This paper proposes a Bayesian model for adversarial learning problem. Empirical studies on Fashion-MINST and traffic sign recognition show that the proposed methods is slightly better than other adversarial learning baselines.  Below I list my concerns about the paper: For modeling, 1. This paper ignore a highly relevant work ‘Bayesian GAN’ [1]. The non-cooperative game between ‘data generator’ and ‘learner’ established in this paper is almost the same as the vanilla GAN. And the fully Bayesian treatment introduced is exactly the same as in [1]. 2. The author mentioned the posterior inference over learner’s parameter can be achieved by Gibbs sampling on the two defined conditional posterior. The analysis of the underlying joint posterior distribution is missing. It is hard for readers to understand what actually the distribution over learner is achieved when the algorithm converges. 3. It also remains unclear that whether the iteration introduced in Eqn. (3) and (4) is guaranteed to converge.  For inference, 1. In the consideration of the scalability, the author proposed to only update a mini-batch of training data points. However, no theoretical insight is provided to validate this stochastic approximation. Does this stochastic process on expectation match the iteration defined in Eqn. (3) and (4)?  For experiments, 1. In section 5, the author suggests a sample size of 5 and claims that better performance can be achieved with a larger sample size. I recommend including results with different sample size to support the augment.   Overall, I think this is an interesting paper exploring the functionals of Bayesian modeling in the context of adversarial learning. However, the novelty of proposed method is limited, and the relationship between the current work and [1] is totally ignored in the paper. I recommend weak rejection for this paper.  [1] Bayesian GAN; Yunus Saatchi, Andrew Gordon Wilsons ----------------------------- Update: I have read the author feedback and I appreciate the authors’ reply on my concerns.   I believe given the previous work ‘Bayesian GAN’, another way to frame the contribution would be adapting the techniques in Bayesian GAN for the problem of adversarial attacks. In terms of methodology, the only main difference is that Bayesian GAN generates samples conditioned on random noise while BAL generates samples conditioned on the input data (as mentioned in the first point of the author feedback). The other parts are very similar.  The application itself is important and interesting. I am happy to see the Bayesian principle help design a good adversarial defense framework that achieves good empirical results.  Based on the reasons above, I will slightly upgrade my score (from 5 to 6).  If this paper is accepted, I hope my following comments about *target posterior distribution*  can be addressed in the final version.  Surely L88-L89 gives a formula of the parameter posterior. However I urge authors to articulate what is the conditional distribution p(\tilde{D} |D). Since in the previous text, only p(\tilde{D} |\theta, D) is defined. It is very important to have a clear idea about what is the target of the learning algorithm. Missing this critical part may confuse the reader.  For the inference part, giving a verification of mini-batch sampling as the authors suggested in the rebuttal will also make this paper more self-contained.


Bayesian Pose Graph Optimization via Bingham Distributions and Tempered Geodesic MCMC
We introduce Tempered Geodesic Markov Chain Monte Carlo (TG-MCMC) algorithm for initializing pose graph optimization problems, arising in various scenarios such as SFM (structure from motion) or SLAM (simultaneous localization and mapping). TG-MCMC is first of its kind as it unites global non-convex optimization on the spherical manifold of quaternions with posterior sampling, in order to provide both reliable initial poses and uncertainty estimates that are informative about the quality of solutions. We devise theoretical convergence guarantees and extensively evaluate our method on synthetic and real benchmarks. Besides its elegance in formulation and theory, we show that our method is robust to missing data, noise and the estimated uncertainties capture intuitive properties of the data.

