Cross-validation with SINDy about pysindy HOT 6 CLOSED

You can use the sklearn gridsearch on nested or composed estimators as well: https://scikit-learn.org/stable/modules/grid_search.html#composite-estimators-and-parameter-spaces

We need to make sure though, that all nested objects inherit properly from the BaseEstimator class, as this implements the two methods (set_params and get_params) needed.

Also, internally we are using a MultiOutput(Pipeline). As you said, this might clutter the parameter names. If this is the case, we can overwrite set_params and get_params for a cleaner interface.

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Should be interesting an example at documentation

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I was looking into this again and your suggestion, @Ohjeah, now works smoothly (since we have refactored the optimizer code).

However there's another problem: the SINDy fit and score methods take an optional parameter t which isn't standard for scikit-learn. When a uniform time step other than 1 is used, the cross validation object doesn't have a way to pass it into both the fit and score methods. You can pass in a fixed time step to SINDy.fit via the **fit_params argument of the cross validation object, but not the score function.

One option is to not try to feed t in and assume a uniform time step of 1. If you then divide the coefficients of the resulting model by the true time step you'll arrive at the correct equation, but you'll also have to shrink the thresholds by the same factor.

Another option could be to add a parameter to the SINDy constructor allowing you to specify a fixed uniform time step that would be used as a default if other values are not passed in. I think this might be the cleanest solution. I'll play around with it and see how it looks.

Nonuniform time steps or control variables are another story. I haven't thought much about how to incorporate them into this framework.

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Closed with #84

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@briandesilva I overlooked your last comment and assumed this issues was closed with the corresponding PR.

Should we re-open, or open a separate issue to discuss parameters for the derivative?

Btw: you can also use a custom scorer in gridsearches/crossvalidation.

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I don't think we need to re-open the issue. I'm satisfied with our current cross-validation capabilities.

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