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python-adaptive / adaptive

:chart_with_upwards_trend: Adaptive: parallel active learning of mathematical functions
http://adaptive.readthedocs.io/
BSD 3-Clause "New" or "Revised" License
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Promote AveragingLearner to LinearFitLearner #122

Open jbweston opened 5 years ago

jbweston commented 5 years ago

(original issue on GitLab)

opened by Anton Akhmerov (@anton-akhmerov) at 2017-09-06T09:31:46.601Z

A more advanced version of averaging would be performing a linear fit. The logic here should be largely similar, but instead of using the mean, we should use fit coefficients.

jbweston commented 5 years ago

originally posted by Bas Nijholt (@basnijholt) at 2018-05-29T19:42:12.834Z on GitLab

@anton-akhmerov I could really use this right now.

Could you perhaps elaborate on your ideas of how the LinearFitLearner would work?

jbweston commented 5 years ago

originally posted by Anton Akhmerov (@anton-akhmerov) at 2018-05-29T20:19:23.515Z on GitLab

You basically need to incrementally update this formula, so you need to accumulate a matrix of $\sum x_i x_i^T$ and $\sum x_i y_i^T$. For the error estimate you would need to store higher moments as well.