This paper presents a stochastic gradient Monte Carlo approach defined on a Cartesian product of SE(3), a domain commonly used to characterize problems in structure-from-motion (SFM) among other areas.  The algorithm is parameterized by an inverse temperature such that when the value goes to inifinity, the algorithm is implicitly operating on a delta function with it's peak at the maximum of the base distribution.  The proposed algorithm is formulated as a SDE and a splitting scheme is proposed to integrate it.  A theoretical analysis on the SDE and its discretization is explored, showing that 1) the resulting Markov process has the appropriate invariant distribution and 2) the sampler will draw samples close to the maximum of the posterior (in terms of expectation of the unnormalized log posterior).  Along with the algorithm, a model is defined using the Bingham distribution to characterize typical SFM posteriors which is then used to perform experiments with the algorithm.  The algorithm is validated on synthetic experiments along with some real SFM datasets.  The problem that is considered (sampling and optimization over pose graphs on SE(3)^n) is an important one.  The proposed algorithm seems suitable and has at least a small amount of novelty.  However, there are some problems with both the theoretical and experimental analysis which are detailed below.  The paper has potential, but the issues need to be addressed before it is suitable for publication.  - The theorem as stated in the paper has omitted a key condition which somewhat limits its applicability to the scenario indicated in the paper.  Specifically, according to Lemma S1, the theorem only applies for values of \beta \leq D for some finite constant D.  This is not discussed at all in the main paper and only shows up in the statement of the lemma in the supplementary.  Importantly, it undermines a major line of argument for the paper, namely that the method provides a mechanism for either MCMC sampling from the posterior *and* a way to find the maximum of the posterior by setting \beta = \infty.  As far as I've understood the results, the proof of the theorem is not valid as \beta approaches \infty.  - The paper makes claims which are unsubstantiated by the theoretical results.  In particular, lines 248-250 claims that the theorem shows that the algorithm will sample close to the global optimizer x^*.  This is not what is actually said by the theorem.  Rather the theorem states that expected value of U(x) = -\log(p(x)) will be close to U(x^*). Note that this is significant in the case where the posterior non-convex and may be multimodal which line 248 specifically mentions.  - A discussion of the tuning of several key hyperparameters is missing in the paper, limiting reproducibility.  In particular, how are N (number of integration steps) and h (step size) set experimentally?  Are they tuned per experiment or fixed?  How sensitive are the results to these (and other) hyperparameters. Similarly, how exactly is the synthetic data generated?  Is source code going to be released?  This will address some (though not all) of these concerns.  There are also several other less significant issues.  - Figure 2 (in particular 2(e)) is not well explained, 2e in particular is never even referenced and the caption doesn't explain it clearly. - Fig 2e implies and Lines 284-5 discuss combining error in rotation with error in translation.  How is this done?  === UPDATE: I have read and considered the authors feedback and would not argue against acceptance of this paper.  However, I remain concerned about the looseness of the arguments around the applicability of the theoretical results and, in particular, the disconnect between how they're presented in the paper vs how they're actually defined in the appendix.


Stein Variational Gradient Descent as Moment Matching
Stein variational gradient descent (SVGD) is a non-parametric inference algorithm that evolves a set of particles to fit a given distribution of interest. We analyze the non-asymptotic properties of SVGD, showing that there exists a set of functions, which we call the Stein matching set, whose expectations are exactly estimated by any set of particles that satisfies the fixed point equation of SVGD. This set is the image of Stein operator applied on the feature maps of the positive definite kernel used in SVGD. Our results provide a theoretical framework for analyzing properties of SVGD with different kernels, shedding insight into optimal kernel choice. In particular, we show that SVGD with linear kernels yields exact estimation of means and variances on Gaussian distributions, while random Fourier features enable probabilistic bounds for distributional approximation. Our results offer a refreshing view of the classical inference problem as fitting Stein's identity or solving the Stein equation, which may motivate more efficient algorithms.

