Poisson autoregressive count models have evolved into a time series staple for correlated count data. This paper proposes an alternative to Poisson autoregressions: count echo state networks. Echo state networks can be statistically analyzed in frequentist manners via optimizing penalized likelihoods, or in Bayesian manners via MCMC sampling. This paper develops Poisson echo state techniques for count data and applies them to a massive count data set containing the number of graduate students from 1,758 United States universities during the years 1972-2021 inclusive. Negative binomial models are also implemented to better handle overdispersion in the counts. Performance of the proposed models are compared via their forecasting performance as judged by several methods. In the end, a hierarchical negative binomial based echo state network is judged as the superior model.

Existing score-based methods for directed acyclic graph (DAG) learning from observational data struggle to recover the causal graph accurately and sample-efficiently. To overcome this, in this study, we propose DrBO (DAG recovery via Bayesian Optimization)-a novel DAG learning framework leveraging Bayesian optimization (BO) to find high-scoring DAGs. We show that, by sophisticatedly choosing the promising DAGs to explore, we can find higher-scoring ones much more efficiently. To address the scalability issues of conventional BO in DAG learning, we replace Gaussian Processes commonly employed in BO with dropout neural networks, trained in a continual manner, which allows for (i) flexibly modeling the DAG scores without overfitting, (ii) incorporation of uncertainty into the estimated scores, and (iii) scaling with the number of evaluations. As a result, DrBO is computationally efficient and can find the accurate DAG in fewer trials and less time than existing state-of-the-art methods. This is demonstrated through an extensive set of empirical evaluations on many challenging settings with both synthetic and real data. Our implementation is available at https://github.com/baosws/DrBO.

This is an interesting paper, and well written. Overall I like the contributions. I have the following comments to consider. I am not sure "feedforward" is an appropriate prefix for the technique, as it seems to suggest that the approach is feedforward neural networks based. Though, it is completely upto the authors.

This paper proposes two algorithms for recovering ground truth labels in crowd sourcing tasks for binary classisification. The problem is formulated as an online Bayesian version of the Dawid & Skene model (with beta priors) which is quite natural. The algorithms are based on variational approximations of the posterior (i.e. they try to find the best approximation that is product distribution). From this approach two algorithms are derived. The other one is more accurate and but slower (still polynomial time).

Given the space constraint of the rebuttal, I will trust the authors to indeed incorporate the changes as promised, and given this I increased my score. However, at several places in this paper, it is too dense to follow. More detailed comments are as follows. First, this paper lacks a dedicated related work section. There is some brief discussion about how this work differs from existing literature, in the introduction, yet it is not enough.

This paper proposes a Bayesian formulation for SPN models. All reviewers felt this formulation had merit, and there was agreement with the authors on possible improvments.

Weaknesses: The paper emphasizes its focus on causal structure learning. In doing so it assumes "causal sufficiency", that is, it assumes that there are no latent confounders of the measured variables. Generally, there are many latent confounders of the measured variables in most domains. In the past 20 years, there has been substantial progress in developing graphical representations and algorithms for learning equivalence classes of causal networks from observational data. When causal sufficiency is assumed, the learning of DAG structure is generally called Bayesian network structure learning, not causal structural learning, as in the title of the paper. It would be helpful for the paper to more prominently highlight this assumption.

All of the reviewers agree that this paper is both theoretically and modeling-wise a solid contribution to NeurIPS. My only concerns are that some of the author rebuttal points have not made it into the paper -- all of them should be added I think, in particular the related work (extended), the causal sufficiency clarification, and the run times.

The marginalisation of variables within some steps of an MCMC algorithm is delicate. The main proposal here appears well justified, but it would have been nice to see the argument made a little more explicitly. The type of marginalisation described here seems to be more or less what would be described as a (partially) collapsed Gibbs sampler in the sense of [David A Van Dyk and Taeyoung Park. "Partially collapsed Gibbs samplers: Theory and methods". It was less clear to me exactly how the "blocking" strategy detailed in Section 4.1 would be justified from a formal perspective, and I do think that this needs clarifying. I.e. the collection of variables to be sampled is divided into three parts -- x', x and theta and the decomposition of the kernel seems to involve sampling: x from a kernel invariant to its distribution conditional on both x' and theta (starting from the previous x) x' from a kernel invariant with respect to its distribution conditional only upon x (starting from the previous x') \theta from its full conditional distribution and it's not completely transparent how one knows that this is invariant with respect to the correct joint distribution.

This paper makes a solid contribution to improving inference in certain state space models that a used extensively in practice, particularly when implementing such models in a probabilistic programming language.