Perturbative adaptive importance sampling for Bayesian LOO cross-validation

arXiv:2402.08151v4 Announce Type: replace-cross Abstract: Importance sampling (IS) is an efficient stand-in for model refitting in performing (LOO) cross-validation (CV) on a Bayesian model. IS inverts the Bayesian update for a single observation by reweighting posterior samples. The so-called importance weights have high variance -- we resolve this issue through adaptation by transformation. We observe that removing a single observation perturbs the posterior by $\mathcal{O}(1/n)$, motivating bijective transformations of the form $T(\theta)=\theta + h Q(\theta)$ for $0