In "Stein Variational Gradient Descent as Moment Matching," the authors first introduce the algorithm known as Stein Variational Gradient Descent (SVGD). While some work has been done trying to provide a theoretical analysis of this method, the consistency of SVGD is largely still open for finite sizes of n. (In fact, the analysis is still completely open when the domain is not compact either.)  The authors of this paper make headway on this problem. By studying the fixed point solution to SVGD, they show there are a set of functions for which the the fixed point solution perfectly estimates their mean under the target distribution (they call this the Stein set of functions). They argue that using a polynomial kernel when the target is a Gaussian will force any fixed point solution of SVGD to exactly estimate the mean and covariance of the target distribution, assuming the SVGD solution points are full rank.  The major contribution of this paper is that by studying the properties of finite dimensional kernels, they are able to employ random Fourier features to provide a theoretical analysis of the fixed points for these "randomized" kernels. By using this formulation of a randomized kernel Stein discrepancy, the authors provide a VC-like bound on the (randomized) kernel Stein discrepancy's value at a fixed point solution that converges at a O(m^{-1/2}log^{3/2}m) rate, where m indexes the number of random Fourier features. Their results do also require the domain to be compact, but the work does appeal to the finite sample regime and thus is a solid theoretical finding.  My biggest critique of this paper are the assumptions in 3.4. Because they have modified the kernel with a randomized, low rank approximation, their results do not immediately carry over to the non-randomized version. For example, for the Gaussian kernel and Gaussian target on a truncated or unbounded domain, can the assumptions of 3.4 be checked? I would be very interested in knowing what conditions on n (the number of SVGD samples), m, the target distribution P, and the kernel k are enough to assure the first assumption of 3.4 holds. While I would love to see this included in the paper, I think the rest of the paper is strong enough to merit publication at the conference.  ** Quality  L30-31, 110-111: Perhaps it is worth emphasizing here that these results typically only hold on compact domains as well?  Eqn 2, L103, Eqn 9, etc.: Isn't k the kernel for H_0 and thus how can the Stein operator be defined for a R-valued function?  Eqn 8: Where is P_{x_j} defined? I think it might be more clear to leave P_x for this.  L158-171: These lines seem a bit too generic to be included in this paper in my opinion. There are formulations which are solutions to Stein's equation, e.g., see Theorem 5 of Gorham et al "Measuring Sample Quality with Diffusions." Studying solutions to Stein's equation is an active field of research.  L224-225: I can't tell how strong this assumption is. Most importantly, are fixed point solutions for SVGD in the original kernel  "close" to the fixed point solutions to SVGD in the random Fourier kernel? That piece seems necessary to push the theory forward for a non-randomized kernel.  ** Clarity  The paper is for the most part clearly written. There is some sloppiness where the authors commonly apply the Stein operator to a R-valued function, but otherwise the ideas are well explained. I recommend the authors address this issue throughout the paper.  ** Originality This paper does identify some new ways to view the kernel Stein discrepancy and uses those to provide a finite sample analysis of a related, randomized problem.  The theory here does only apply to these "randomized" kernels (via the random Fourier formulation), while the kernels used in practice are not random. Hence there is a little left to be shown, in particular, that the fixed point solutions are not too different between the randomized kernel and the original (nonrandom) kernel. See the last paragraph of the summary section.  ** Signifance SVGD has become a popular (though expensive) black box method for doing posterior inference, despite it having no great theoretical guarantees. This paper provides the best analysis of this method to date in the finite sample regime and thus is a nice contribution.


Trajectory Convolution for Action Recognition
How to leverage the temporal dimension is one major question in video analysis. Recent works [47,36] suggest an efficient approach to video feature learning, i.e., factorizing 3D convolutions into separate components respectively for spatial and temporal convolutions. The temporal convolution, however, comes with an implicit assumption -the feature maps across time steps are well aligned so that the features at the same locations can be aggregated. This assumption can be overly strong in practical applications, especially in action recognition where the motion serves as a crucial cue. In this work, we propose a new CNN architecture TrajectoryNet, which incorporates trajectory convolution, a new operation for integrating features along the temporal dimension, to replace the existing temporal convolution. This operation explicitly takes into account the changes in contents caused by deformation or motion, allowing the visual features to be aggregated along the the motion paths, trajectories. On two large-scale action recognition datasets, Something-Something V1 and Kinetics, the proposed network architecture achieves notable improvement over strong baselines.

