  Normalising flows (NFS) map two density functions via a differentiable
bijection whose Jacobian determinant can be computed efficiently. Recently, as
an alternative to hand-crafted bijections, Huang et al. (2018) proposed neural
autoregressive flow (NAF) which is a universal approximator for density
functions. Their flow is a neural network (NN) whose parameters are predicted
by another NN. The latter grows quadratically with the size of the former and
thus an efficient technique for parametrization is needed. We propose block
neural autoregressive flow (B-NAF), a much more compact universal approximator
of density functions, where we model a bijection directly using a single
feed-forward network. Invertibility is ensured by carefully designing each
affine transformation with block matrices that make the flow autoregressive and
(strictly) monotone. We compare B-NAF to NAF and other established flows on
density estimation and approximate inference for latent variable models. Our
proposed flow is competitive across datasets while using orders of magnitude
fewer parameters.
