Summary and Contributions: The paper derives analytical expressions of optimal predictors in the presence of Missing Completely At Random (MCAR), Missing At Random (MAR) and self-masking missingness in the linear Gaussian case. Then, the paper proposes Neumann Network for learning the optimal predictor in the MAR case and show the insights and connection to the neural network with ReLU activations. There are two challenges of learning the optimal predicator from data containing missing values: 1) computing the inversion of covariance matrices in the MAR optimal predicator; 2) 2 d optimal predictors with different missingness patterns required to learn the optimal predictor, where d is the number of features/covariates. For the first one, the paper provides a theoretical analysis, which is approximated in a recursive manner with the convergence and upper bounder guarantee. For the second one, the Neumann Network shares the weights of optimal predictors with different missing patterns, which turns out empirically more data efficient and robust to self-masking missingness cases.

The paper attacks the classical problem of linear regression with missing values. It computes the Bayes predictor in several cases with missing values and then uses Neumann series to approximate the Bayes predictor. This approximation is then used to design Neural Networks with RelU functions. The propositions describing self-masking missingness, appears to be a novel concept, are interesting but can be considered slightly restrictive because of Linear Gaussian assumptions. However, both the results and the methods should be of interest to NeuriPS 2020 community.

The main contribution of this paper is in setting up a 3 player game for semi-supervised learning where the generator tries to maximize the margin of the examples it generates in competition with a classifier the traditional GAN approach of fooling a discriminator. This idea is novel to my knowledge. One small reservation I have with this method is that as the quality of the GAN and generated images increases the margin maximization for the classifier for generated examples becomes counter productive (as acknowledged by the authors) which requires careful early stopping. But this is standard practice with GANs and it should not be held against this paper. The paper is generally of high quality and significance but these could be improved by a broader treatment of related works.

The paper formulates semi-supervised learning as a 3 player game among a generator, a classifier, and a discriminator. The generator and discriminator compete to train realistic examples, as in usual GANs, and the key new idea is that the classifier tries to maximize the margin of real examples and minimize the margin of fake examples. The method both improves predictive performance and greatly reduces training time. The reviewers agree that it is a significant contribution.

Summary and Contributions: This paper introduces a method for generating *counterfactual* visual features for augmenting the training of vision-and-language navigation (VLN) models (which predict a sequence of actions to carry out a natural language instruction, conditioning on a sequence of visual inputs). Counterfactual training examples are produced by perturbing the visual features in an original training example with a linear combination of visual features from a similar training example. Weights (exogenous variables) in the linear combination are optimized to jointly minimize the edit to the original features and maximize the probability that a separate speaker (instruction generation) model assigns to the true instruction conditioned on the resulting counterfactual features, subject to the constraint that the counterfactual features change the interpretation model's predicted timestep at every action. Once these counterfactual features are produced, the model is trained to encourage it to assign equal probability to actions in the original example when conditioning on the original and the counterfactual features (in imitation learning), or to obtain equal reward (in reinforcement learning). The method improves performance on unseen environments for the R2R benchmark for VLN, and also shows improvements on embodied question answering.

The authors prove that the probabilities they obatin are equivalent to the probabilities yielded by the Random Walker algorithm. The authors state that this result has been shown in the original Random Walker work, yet is little known, and their proof is different and more self-contained, not relying on potential theory. Excitingly, their way of proof yields a novel interpretation of the Random Walker / Probabilistic Watershed probabilities in terms of the triangle equation on effective resistances between graph nodes. Last but not least the authors relate their theory to the Power Watershed, again yielding an exciting new insight, namely that for parameters beta 2 and alpha towards infinity, the latter computes marginals over all seed-separating *maximum* spanning forests (i.e.

Brings new insights to old algorithms accept.

Is there any comparison with the baselines in terms of the number of network parameters? What is the performance of baselines with the same number of parameters as GAM? This seems to be a fairer comparison.

This paper proposed a novel graph learning method for graph-based semi-supervised learning. Besides the model of the classifier (the classification model in the paper), another model of the graph is considered (the agreement model in the paper), and the contribution to the loss of each edge is determined by the model of the graph. Although there are still concerns about the novelty in the end, we all agree that the proposed method is simple, well-explained and can still achieve good performance. This may have impacts to practitioners using semi-supervised learning in their projects, and as a result, I recommend an acceptance. Please survey this direction and include your survey in the final version.

Summary and Contributions: This paper introduces a new class of algorithms for local graph clustering, based on Lp objectives (for p 2) rather than the standard L2 (used in reference works like Anderson-Chang-Lang), or L_infinity (which corresponds to minimum cut). The authors make a clear point that the p 2 regime corresponds to the primal objective which optimizes in the space of flows, whose dual problem corresponds to optimizing an Lq norm (1 q 2) in the space of cuts. For the purpose of this paper, they stick to the cut problem, since it is more naturally connected to the algorithm described here. Essentially, the presented algorithm is a generalization of ACL for Lq norms. It performs a sequence of steps, in each step, it picks a node with excess residual and performs "push" operation.