The Laplace approximation accuracy in high dimensions: a refined analysis and new skew adjustment

Understand

In Bayesian inference, making deductions about a parameter of interest requires one to sample from or compute an integral against a posterior distribution.

• A popular method to make these computations cheaper in high-dimensional settings is to replace the posterior with its Laplace approximation (LA), a Gaussian distribution.
• In this work, we derive a leading order decomposition of the LA error, a powerful technique to analyze the accuracy of the approximation more precisely than was possible before.
• It allows us to derive the first ever skew correction to the LA which provably improves its accuracy by an order of magnitude in the high-dimensional regime.