This paper develops a novel method to infer directional relationships between cortical areas of the brain based on simultaneously acquired EEG and fMRI data. Specifically, the fMRI activations are used to select ROIs related to the paradigm of interest. This information is used in a coupled state-space and forward propagation model to identify robust spatial sources and directional connectivity. The authors use a variational Bayesian framework to infer the latent posteriors and noise covariances. They demonstrate the power of joint EEG/fMRI analysis using two simulated experiments and a real-world dataset.

Summary and Contributions: This paper presents an approach to the problem of inferring a functional network across many neurons using noisy group testing. The authors formulate the connections across a population of neurons as a binary network that encodes the presence or absence of functional (not necessarily synaptic) connections between pairs of neurons, with a noisy Bernoulli observation model to capture neurons occasionally not being activated even when neurons they are functionally connected to are stimulated. Inference over the connections is initially formulated as a maximum likelihood problem, which can be rewritten as an integer optimization problem. The authors further extend this formulation by relaxing the variables to restricted continuous values and reformulating the problem as approximate Bayesian inference to infer the posterior probability of each connection. A dual decomposition algorithm is presented for solving the problem, which can be adapted to perform online inference in the setting where an experimenter might want to update the posterior probabilities as new tests are performed or adaptively select tests based on the current network estimate.

Weaknesses: The novelty of the paper is very limited. The ais authors concentrate on computational tricks, tries to improve the scalability of the algorithm. And they achieve some success. However, for NIPS paper I would expect not only to improve implementation of the algorithm but also some new concepts. I do not found any new ideas in that sense.

This paper presents a collection of useful tricks to speed up Bayesian computations for causal discovery algorithms. Despite some concerns regarding novelty, all reviewers agreed that this paper is well-written and could help spur interest and further developments in Bayesian algorithms for BNSL.

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.