This work proposes a novel convolutional operation and corresponding network architecture for action recognition in videos. Starting from 3D convolutions, the authors introduce a trajectory convolution approach where the convolutional aggregation is performed in a dynamic manner through tracked points, rather than fixed locations. Experiments and ablation studies show the effect of the primary components of the new network, as well as decent overall performance on two large-scale action datasets.  Paper strengths: - The first strength of the paper is that it is well written. The main motivation of the paper is presented in a clear and intuitive manner. Where current 3D convolutional operators perform an aggregation within a fixed cube, this work posits that the temporal aggregation should be dynamic by following points over time. This way, it should be possible to aggregate features based on the primary motion of interest.  Furthermore, from a presentation point of view, the embedding of the proposed trajectory convolution in recent convolutional literature adds to the clarity and insight of the trajectory convolution itself. The embeddings is also unclear at several instance, as discussed later. Positive embedding discussions include: -- The difference and novelty with respect to the Trajectory-Pooled Deep-Convolutional Descriptor (TDD) is clear and fair. -- A link is made with deformable convolutions, which helps the authors with the implementation of the trajectory convolution. -- A link is also made with separable convolutions. This makes sense in isolation, although it is unclear how it all combines with deformable convolutions.  - The second strength of the paper is that care is taken to perform the necessary ablation studies. The trajectory convolution is evaluated, as well as the fusion with motion and the learning trajectory component. This paints a fair picture of the method and where it can best be employed. Such ablation studies are a necessity to gain insight into the method and to understand how it works.  Paper weaknesses: - The first weakness of the paper is that the paper is unclear in its method and missing details. -- While Section 3.1 is clear, the rest of Section 3 is unclear at several occasions. In Section 3.2, a link is made with deformable convolutions with the note that the trajectory convolution can be implemented in this manner (lines 152-153). Section 3.4 in turn discusses the implementation by extending separable 3D-convolutional networks. Does this mean that the proposed trajectory convolution combines both notions? If so, these subsections should be combined and rewritten to better describe how the proposed approach incorporates both. If not, the distinction should be made more clear. -- Section 3.3 discusses the addition of motion information by adding offset coordinates as features. This is also done e.g. in Dense Trajectories themselves and in TDD. From Section 3.3, it is however unclear how this is performed in this context. To what are these offsets added and where in the network are they used? The explanation on lines 159-160 is not intuitive. A figure would also really help here. -- Section 3.5 is not clear at all. The method jumps from using a small 3D CNN to estimate estimate trajectories, to preliminary experiments, to MotionNet, to FlowNet-SD, to replacing optical flow. The same subsection discusses multiple topics in half a page without proper explanation and details, making it unnecessarily hard to read. Please rewrite this subsection and again consider a figure to make things clear to the reader. -- On a general note, it remains unclear from the paper which elements form a trajectory. I.e. which points are tracked, how densely this is done, etc. Without these details, the paper remains abstract and hard to interpret.  - The second weakness of the paper is that the experiments are not fully convincing in three aspects. -- The first aspect is that the proposed trajectory convolution does not add much to the current 3D convolutional network setup. While large improvements are not always a requirement, it is difficult to assess whether the improvements in Tables 1 through 3 are even due to the method, or due to randomness within the networks. Rerunning the baselines and methods multiple times with different seeds followed by significance tests seem like a requirement for these ablation studies given the small improvements. On face value, the current improvements are small.  -- The second aspect is that it remains unknown why the method works and when it fails. Next to the missing details on the trajectories themselves, their impact also remains abstract and unknown. Figure 2 provides a qualitative result, but does not really add to the understanding of the trajectory convolution itself. What do the trajectories focus on? Where and when are the trajectories used within a video? For which actions do they work and why? For which actions to they not work? How different are the learned trajectories from straight lines through the temporal axis? The lack of such analyses limit the impact and insight into the proposed network.  The listed strengths and weaknesses of the paper paint an overall interesting work. The trajectory convolution is a natural extension from the current literature on action recognition. Furthermore, the paper is clearly written. The paper does however have several weaknesses that require attention and warrant discussion. The method itself is not well explained and requires thorough rewriting, while the experiments are not fully convincing due to lack of effect. It should however be noted that the method itself makes sense within the current action recognition literature and the lack of big improvements should not be a direct cause for rejection, as it might still be an interesting result for researchers investigating similar avenues.


