  The learning and evaluation of energy-based latent variable models (EBLVMs)
without any structural assumptions are highly challenging, because the true
posteriors and the partition functions in such models are generally
intractable. This paper presents variational estimates of the score function
and its gradient with respect to the model parameters in a general EBLVM,
referred to as VaES and VaGES respectively. The variational posterior is
trained to minimize a certain divergence to the true model posterior and the
bias in both estimates can be bounded by the divergence theoretically. With a
minimal model assumption, VaES and VaGES can be applied to the kernelized Stein
discrepancy (KSD) and score matching (SM)-based methods to learn EBLVMs.
Besides, VaES can also be used to estimate the exact Fisher divergence between
the data and general EBLVMs.
