Xuechen Li

Xuechen Li coauthored Inference Suboptimality in Variational Autoencoders by Chris Cremer and others with Chris Cremer and David Duvenaud. Their numerical method refits variational parameters per observation and uses the Monte Carlo method with 100 samples to estimate the evidence lower bound during that optimization.^[ref]

An original sampling calculation explains why sample count matters. Suppose independent contributions to a bound estimate have standard deviation two nats. A sample mean from $N$ such contributions has standard error $2/\sqrt{N}$ nats: $0.4$ at $N=25$ and $0.2$ at $N=100$. Quadrupling the sample count halves this sampling error under the independence assumption. These are assumed variances, not measured performance figures from the paper.

Reducing this error helps compare trial distributions, but neither a stable noisy bound nor a numerical stopping rule certifies the globally best member of the family. The mathematical variational approximation gap and amortization gap use that optimum; a measured local improvement can underestimate the latter. This distinction connects the joint experimental method to uncertainty in the numerical diagnostic.