Incorporate uncertainty on non Bayesian forecasting

[jarroyoe]

I went deep through the rabbit hole of uncertainty quantification in forecasting of neural networks. A faster method of quantifying uncertainty than what was proposed by Lapeyrolerie et al, 2022 of fitting several neural networks and doing an ensemble forecast is to do a Laplace approximation of the neural network. This has been tested for NODEs and implemented in Julia as LaplaceRedux.jl.

The idea of Laplace approximation is to linearize the neural network from the Maximum a Posteriori estimation of the parameters. Ott et al proposes this linearization to occur using the final iteration of SGD as the MAP.

Thoughts?

[jarroyoe]

This paper was recently submitted to arxiv, might be worth considering.