TopRank: A Practical Algorithm for Online Stochastic Ranking
Online learning to rank is a sequential decision-making problem where in each round the learning agent chooses a list of items and receives feedback in the form of clicks from the user. Many sample-efficient algorithms have been proposed for this problem that assume a specific click model connecting rankings and user behavior. We propose a generalized click model that encompasses many existing models, including the position-based and cascade models. Our generalization motivates a novel online learning algorithm based on topological sort, which we call TopRank. TopRank is (a) more natural than existing algorithms, (b) has stronger regret guarantees than existing algorithms with comparable generality, (c) has a more insightful proof that leaves the door open to many generalizations, and (d) outperforms existing algorithms empirically.

This paper tackles the problem of learning to rank items in the online setting. This paper proposes a new algorithm that uses confidence intervals on items preferences ordering in order to decide which item to assign to each position. Results show that the proposed approach empirically outperforms the current state-of-the-art in the re-ranking setting. The paper also provides an upper bound on the regret for the proposed approach, and a lower bound on the regret in ranking problems.   Quality:  I found the paper of overall good quality. Considering that there is some space left at the end, the paper could benefit from some more details to backup its claims:  The abstract (line 8) claims that the proposed approach is "more natural than existing algorithms". Though I agree that this approach feels natural, other models are not discussed here. This makes it difficult to judge of how natural (or not) they are compared in comparison.  The abstract (lines 8-9) and conclusion (line 241) claim that the proposed algorithm "enjoys stronger regret guarantees" than existing models, but the bounds of other algorithms are not reported nor discussed. How does the theoretical result of Thm. 1 compare with the bounds of other models (e.g. CascadeUCB, BatchRank)?   Clarity:  The paper reads well.  It would be good to remind the reader what are K and L at the beginning of Sec. 2.  Figures used to illustrate the model (in Sec. 3) and the algorithm (in Sec. 4) do not have a caption. I understand that this was meant to save space and/or alleviate the general presentation but there is empty space at the end of the paper.  Nitpicking: - Reference [22] is a duplicate of [21].   Originality:  This work addresses an existing problem with a novel approach. The proposed algorithm is intuitive and compares really well to the state of art.  The consfidence intervals in Lem. 6 hold simultaneously for all times, which could be interesting for further analysis.  Thm. 2 appears to be the first lower bound obtained by unifying different existing results.   Significance:  While the paper does not address a new problem, the learning to (re-)rank problem is still of interest for many people. The proposed algorithm empirically outperforms existing approaches, it would become one of the state-of-the-art baselines to consider. However, the significance of its regret upper bound (Thm. 1) is hard to evaluate without comparison with similar results of existing models. Thm. 2, on the other hand, might be the only current regret lower bound instance in the ranking problem.


Multi-View Silhouette and Depth Decomposition for High Resolution 3D Object Representation
We consider the problem of scaling deep generative shape models to high-resolution. Drawing motivation from the canonical view representation of objects, we introduce a novel method for the fast up-sampling of 3D objects in voxel space through networks that perform super-resolution on the six orthographic depth projections. This allows us to generate high-resolution objects with more efficient scaling than methods which work directly in 3D. We decompose the problem of 2D depth super-resolution into silhouette and depth prediction to capture both structure and fine detail. This allows our method to generate sharp edges more easily than an individual network. We evaluate our work on multiple experiments concerning high-resolution 3D objects, and show our system is capable of accurately predicting novel objects at resolutions as large as 512×512×512 -the highest resolution reported for this task. We achieve state-of-the-art performance on 3D object reconstruction from RGB images on the ShapeNet dataset, and further demonstrate the first effective 3D super-resolution method.

