  We perform approximate inference in state-space models with nonlinear state
transitions. Without parameterizing a generative model, we apply Bayesian
update formulas using a local linearity approximation parameterized by neural
networks. This comes accompanied by a maximum likelihood objective that
requires no supervision via uncorrupt observations or ground truth latent
states. The optimization backpropagates through a recursion similar to the
classical Kalman filter and smoother. Additionally, using an approximate
conditional independence, we can perform smoothing without having to
parameterize a separate model. In scientific applications, domain knowledge can
give a linear approximation of the latent transition maps, which we can easily
incorporate into our model. Usage of such domain knowledge is reflected in
excellent results (despite our model's simplicity) on the chaotic Lorenz system
compared to fully supervised and variational inference methods. Finally, we
show competitive results on an audio denoising experiment.
