This paper offers a new approach to learning discrete models for human-robot interaction (HRI) from small data. In the motivating application, HRI is an integral part of a pediatric rehabilitation paradigm that involves a play-based, social environment aiming at improving mobility for infants with mobility impairments. Designing interfaces in this setting is challenging, because in order to harness, and eventually automate, the social interaction between children and robots, a behavioral model capturing the causality between robot actions and child reactions is needed. The paper adopts a Markov decision process (MDP) as such a model, and selects the transition probabilities through an empirical approximation procedure called smoothing. Smoothing has been successfully applied in natural language processing (NLP) and identification where, similarly to the current paradigm, learning from small data sets is crucial. The goal of this paper is two-fold: (i) to describe our application of HRI, and (ii) to provide evidence that supports the application of smoothing for small data sets.