Additional Feedback: As mentioned above, I think this method is very nice, but should be framed differently. In particular, the issue being addressed is not confounding _bias_; it is sample inefficiency when estimating the regression model f_{\theta_p}. This distinction is important in the causal inference literature, because a bias does not disappear with sample size. However, in this context, under the unconfoundedness assumption, if the model f_{\theta_p} is sufficiently flexible, it will converge to the same true counterfactual model in the large sample limit regardless of how the data are weighted (this is consistent with the experiments in the paper). In other words, the population risks E_{cf} and E_f w are minimized at the same function.

The authors propose a method for doing weighted sample adjustment for learning counterfactual regression models when treatments are high-dimensional. The reviewers, after some discussion, converged on the view that the paper is a nice contribution to the estimation theory for causal effects. One area where the paper could benefit is a discussion of the connections of the author's results to results on semi-parametric efficiency theory and influence functions (see e.g. It is likely there is a close relationship between the role weights play in improving efficiency and efficient influence functions for the problem (even under randomization).

The authors identify a strategy for compensating agents to disclose private and relevant data. The strategy draws on interesting ideas from the machine learning literature, including the use of the stochastic gradient descent algorithm to set the payment for the data. This allows effective compensation of agents while maintaining a limited budget. The authors also include mechanisms for preserving the privacy of agents, and identification of different "profit maximizing" strategies for agent to select given their confidence in their data. It appears that the substantive contribution is in identifying a mechanism that compensates agents for their data while maintaing a bounded budget.

This paper proposes a computationally efficient way of scaling kernel non-linear component analysis. Each of these methods works effectively in certain settings but the number of samples/features may be prohibitively large in some settings. This paper proposes a doubley-stochastic gradient algorithm for solving kernel eigenvalue problems encompassing kernel PCA, CCA, and SVD. It is called doubly-stochastic because sampling is performed in the data samples and the random features (for this paper, limited to stationary kernels whose Fourier transform is well-defined). The paper claims convergence rate of \tilde{O}(1/t) to the global optimum for the recovered eigensubspace (in terms of principal angle), but with a caveat being that the step sizes are chosen properly and the mini-batch size is sufficiently large.

Weaknesses: While the general idea of the paper is appealing and has been evaluated extensively, the presentation of the methodology is lacking in clarity at times. After reading section 3, some issues could have been addressed more clearly: • Regarding line 171/172: what do the authors mean by "regret reaches the plateau"? Consider the case of the 1D sine function and we have data points only at increments of pi. K-means would result in two clusters, i.e., the points with values 1 and -1, respectively. What would be the resulting domain for TuRBO then?

The paper introduces covariance-controlled adaptive Langevin thermostat (CCAdL), a Bayesian sampling method based on stochastic gradients (SG) that aims to account for correlated errors introduced by the SG approximation of the true gradient. The authors demonstrate that CCAdL is more accurate and robust than other SG based methods on various test problems. In general, the paper is well written but sometimes a bit hard to follow for someone who is not familiar with these type of sampling algorithms. The paper starts by reviewing various SG methods for efficient Bayesian posterior sampling (SGDL, mSGDL, SGHMC, SGHNT). It would be quite helpful if the authors could provide, for example, a table or figure that gives on overview over the different SG variants and highlights their commonalities and differences.

This paper addresses the problem of generating 3D object proposals given a stereo image pair from an autonomous driving vehicle. The paper proposes a set of features for a 3D cuboid over a point cloud and ground plane derived from the stereo image pair. The features include point cloud density, free space, object height prior, and object height relative to its surroundings. Note that the features are dependant on knowledge of the object class (other "objectness" proposal methods are agnostic to the object class). A structural SVM is trained to predict the "objectness" of the 3D cuboid proposal.

Dear authors, The reviewers discussed your document and carefully considered your rebuttal. All agree that the main contribution is the framework for dealing with missing values using bipartite graphs. This is an interesting idea, both for imputing missing values and for making predictions with missing values. They also appreciated that you added experimental comparisons to two reference methods (missMDA and MIWAE) and included the results in your response, as well as experiments on two additional high-dimensional data sets. Nevertheless, although they emphasized that GNNs are used here as a toolbox and not as the focus of the study, you need to be specific about important aspects of their application (such as discussions of architectural novelty and scalability), as noted by two reviewers.

In particular, what does mean "a basis with complete discriminative information", and what are the coefficients mentioned for the testing phase?

The paper starts by situating the problem and motivating their approach - essentially, enabling embeddings for weighted graphs by extending the original implicit embedding performed in Lovasz "Shannon capacity of a graph" paper, which operated on binary graphs. The paper then presents the connection between kernel machines and the Lovasz number in the unweighted case, and extends previous work for vertex-weighted, edge-weighted, and LS-labelled graphs. Section 3 provides practical details for computation, and section 4 motivates the use of their approach for the clustering problem - setting the number of clusters by using their \vartheta 1 bound, and initialising the clusters by starting by vertices with large alpha_i values. Finally, they show results on max-cut, clustering, overlapping clustering, and summarization tasks. The paper ties together very different work to propose a coherent approach to graph embedding. The contributions are clearly laid out, and the references to previous work is well established and used.