Summary: This paper proposes a 3d super resolution method. It first projects the reconstructed 3D model to 6 low resolution orthographic depth maps. A mask network and a depth network are trained to up-sample the corresponding  depth maps to high resolution ones, and a 3D model carving strategy is applied to produce high resolution reconstructed result.   In their experiments, the reconstructed results are out perform the previous state-of-the-art pix2mesh algorithm by first do a low resolution reconstruction & then do super-resolution.  Novelty: The insight of the paper is leverage the difficulty of super-resolution in 3D to the field of well studied image super-resolution, so that the learning could be much easier.   Several questions seems not presented in the paper:  1: Is it still necessary to estimate the view point of the object in order to align the model to canonical views for up-sampling networks ?    2: For single image reconstruction task, the super-resolution in 3D is independent with image after low-res reconstruction. how is the result when the single image low resolution reconstruction fails, will the super-resolution enlarge the error ?  Maybe some failure case show be shown.  3: In L87, "[41] show the results up to 256^3". I think  this is because the dataset has ground truth at the resolution of 256^3, while the method has the capability to extend to 512^3 (as also shown in their paper), and they have the code released. The author should show a comparison on the same resolution (either visually or numerically).  Another problem of the paper is that the description is not good, e.g. L116: structure -> structural L125: passed -> passed in ?  the math symbols to represent different contents are somewhat sloppy ( what is the j, k in Eqn. (1) and (2), why depth map for high resolution is \hat{D}_H while for low resolution is C_L?  rather than  \hat{D}_L).   Experiments: The ablation study of how many canonical view (ODM) is needed w.r.t the final performance ? Since most object are symmetric in shapenet, maybe 3 is already good enough ?   How is the visual comparison between the proposed method with [41] ? It is important to have the intuition of the place of improvement for supporting the numbers.   Overall, although the method gives impressive results on reconstruction, I still have concern about the representation could be limited in real-world images since canonical views may not be easy to infer for non-rigid deformation and when occlusion happens. However, the paper proposes a effective method to alleviate the curse of dimension in 3D when the object is relative simple or symmetric.


Adversarially Robust Optimization with Gaussian Processes
In this paper, we consider the problem of Gaussian process (GP) optimization with an added robustness requirement: The returned point may be perturbed by an adversary, and we require the function value to remain as high as possible even after this perturbation. This problem is motivated by settings in which the underlying functions during optimization and implementation stages are different, or when one is interested in finding an entire region of good inputs rather than only a single point. We show that standard GP optimization algorithms do not exhibit the desired robustness properties, and provide a novel confidence-bound based algorithm STABLEOPT for this purpose. We rigorously establish the required number of samples for STABLEOPT to find a near-optimal point, and we complement this guarantee with an algorithm-independent lower bound. We experimentally demonstrate several potential applications of interest using real-world data sets, and we show that STABLEOPT consistently succeeds in finding a stable maximizer where several baseline methods fail.

The authors consider a problem of black-box optimisation with additional robustness requirements. As opposed to standard Bayesian optimisation, where the unknown function f is modelled typically with GP and new evaluation location chosen to improve the knowledge of the global optimiser sequentially, the authors instead want to find a point whose objective function value remains almost optimal even after some perturbation of the point. In this setting e.g. a global optimiser that lies on top of a narrow peak might be suboptimal choice because even a small change of the point could change its value drastically while a point having smaller objective function value but lying in a more flat region might be better choice.  The authors formulate the problem so that instead of trying to find a global optimiser, they look for a point that is the maximiser of the minimum of f over some \epsilon-neighbourhood of the point. They extend the well-known GP-UCB/LCB strategy to this robust setting and provide both theoretical and empirical support for their method. Also, they show that many "max-min" type of optimisation problems in literature can be seen as special cases of their approach.  This is a very strong and well-written paper on an interesting problem and, as far as I know, the topic has not been studied in such detail previously. The authors also list some practical applications for their method. While I consider myself as an expert in BayesOpt and related methods and could understand the paper quite well, I am not familiar with the underlying theoretical framework (based on e.g. [30]) and could not check the proofs of the theoretical results. However, the theoretical results also look carefully done.   I have the following minor concerns and comments/questions of the paper:  - I found no discussion on how the optimisation of (10) is carried out and what is the computational cost as compared to standard BayesOpt methods like GP-UCB or the time required to evaluate f.  Optimisation of (10) may not be straightforward because the nested minimisation over the \epsilon ball. Perhaps these computational aspects could be briefly discussed in the supplement. Experiments focus on rather low-dimensional cases where grid optimisation might already work just fine but I also wonder how would the approach work in high-dimensions?  - There appears to be large difference between GP-UCB and STABLE-GP-UCB in Fig2c and especially in Fig7c although the only difference between these two appears to be the selection of the reported point. I thus wonder if MAXIMIN-GP-UCB would work better if the reported point was chosen similarly as with STABLE-* methods.   - lines 118-220: Generally, I am a bit puzzled on how the reported point should be chosen in the first place. Maybe I am missing something here but why not just use the GP mean function as a proxy to the unknown function f and then use (5) to select the final reported point? Or is it author's experience that the (pessimistic) estimate based on the lcb criteria actually works better in practice?  - line 225: Comparison to only GP-UCB-based methods seems reasonable but I believe that one could also extend EI and entropy search to this robust setting (evaluating the resulting acquisition function might require numerical computations though).  - line 221: Choosing \beta_t^{1/2}=2 seems a bit arbitrary choice and I wonder what is actually going on here. I could imagine that a more conservative strategy that produces more exploration of the parameter space might actually be useful here.  - Distance d(x,x') is also an input of Algorithm 1, right?  - I wonder what GP model was used in Robust robot pushing experiment with the two functions f_i, i=1,2?  - For consistency, the order of the methods in the legend box of Fig3 could be the same as in other Figs.   Edit after author rebuttal: After reading the rebuttal and other reviews I remain confident that this is high quality work and should be accepted. However, I am still a bit puzzled about some design choices and how they would affect the experimental results in practice, so I hope the authors can indeed clarify these in the final version.


