= Chris Cremer
{c}
<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>.<Inference Suboptimality in Variational Autoencoders by Chris Cremer and others>[Title-page byline; §§3.1–3.2 and Figure2]{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> remains
$$
\frac12\left(\log4+\frac14-1\right)\approx0.3181
$$
nats. 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.
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