The main idea builds upon the inducing-point formalism underpinning most sparse methods for GP inference. As the computational cost of traditional sparse methods in GPs based on inducing points is O(NM 2), where N is the number of observations and M is the number of inducing points, the paper addresses the problem of large-scale inference by making conditional independence assumptions across inducing points. More specifically, the method proposed in the paper can be seen as a modified version of the partially independent conditional (PIC) approach, where not only the latent functions are grouped in blocks but also the inducing points are clustered in blocks (corresponding to those latent functions) and statistical dependences across inducing point blocks are modeled with a tree. These additional independence assumptions make the resulting inference algorithm much more scalable as it only scales (potentially) linearly with the number of observations and the number of inducing points. The method is evaluated on 1D and 2D problems showing that it outperforms standard sparse GP approximations.

Submitted by Assigned_Reviewer_1 Q1 The paper proposes a modified version of the epsilon greedy algorithm for finding approximate solution to the generalized problem of submodular cover on the integer lattice. It is shown that the proposed algorithm provides a bicriteria approximation guarantee while having a running time which is polynomial in the input size. The paper is among a class of resent papers that have been working on accelerating and hence scaling up the optimization methods to be practical for large modern data sets (as is commonly seen in machine learning tasks). Q2 Overall, I think the paper is well-written and through and does a good job of providing theoretical guarantees for the proposed algorithms for submodular maximization over an integer lattice. The proposed problem has real world applications and the quality of the solution is shown through experiments on real and artificial datasets. Submitted by Assigned_Reviewer_2 Q1 PAPER SUMMARY The paper proposes a generalization of submodular cover to integer lattices.

Too many technical details for simulations are missing-e.g., sure rewards, cost of sampling, discount factor. As noted on line 256, coherence is observable to the experimenter, but not to the subject. The virtues of normativity for modeling human behaviour are not adequately defended here. Why would normativity be good in and of itself? Does the model make any clear, testable predictions?

Submitted by Assigned_Reviewer_1 Q1 This paper extends Poisson linear dynamical systems (PLDS) to account for the non-stationarity in neural spike trains. Their method (NPLDS) uses a hierarchical framework to find the latent variables for each trial, and also scale those latent variables multiplicatively for each trial. The latent variables are found with a linear dynamical system, and the inter-trial modulators are enforced to be smooth across trials with a Gaussian process. To fit the model, the authors devised the Bayesian Laplacian propagation and used an iterative procedure, which may be of interest to those outside the neuroscience field. The results are shown to be more predictive than the previous PLDS method, which suggests the added complexity helps performance.

The paper presents a new algorithm for estimating multi-step transition probability (MSTP) for first order time homogeneous Markov chains with finite state space. In the introduction the authors give a clear overview of their results and discusses existing approaches for MSTP estimation. This is followed by a description of their Bidirectional-MSTP algorithm and a theoretical analysis of the algorithm. Finally the authors describe a list of applications of the algorithm and show that their algorithm empirically gives a speed up of at least two orders of magnitude for estimating heat kernels on four standard datasets. The paper is in general well writing.

Abstract: the paper introduces LearnSDD an algorithm that learns log-linear models for discrete random variables but adds a penalty term for models that are expensive at query time. Compared to earlier work in this direction the paper studies a new way of describing models (SDDs instead of ACs) and is interested in "complex queries", e.g. The computational complexity of complex queries are not directly addressed in the algorithm, but as it turns out the choice of SDD as model space also has good run-time performance for certain complex queries (Theorem 1). Quality: there are no obvious errors, but some definitions in the proof are missing. Some key elements in the algorithm are not motivated/discussed (see comments below) Clarity: The presentation is good enough, but can be improved.

In this paper, the authors extend the "resource allocation with semi-bandit feedback", proposed by Lattimore et al. [2014], to the multi-resource case. The paper has provided two regret bounds, one for the worst case (Theorem 2) and the other for the "resource-laden" case (Theorem 7). The authors also provide a new result on the "weighted least squares estimation", which is independently interesting. The paper is well-written and very interesting, the analysis in this paper is also rigorous. The extension to the multi-resource case is non-trivial, and the new result on the "weighted least squares estimation" is very interesting and might be reused by researchers in the field of bandit/RL in the future. Thus, I think this paper meets the acceptance threshold.

We thank the reviewers for their helpful comments and questions. We will implement all their valuable suggestions for improving the presentation and the readability of the text and the figures. For clarity, the practical contributions of this work can be summarized as follows. We present a general scheme for approximate inference in pairwise binary graphical models. The scheme requires constructing an "attractive" 2-cover of the base graph and performing belief propagation on this cover.

This paper proposes a model of spatio-temporal dynamics that models a global latent process that governs the interactions between high level clusters of points together with a local observed process in which interactions are decoupled from points outside of one's cluster. Both levels can be thought of as vector autoregressive models. The authors apply their method to modeling data from a numerical simulation of a geologic model of fluid flow under the earth's subsurface. In general, this was a technically strong paper and shows off some state of the art optimization techniques. On the other hand it was also a difficult paper to get through as it was notation heavy and quite dense.