Learning to Infer Graphics Programs from Hand-Drawn Images
We introduce a model that learns to convert simple hand drawings into graphics programs written in a subset of L A T E X. The model combines techniques from deep learning and program synthesis. We learn a convolutional neural network that proposes plausible drawing primitives that explain an image. These drawing primitives are a specification (spec) of what the graphics program needs to draw. We learn a model that uses program synthesis techniques to recover a graphics program from that spec. These programs have constructs like variable bindings, iterative loops, or simple kinds of conditionals. With a graphics program in hand, we can correct errors made by the deep network and extrapolate drawings.

This paper presents a model for synthesizing Latex code from (hand) drawn diagrams. It does so by combining two approaches: i) a NN-based model for generating graphics primitives that reconstruct the image, and ii) synthesize a program from these generated primitives to achieve a better/compressed/more general representation than just a ‘list’ of graphics primitives.  Strengths: - I quite enjoyed reading the paper as the work in it seems original, solid and complete (even a bit more than enough). The conclusions are well supported by concrete (and importantly, relevant) evaluation.  Weaknesses: - my only objection to the paper is that it packs up quite a lot of information, and because of the page-limits it doesn’t include all the details necessary to reconstruct the model. This means cuts were made, some of which are not warranted. Sure, the appendix is there, but the reader needs to get all the necessary details in the main body of the paper.  I quite enjoyed the paper, I think it’s definitely NIPS material, but it needs some additional polishing. I added my list of suggestions I think would help improve readability of the paper at the end of the review.  Questions: - I might have missed the point of section 4.2 - I see it as a (spacewise-costly) way to say “programs (as opposed to specs) are a better choice as they enable generalization/extrapolation via changing variable values“? What is the experiment there? If it’s just to show that by changing variables, one can extrapolate to different images, I would save space on 1/2 of Figure 9 and focus on lacking parts of the paper (190 - extrapolations produced by our system - how did the system produce those extrapolations? was there a human that changed variable values or is there something in the system enabling this?) - What is + in Figure 3? If elementwise addition, please specify that - Figure 4 caption explains why the number N of particles is not the same across models. However, that still doesn’t stop me from wondering whether there is a significant difference in performance in case all models are using the same number of particles. Do you have that information? - Line 54 mentions that the network can ‘derender’ images with beam search. Is beam search used or not? What is the size of the beam? Is beam search used for each of the N particles? - From what I understood, the model does not have access to previously generated commands. Can you confirm that? - The order of (generated) specs is irrelevant for rendering, but it is for the generation process. How do you cope with that? Do you use a particular order when training the model or do you permute the specs? - Table 2 - “;” denotes OR, right? I would personally use the BNF notation here and use “|” - 153 - ‘minimized 3 using gradient descent’  - how did you treat the fact that min is not differentiable? - Table 5 - this is evaluated on which problems exactly? The same 100 on which the policy was trained? - Please provide some DeepCoder -style baseline details - the same MLP structure? Applied to which engine? A search algorithm or Sketch? - I find 152 - 153 unclear - how did you synthesize minimum cost programs for each \sigma ? \sigma represents a space of possible solutions, no? - Please provide more details on how you trained L_learned - what is the dataset you trained it on (randomly selected pairs of images, sampled from the same pool of randomly generated images, with a twist)? How did you evaluate its performance? What is the error of that model? Was it treated as a regression or as a classification task? - Figure 7 introduces IoU. Is that the same IoU used in segmentation? If so, how does that apply here? Do you count the union/intersection of pixels? Please provide a citation where a reader can quickly understand that measure.   Suggestions: - full Table 3 is pretty, but it could easily be halved to save space for more important (missing!) details of the paper - the appendix is very bulky and not well structured. If you want to refer to the appendix, I would strongly suggest to refer to sections/subsections, otherwise a reader can easily get lost in finding the details - Section 2.1 starts strong, promising generalization to real hand drawings, but in the first sentence the reader realizes the model is trained on artificial data. Only in line 91 it says that the system is tested on hand-written figures. I would emphasize that from the beginning. - Line 108 - penalize using many different numerical constants - please provide a few examples before pointing to the supplement. - Line 154 - a bit more detail of the bilinear model would be necessary (how low-capacity?) - 175-176 - see supplement for details. You need to provide some details in the body of the paper! I want to get the idea how you model the prior from the paper and not the supplement - Table 5 - there’s a figure in the appendix which seems much more informative than this Table, consider using that one instead   The related work is well written, I would just suggest adding pix2code (https://arxiv.org/abs/1705.07962) and SPIRAL (https://arxiv.org/abs/1804.01118) for completeness.  UPDATE: I've read the author feedback and the other reviews. We all agree that the paper is dense, but we seem to like it nevertheless. This paper should be accepted, even as is because it's a valuable contribution, but I really hope authors will invest additional effort into clarifying the parts we found lacking.


