We address the problem of estimating heterogeneous treatment effects in panel data, adopting the popular Difference-in-Differences (DiD) framework under the conditional parallel trends assumption. We propose a novel doubly robust meta-learner for the Conditional Average Treatment Effect on the Treated (CATT), reducing the estimation to a convex risk minimization problem involving a set of auxiliary models. Our framework allows for the flexible estimation of the CATT, when conditioning on any subset of variables of interest using generic machine learning. Leveraging Neyman orthogonality, our proposed approach is robust to estimation errors in the auxiliary models. As a generalization to our main result, we develop a meta-learning approach for the estimation of general conditional functionals under covariate shift. We also provide an extension to the instrumented DiD setting with non-compliance. Empirical results demonstrate the superiority of our approach over existing baselines.

We thank the reviewers for their careful reading of the manuscript and insightful comments. R1: We agree with the remark, there are similarities between the two stick breaking constructions. However, the generative process of section 2.1 and Pitman (2003) is more general, it is valid for any member of the class of Poisson Kingman processes (PKP). Most members of this class do not have a stick breaking construction in terms of independent random variables, see lines 135-136 and Pitman (1996) for further details. However, for the Pitman Yor process, the stick breaking construction does reduce to the one in Ishwaran and James (2001) after integrating out the random variable T and a change of variables given in line 128.

This paper proposes a new adaptive learning rate scheme for optimizing nonlinear objective functions that arise during the training of deep neural networks. The main argument is based on recent results that indicate that the difficulty of the optimization stems from the presence of saddle points rather than local minima in the optimization path. The saddle points slow down training since the objective function tends to be flat in many directions and ill-conditioned in the neighbourhood of the saddle points. The authors propose a new method for reducing the ill-conditioning (the problem of pathological curvature) by "preconditioning" the objective function through a linear change of variables, which reduces to left-multiplying the gradient descent update step with a learned preconditioning matrix D. They focus specifically on the case where D is diagonal, and they show how a diagonal D reduces to methods for learning parameter-specific learning rates, such as the well-known Jacobi preconditioner or RMSProp. This is a nice framework within which to consider different schemes for adaptive learning rates.

Are these based on a parametric estimate of the distribution, where the parameter samples are aggregated with an average? My overall takeaway from the toy examples (which exhibit skewness and/or multiple modes) is that, with averaging techniques such as mean, the resulting aggregated posterior is a poor representation of the true posterior. However, I have questions about whether such comparisons are fair, since (at least in the case of a known bimodal distribution) averaging techniques are clearly a poor choice. Therefore it feels that the comparison is a bit unfair.

It introduces an algebraic approach based on tensor factorization. For k spikes, suggests taking about k log k random locations in Fourier space, plus d deterministic locations, and then sampling on a grid of size (k log k d) 3 corresponding to all ways of summing three of these locations. Because of the algebraic properties of Fourier measurements, the resulting 3-tensor is of rank k (up to noise). The paper proves that with high probability in the sample locations, the matrix of factors is well-conditioned, and hence the factors can be stably recovered using linear algebraic manipulations. These results are stable under small deterministic noise.

Additional Feedback: edit I have read the rebuttal, and I would have liked the authors to point out precisely *what* technical points change and are difficult to handle. I think it would be great to actually highlight them in a revision of the paper. On a side note, I still believe that it is possible to get rid of the consensus step on y_t, and closeness between y_t and \bar{y}_t should be enforceable by the consensus step on x_t. This should be better in practice, since the consensus steps that are currently performed on y_t would also benefit x_t. A comparison with higher values of K would also have been welcome.

The paper gives an accelerated gradient method for decentralized optimization on composite objectives. It achieves this by mimicking centralized accelerated proximal gradient descent. Slight concerns remained about the level of novelty over the Mudag algorithm, which should be expanded in the discussion more precisely, as well as the (theory) requirement of K 1 communications after every step and the not yet fully explained dependence of K on the graph parameter. We expect the authors to incorporate the feedback and improvement suggestions from the 4 reviews in the camera ready version.

Weaknesses: Any kind of predictive model, and especially deep neural networks, will tend to overfit to the training set, generally causing predictions on a separate test set to be too extreme (shrinkage, or calibration slope of less than 1). The authors' X-cal procedure ensures good calibration on the training set. But that could result in disappointing calibration when applied to the test set. It seems to me that one would want a procedure to maximize calibration on a validation set, not the training set. That would then lead to good calibration on the separate test set.

For survival analysis, where calibrated models obviously are important, this paper introduces a differentiable plug-and-play regularizer which allows optimizing calibration, and choosing a trade-off between prediction accuracy and calibration. This was considered important and the first of its kind. The paper was intensively discussed among the reviewers. In particular, the reviewers argued whether the paper has shown convincingly enough that the method is necessary, because earlier results indicate other methods may produce calibrated results without the added regularizer (Haider et al. 2018). However, the results the authors point at in their response indicate a positive result, which the authors clarified in their anonymous email. The authors are strongly requested to include the additional results in their paper, as this was the bottleneck issue in recommending acceptance, and to take into account the other important points the reviewers raised.

Determinantal point processes (DPPs) have been receiving a significant amount of recent attention in the machine learning literature, due to their ability to model repulsion within realizations of a set of points. This repulsion is specified via a positive definite kernel function. One challenge, however, is learning the appropriate parameters of this kernel, given example point realizations. This estimation is difficult due to a difficult-to-compute normalization constant that, in effect, sums over all possible cardinalities and point configurations. A recent proposal [7] has provided a way to do this by observing that the spectrum can be estimated and used to provide incremental upper and lower bounds, resulting in a provably-correct scheme for "retrospective" Markov chain Monte Carlo (MCMC) of the kernel parameters.