Weaknesses: The problem in the paper is that it fails in showing the actual scope of the new results, especially in the global context of BNs learning. In fact their methods apparently can only applied to the continuous case: no mention is ever made if the same method can work with categorical variables. This is reflected to the selected set of "state-of-the-art" methods against which they compare their methods, that is a narrow subset of the whole literature on BNs learning. Saying something like "As mentioned, this paper is most closely related to the fully continuous framework of ... " is definitely not enough: a more precise and thorough description of the limitations of this work, and its position in the whole BNs learning literature, is needed. The title and the abstract should modified as well with same reasoning.

After discussions, there has been consensus that the paper's ideas deserve publication, even though they are somewhat incremental and without guarantees, as they build on NOTEARS. It has been appreciated the discussion on the issues with NOTEARS and an attempt to improve on them.

Summary: This paper introduces Poisson auxiliary variables to facilitate minibatch sampling. The key insight is with the appropriate Poisson parameterization, the joint distribution (Eq. The authors apply this insight to discrete-state Gibbs sampling (Algorithm 2), Metropolis Hastings (Supplement), and continuous-state Gibbs sampling (Alg 3. and 5). The authors also develop spectral gap lower bounds for all proposed Gibbs sampling methods, which provides a rough guideline for choosing a tuning parameter \lambda and comparing the (asymptotic) per iteration runtime of the methods (Table 1). Finally the authors evaluate the Gibbs methods on synthetic data, showing that their proposed method performs similarly to Gibbs while outperforming alternatives.

Congratulations on an elegant idea that, particularly with the addition of the experiments described in the rebuttal, could be of practical interest while also coming equipped with useful error bounds.

Summary and Contributions: The paper presents a new hierarchical Bayesian model -- convolutional Poisson-Gamma Dynamical Systems (conv-PGDS) -- for generating the observed words in a document corpus. Globally, the model assumes there are K "topic filters", D_1, ... D_K, which are distributions over 3-grams from a finite size vocabulary (size V). Each "topic" (indexed by k) has an appearance probability weight v_k 0 for appearing in a document, and we define transition probability vectors \pi_k Given this global structure, the model generates each document iid. To generate a document j, we use a Gamma dynamical system (with transitions \pi) to obtain a sequence of un-normalized membership "weight embeddings", w_j1 ... w_jT, one for each sentence (indexed by t). Each weight embedding vector w_jt indicates the relative weight of topic k across all words in the sentence t.

This is a novel combination of existing techniques that appears well-formulated with intriguing experimental results. In particular, this work leverages the strengths stochastic gradient MCMC methods with stochastic approximation to form an adaptive empirical Bayesian approach to learning the parameters and hyperparameters of a Bayesian neural network (BNN). My best understanding is that by optimizing the hyperparameters (rather than sampling them), this new method improves upon existing approaches, speeding up inference without sacrificing quality (especially in the model compression domain). Other areas of BNN literature could be cited, but I think the authors were prudent not to distract the reader from the particular area of focus. This work demonstrates considerable theoretical analysis and is supported by intriguing experimental evidence.

All reviewers acknowledged that the authors addressed their concerns well in the feedback, and agreed to accept the paper.

You rely on two case studies only so more a proof of concept.

As pointed out by the reviewers, these are the strengths and weaknesses of the paper: STRENGTHS The paper addresses the problem of converting a continuous-time Markov process model (MPM) to a structural causal model (SCM). The main advantage of such conversion is that it enables counterfactual inference in non-linear dynamic systems. This is demonstrated through two molecular biology case studies. FOR IMPROVEMENT The authors need to improve the presentation significantly, in order to make the paper accessible and readable. Another important point that should be addressed is the soundness and completeness of converting MPM to SCM.

Summary and Contributions: This paper considers a dynamic resource pricing problem. Agents arrive over time requesting resources, and the resources themselves become available and unavailable over time. The system sets (dynamic) prices on resources at each moment in time, and agents then choose the resources that maximize their utility given the prices. The agent requests are adversarial, and the goal is to select a pricing policy minimizes regret. The main contribution is a policy with vanishing regret for a very general formulation of such allocation problems.