  Variational Auto-encoders (VAEs) are deep generative latent variable models
consisting of two components: a generative model that captures a data
distribution p(x) by transforming a distribution p(z) over latent space, and an
inference model that infers likely latent codes for each data point (Kingma and
Welling, 2013). Recent work shows that traditional training methods tend to
yield solutions that violate modeling desiderata: (1) the learned generative
model captures the observed data distribution but does so while ignoring the
latent codes, resulting in codes that do not represent the data (e.g. van den
Oord et al. (2017); Kim et al. (2018)); (2) the aggregate of the learned latent
codes does not match the prior p(z). This mismatch means that the learned
generative model will be unable to generate realistic data with samples from
p(z)(e.g. Makhzani et al. (2015); Tomczak and Welling (2017)). In this paper,
we demonstrate that both issues stem from the fact that the global optima of
the VAE training objective often correspond to undesirable solutions. Our
analysis builds on two observations: (1) the generative model is unidentifiable
- there exist many generative models that explain the data equally well, each
with different (and potentially unwanted) properties and (2) bias in the VAE
objective - the VAE objective may prefer generative models that explain the
data poorly but have posteriors that are easy to approximate. We present a
novel inference method, LiBI, mitigating the problems identified in our
analysis. On synthetic datasets, we show that LiBI can learn generative models
that capture the data distribution and inference models that better satisfy
modeling assumptions when traditional methods struggle to do so.
