State aggregation is a popular model reduction method rooted in optimal control. It reduces the complexity of engineering systems by mapping the system's states into a small number of meta-states. The choice of aggregation map often depends on the data analysts' knowledge and is largely ad hoc. In this paper, we propose a tractable algorithm that estimates the probabilistic aggregation map from the system's trajectory. We adopt a soft-aggregation model, where each meta-state has a signature raw state, called an anchor state.

This paper studies the problem of learning soft state aggregation of a Markov model, where there are r hidden meta states, each corresponds to a distribution over the observed state of the Markov model. Under the anchor state assumption, the authors propose an algorithm that provably learns the state aggregation model from the Markov chain's trajectory. They evaluated their algorithm on a Manhattan taxi-trip dataset which yields interesting discoveries. There has been lots of work on estimating the low rank transition matrix itself and on matrix factorization in the topic modelling setting, and this work seems to be connecting the two problems. The paper is presented well and easy to follow. I have the following questions regarding the novelty and impact of this paper.

State aggregation is a popular model reduction method rooted in optimal control. It reduces the complexity of engineering systems by mapping the system's states into a small number of meta-states. The choice of aggregation map often depends on the data analysts' knowledge and is largely ad hoc. In this paper, we propose a tractable algorithm that estimates the probabilistic aggregation map from the system's trajectory. We adopt a soft-aggregation model, where each meta-state has a signature raw state, called an anchor state.