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From my understanding, the paper makes a good technical contribution, unifying a large body of work on isotonic regression (IR). The basic idea seems intuitive, and is to employ techniques from the fast solvers of linear systems. Thus, from the perspective of novelty and technical content, I cannot raise any issues (based on my limited understanding -- regrettably, I do not have the background to check the proofs). But my concern with the paper is simply that it may be better suited to a algorithms/theoretical CS conference or journal, such as those where the work it improves upon ([16] -- [20]), and the work it employs in developing the algorithm ([21] -- [29]) were published. It is unclear to me whether the results in the paper would be of sufficient interest to the broader NIPS community. In particular: - while IR has seen some interesting applications to learning problems of late, it is not (in my estimation) a core ML tool for which a faster algorithm is by itself of wide interest.