Chris Cremer

Chris Cremer coauthored the 2018 inference-suboptimality study with Xuechen Li and David Duvenaud. It compares shared inference with separately optimized distributions and considers richer approximations built using normalizing flows.^[ref]

For an original illustration of family enrichment, suppose the target posterior distribution is $N(0,4)$ while the family is $\{N(m,1):m\in \mathbb{R}\}$. Its optimum is $m=0$, but the Kullback-Leibler divergence between normal distributions remainsnats. A shared inference rule cannot remove that deficit just by choosing a better mean. Allowing the invertible scale transformation $z=2u$, with $u$ having the standard normal distribution, includes the exact target and makes the variational approximation gap zero in this example.

The example isolates distribution-family expressiveness. It does not imply that adding a normalizing flow always finds the optimum, or that every improvement in a trained variational autoencoder comes from this source alone. The paper's conclusions and method are collaborative; no division of individual authors' roles is inferred from author order.