The paper proposes BatchBALD, a batch acquisition function for sample selection in active learning. A greedy optimization algorithm is presented for efficient sample selection and BatchBALD score maximization. The reviewers and AC agree that this is an interesting work and that the approach is clearly presented and convincing. In addition the author response satisfactorily addresses the points raised in the reviews.

One contribution is a new approach for training neural networks with binary activations. The second contribution is PAC-Bayesian generalization bounds for binary activated neural networks that, when used as the training objective, come very close to test accuracy (i.e. The gap between the training and test performance is also much smaller. I think this is very promising for training more robust networks. The method actually recovers variational Bayesian learning when the coefficient C is fixed, but in contrast to it, this coefficient is learned in a principled way.

There are various models proposed on how knowledge is generated in the human brain including the semantic networks model. Although this model has been widely studied and even computational models are presented, but, due to various limits and inefficiencies in the generation of different types of knowledge, its application is limited to semantic knowledge because of has been formed according to semantic memory and declarative knowledge and has many limits in explaining various procedural and conditional knowledge. Given the importance of providing an appropriate model for knowledge generation, especially in the areas of improving human cognitive functions or building intelligent machines, improving existing models in knowledge generation or providing more comprehensive models is of great importance. In the current study, based on the free energy principle of the brain, is the researchers proposed a model for generating three types of declarative, procedural, and conditional knowledge. While explaining different types of knowledge, this model is capable to compute and generate concepts from stimuli based on probabilistic mathematics and the action-perception process (active inference). The proposed model is unsupervised learning that can update itself using a combination of different stimuli as a generative model can generate new concepts of unsupervised received stimuli. In this model, the active inference process is used in the generation of procedural and conditional knowledge and the perception process is used to generate declarative knowledge.

Post-rebuttal: The authors have promised to incorporate an exposition of the sampler in the revised paper, I believe that will make the paper a more self-contained read. I maintain my rating of strong accept (8). I think this paper makes very nice contributions to the fundamental question of estimating the MLE distribution given a bunch of observations. I think the key contributions can be broken up into two key parts: - A bunch of simple but elegant structural results for the MLE distribution in terms of'tent distributions' -- distributions such that its log-density is piecewise linear, and is supported over subdivisions of the convex hull of the datapoints. This allows them to write a convex program for optimizing over tent distributions.

The submission provides a polynomial-time approximation algorithm for finding the maximum-likelihood log-concave density for a given set of data points in R d, for arbitrary d. The work is theoretical in nature, with proofs and no experiments. The problem is very interesting, since log-concave distributions include may of the commonly used parametric families (such as Gaussian), and the log-concave MLE has also other interesting properties. Previously the sample-complexity of learning a log-concave distribution has been studied, but a polynomial-time algorithm has been lacking. The present work provides such an algorithm.

Since everything is parametric, I'd expect explicit rates of convergence involvind all probalem complexity parameters (n, m, p, etc.) To make the rest of my points clear, let me recall the following notations are used in the paper: - n: the dimensionality of the covariate (i.e feature vector) X. Thus X is random vector in R n. BTW, in the context of ML or stats, I'd use another notation here, as n conventionally stands for "sample size".

This paper proposes a method for distributionally robust optimization under KL ambiguity sets for exponential families. Although KL ambiguity sets have their drawbacks, in particular not covering any changes in the inputs x, the present work produces a standard conic problem for a wide problem class via a novel analysis, provides good theoretical analysis, and yields good numerical results for a variety of small-scale classification problems. With the various clarifications that came up in the reviews, this paper makes a solid contribution to the DRO literature and will be quite welcome to the NeurIPS audience.

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.

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.