Reviews: Nearly tight sample complexity bounds for learning mixtures of Gaussians via sample compression schemes

This paper is well written and issues a classical and well known studied problem from a new point of view. The compression based analysis which is indeed deep, although less popular, is gaining more attention on the last couple of years. This paper join this line of work by extending it, proving some interesting properties if sample-compression schemes (such as the them being close under mixture or product) and go on and demonstrates the power of the obtained results by proving state of the art sample complexity upper bound for mixture of Gaussians. I think that the NIPS community will indeed benefit from this paper. Remarks: - there exists a line of work regarding the generalization guarantees of compression based learners.