Exponential Family PSR (EFPSR) models capture stochastic dynamical systems by representing state as the parameters of an exponential family distribution over a short-term window of future observations. They are appealing from a learning perspective because they are fully observed (meaning expressions for maximum likelihood do not involve hidden quantities), but are still expressive enough to both capture existing models (such as POMDPs and linear dynamical systems) and predict new models. While learning algorithms based on maximizing exact likelihood exist, they are not computationally feasible. We present a new, computationally efficient, learning algorithm based on an approximate likelihood function. The algorithm can be interpreted as attempting to induce stationary distributions of observations, features and states which match their empirically observed counterparts. The approximate likelihood, and the idea of matching stationary distributions, may have application in other models.