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CardiacModelling / BenNevis

"Where is Ben Nevis" presents the landscape of Great Britain as a testbed for optimisation and sampling methods.
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Find issue with linear interpolation or plot of linear interpolation #28

Open MichaelClerx opened 2 years ago

MichaelClerx commented 2 years ago

local-line-plot-macdui

Why do we see these some times?

I.E. did the optimiser not find the optimum, is it a plotting issue, or something else?

EricWay1024 commented 2 years ago

I suppose it's because of the discrepancies between a local maximum point of the interpolant and the corresponding hill in the database.

image

I've come up with an idea to solve such discrepancy: find some local optimizer that has a small learning rate, and for each hill in the database, use its location as the starting point of the local optimizer. We'll end up somewhere near our starting point but with a larger height (we must check the proximity), and then we update the database with this point.

Or maybe there's a fixed discrepancy for all the hills? I.e. we simply need to move all the locations in the database by a fixed amount to match the hills with the local maxima. I haven't worked on this yet so I'm not sure.

MichaelClerx commented 2 years ago

Hi Eric, Yeah the hills database doesn't agree with our data set entirely, and that's fine.

What worries me is why the red line above isn't exactly on the maximum of the blue line. Both are from our interpolant, so the hills db doesn't come into play here

EricWay1024 commented 2 years ago

Oh, then I suppose that might have something to do with the optimizer, which might stop iterating only near the highest point, potentially because of its "minimum step"?