Nyquist aliasing with periodic kernels - and defaults about gp-structure-search

[jamesrobertlloyd]

This is fixed (mildly hackily) - but it has raised another issue. What are sensible default values for random restarts of the period of periodic kernels? Problem is that there are lots of local optima at harmonics. I've have inserted a hack of centering the period on -2 for initialisation (the assumption of ~ 10 wiggles?) but this needs some more serious thought. Really, we need a prior on the structure of data sets!

[jamesrobertlloyd]

Currently have hacked in that no period starting value can be smaller than 5 * the smallest inter data gap - this is a magic number but is hopefully vaguely reasonable.

[duvenaud]

Seems to work!

[jamesrobertlloyd]

Improved the heuristic so that it also disallows periods smaller than m * the average distance between data points. This makes the heuristic still work when the data is irregularly spaced.