Max Welling

Max Welling coauthored Auto-Encoding Variational Bayes by Diederik P. Kingma and Max Welling with Durk Kingma. Their work combines a learned approximate posterior with a differentiable transformation of parameter-independent noise, permitting variational inference to use a reparameterization gradient. The original preprint was submitted in December 2013; its historical byline uses Diederik P. Kingma.^[ref]

An original scalar calculation illustrates the computational mechanism. Let $Z=\mu +\sigma ϵ$, where $ϵ$ has a standard normal distribution and $\sigma >0$. For the chosen objective $J=\mathbb{E}[Z^2]$,Holding one noise draw fixed while differentiating its squared transformed value instead gives the stochastic estimates $2Z$ and $2Zϵ$. At chosen $\mu =1$, $\sigma =2$ and $ϵ=1$, these are both $6$, while the exact expectation gradients are $2$ and $4$. Averaging over the noise, rather than treating one draw as the expectation, recovers the exact gradients in this example.

This small calculation isolates the differentiable sampling step. A variational autoencoder also specifies a probabilistic model and an evidence lower bound; a differentiable random transformation alone does not supply those components. The contribution is joint work, not a claim that one coauthor alone originated every part of the method.