GPs are fantastic, but they are not without their drawbacks.
- Computational complexity is one: \(\mathcal{O}(n^3)\) matrix decompositions and \(\mathcal{O}(n^2)\) storage can severely limit data sizes.
Flexibility is another.
- Stationarity is a nice simplifying assumption,
- but it is clearly not appropriate for all data generating mechanisms;
- e.g., the LGBB rocket booster data.
In this segment we'll try to address those issues, ideally simultaneously.
- The literature on GP approximation is booming: approximation and sparsity are common themes.
- The literature on nonstationary modeling is more niche.