4 ms·
A classic demonstration of similar effect - any set of N data points in a time series, e.g. (t,f(t)), can be fit by a N-1 order polynomial to pass through each
by ska 8y ago
A classic demonstration of similar effect - any set of N data points in a time series, e.g. (t,f(t)), can be fit by a N-1 order polynomial to pass through each point. So fit a high order poly to a set of points sampled (esp. with a little noise) from a low order poly. You'll get crazy oscillations, and outside the sampling area it will likely diverge fast. Now add a smoothness term and crank it up until you get more reasonable results - regularization.
It's a simplification, but informative about some ML techniques.
- Gibbon1 8y agoOne of my labs some students curve fitted a sixth order poly onto five data points they collected. The process being measured was y = something something minus ln(x). It fit all five points exactly and smoothly and wildly diverged on either side. The professor was really amused.
- chestervonwinch 8y agoIt’s called https://en.m.wikipedia.org/wiki/Runge's_phenomenon https://en.m.wikipedia.org/wiki/Runge's_phenomenon and can be mitigated eg by non-uniform interpolation grids like chebychev nodes.