I got working a simple (though not fast) system to fit a highly parameterized (what is called, for some reason, non-parametric
) curve to a set of data today, in preparation for a future talk about model complexity. My model has more parameters than data, but it optimizes, and it has a complexity that is continuously variable; the complexity is not the number of parameters.
What's your parameterisation? I sometimes use Gaussian Processes for stuff like this, but they don't always express the prior beliefs that well, and they can get computationally expensive pretty quickly.
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