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.

The reviewers evaluated the paper and there was broad agreement that this is quality work. However, there was still some concerns about readability so we would urge you to revise the submission for the camera-ready.

The paper addresses the issue of exploiting correlation structures in Markov Decision Processes with discrete state spaces. The authors identify a gap that currently makes working with discrete state spaces problematic - that there is no principled method for modelling the state correlations that is flexible enough to accommodate all the ways in which these correlations could be exploited. The paper presents a hierarchical Bayesian model and proposes a variational inference method to find solutions. The model and procedure presented in the paper are an original application of variational inference, and represent a more general method for dealing with correlation structures than anything I have encountered before. The authors have done a great job of demonstrating this by employing three vastly different problem domains. It is unusual to see Imitation Learning, System Identification and Reinforcement Learning all being tested under a new model in one paper.

This paper has a lot of content: Interesting cognitive science question of modelling human decision-making, data fusion of texts and eye movements, modelled with a new dynamic Bayesian nonparametric model, and introduces a new sampler for the model. This paper received a special amount of attention, 5 reviews which were needed because the paper makes several different kinds of contributions. Hence it is not a stereotypical good conference paper having one neat idea and presenting convincing theoretical or empirical support for it. Reviewers discussed the paper intensively, concluding that the paper is likely to be interesting at NeurIPS, and since there is not easy fix to make it more suitable to the format such as dividing it into two papers, it is good enough to be accepted though not among the best papers. Clarity can easily be improved by the authors, and additional details added in both the paper and the supplement.