Reviews: Learning low-dimensional state embeddings and metastable clusters from time series data

This appears to be a detailed, carefully written, and theoretically/empirically supported piece of work. The results are based on RKHS theory and appear to extend the state-of-the-art in a number of ways, including learning KMEs while dealing with dependent samples (e.g. from a Markov chain), low dimensional/rank approximations with state-of-the-art error bounds, and a variational approach for clustering, as well as a robust set of experiments. On the whole, I am satisfied that this clearly meets the acceptance criteria for NeurIPS and I am recommending it for acceptance. I have a few comments below on aspects of the paper, where things were either unclear, or might benefit from a revisit. It is unclear how strong assumption 2 is.