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You still have to deal with the precise definition of interpolation vs. extrapolation. And it does not matter what space you are using as long as you operate u
by Isinlor 5y ago
You still have to deal with the precise definition of interpolation vs. extrapolation.
And it does not matter what space you are using as long as you operate under the convex hull definition of interpolation vs. extrapolation you will need exponentially more samples as intrinsic dimensionality of the space increases.
This means that even under the manifold hypothesis, as long as intrinsic dimensionality is reasonably high i.e. in low hundreds, models will be doing extrapolation.
- urthor 5y agoI think we've just jumped from my "stochastic software engineering tip of the day" to a postgraduate level examination of validation and test set decision boundaries vs dataset boundaries. The thing is also, any individual hyper-dimensional case can be outside of the training set's convex hull itself and be correctly classified. However, you would still have to quantify what the relationship of the dimensions with the highest feature importance were to said space. Which is why the second paper is so fascinating. From the perspective of issues product/engineering teams face in the field, I'd definitely maintain that fire alarms should start sounding once you see any sort of extrapolation and you should dive deeper. Unfortunately the maturity level of this space is still at the point where peer review of data-set transformations before deploying to production and committing Jupyter Notebooks to GitHub is a heated in-office discussion. The majority of the commercial world is a long way from that kind of best practice.