Reviews: The Multiple Quantile Graphical Model

In this paper titled "The Multiple Quantile Graphical Model", the authors introduced the MQGM, which offers a much broader class of conditional distribution estimates by introducing a set of quantile levels . One key contribution of this paper is that the proposed MQGM asymptotically identifies the exact conditional independencies under some conditions, as the size of the graph grows. There is some empirical results of the proposed algorithm and other alternatives. The strength of the paper: an interesting and important problem the idea is simple and sound theoretical proof My concern is mainly for significance of the key idea. The proposed method is very natural, and at a high level, introducing a set of quantile levels and providing more expressive class of estimates, which is not new. The main novelty here might be using multiple quantiles for non-parametric, continuous data.