a psf model with 200 times as many parameters as pixels! That is, far more parameters than data. Because he put on strong smoothness priors, he was able to optimize (on his laptop) no problem. He and I spent lunch discussing spectral modeling. Roweis noted that there are many ways to make the problem scale; in particular you can compute the gradient in parameter space for small blocks of data, make small steps, one for each data block, and iterate over all the data. Apparently this still optimizes the system just fine, and you never have to get everything into memory at once. We assigned me more writing tasks and set the goal of extracting one BOSS fiber by the end of the month.

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