This paper received two strongly favorable reviews and one negative review. The negative review is about writing, and I do share the concern. For example, I'm a lost at the motivation behind the Marker Generation process as described underneath Theorem 1 (first bullet). No intuition is given on why it cannot stop when m_i \in \Mcal_k. The paper does say "Note that it is possible that an event is caused by more than one events before, and we only consider the first causal parent as the true causal parent [11, 9, 8]." But that doesn't forbid a marker from recurring. In fact, Figure 2 does allow m_4 to occur twice. Please clarify it. Theorem 2 looks quite interesting which reduces the complexity by an order of magnitude. But one needs to be convinced that the Marker Generation process makes sense in the first place. Overall the technical merit is solid, allowing latent process from high-dimensional event sequences to be learned. However, I urge the authors take the comment of Reviewer #1 in to serious account when preparing the camera-ready version.