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.

However, the empirical performance of the proposed approach shows huge advantage over NCSN. Can the author elaborate what makes this difference? To my knowledge, the difference are The number of noise-levels (denoted as L): For the diffusion model, L 1000. The scheduling sequence of variance (denoted as beta_t, which is the \sigma 2 in NCSN): For the diffusion model, beta_1 1e-4, beta_T 0.02, and linear schedule is employed. For NCSN, they consider the geometric sequence, and beta_T is much larger for NCSNv2.

The paper gives insights on DSM (Denoising Score Matching) and MCMC method and links it to Probabilistic Diffusion models. This is novel and reviewer agrees that the paper has a good contribution. Concerns: • Algorithmically it is the same algorithm of NCSN with 1) different hyper-parameters motivated from diffusion models ( like scaling of inputs between stages) 2) different architectural choices • The FID is very low, maybe some memorization? Please include in the final version of the paper all the details in answers in rebuttal to R2 on the main comparison with NCSN, architecture choices etc, training time, sampling time, the need for cross-validation etc and how long the full training and cross validation takes. While probabilistic diffusion models are elegant their compute time is intensive please discuss this in the paper, and how you think this can be addressed.

Overall, the paper made significant contribution to both the reinforcement learning community and optimization community. The proposed algorithm is a variant of non-convex SAGA algorithm introduced by [1]. The novelty comes from their proof for the non-convex but strongly concave case. There are several issues which should be addressed: 1, Recasting the policy evaluation as a primal-dual optimization via the Fenchel duality technique is not new. In fact, [2,3,4] have already exploit this reformulation. First, these related work should be referred appropriately.

The main contribution of this paper is in solving the finite-sum minimax problem arising from off-line policy evaluation with nonlinear function approximation. The minimax problem is non-convex in the primal variable and strong convexity in the dual subproblem, and a single time-scale algorithm is proposed to find an approximate stationary point. Although it does not address the full stochastic TD learning problem, the progress in the finite-sum off-line version is quite meaningful.

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.

Originality: The paper builds on ideas developed by Lacoste-Julien et al. (2011) that were introduced to bridge Bayesian decision theory with approximate inference in a meaningful and useful way. The paper takes these ideas and makes them applicable in continuously-valued settings so long as the losses are bounded. For inference, it uses a variation of'black box' type variational inference schemes. Quality: The paper makes an interesting contribution. However, it is undesirable that the losses must be bounded.

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.

Complex Query Answering (CQA) over incomplete Knowledge Graphs (KGs) is a challenging task. Recently, a line of message-passing-based research has been proposed to solve CQA. However, they perform unsatisfactorily on negative queries and fail to address the noisy messages between variable nodes in the query graph. Moreover, they offer little interpretability and require complex query data and resource-intensive training. In this paper, we propose a Neural-Symbolic Message Passing (NSMP) framework based on pre-trained neural link predictors. By introducing symbolic reasoning and fuzzy logic, NSMP can generalize to arbitrary existential first order logic queries without requiring training while providing interpretable answers. Furthermore, we introduce a dynamic pruning strategy to filter out noisy messages between variable nodes. Experimental results show that NSMP achieves a strong performance. Additionally, through complexity analysis and empirical verification, we demonstrate the superiority of NSMP in inference time over the current state-of-the-art neural-symbolic method. Compared to this approach, NSMP demonstrates faster inference times across all query types on benchmark datasets, with speedup ranging from 2$\times$ to over 150$\times$.