Learning Compressed Transforms with Low Displacement Rank
The low displacement rank (LDR) framework for structured matrices represents a matrix through two displacement operators and a low-rank residual. Existing use of LDR matrices in deep learning has applied fixed displacement operators encoding forms of shift invariance akin to convolutions. We introduce a class of LDR matrices with more general displacement operators, and explicitly learn over both the operators and the low-rank component. This class generalizes several previous constructions while preserving compression and efficient computation. We prove bounds on the VC dimension of multi-layer neural networks with structured weight matrices and show empirically that our compact parameterization can reduce the sample complexity of learning. When replacing weight layers in fully-connected, convolutional, and recurrent neural networks for image classification and language modeling tasks, our new classes exceed the accuracy of existing compression approaches, and on some tasks also outperform general unstructured layers while using more than 20x fewer parameters.

# Post rebuttal  Given new results and comparisons provided by the authors I am increasing initial score of (6) to (7).  # Original review  This paper focuses on an low displacement rank matrices used as parametrisations of neural networks and more precisely on defining a rich class of them, which can be used while preserving reasonable VC bounds.  I find presented results interesting and valuable, however it is unclear how significant for the community they really are. Authors seem to view the approach as a way to decrease overparametrisation of the networks with minimal effect on accuracy. However, there are dozens of techniques which try to address this very issue, which are not really compared against. Instead, authors choose to focus on comparing to other, very similar approaches of reparametrising neural network layers with LDRs.  Pros: - Clear message - Visible extension of previous work/results - Showing both empirically and theoretically how proposed method improves upon baselines - Providing implementation of the method, thus increasing reproducability  Cons: - all experiments are relatively low-scale, and the only benefits over not constraining the structure is obtained for MNIST-noise (90 vs 93.5%) and CIFAR-10 (65 vs 66%) which are not very significant differences at this level of accuracy for these problems. Since this paper is not evaluation-centric, I am still in favour of accepting, but in a marginal sense; if provided with stronger empirical evidence for the method I would be keen to change the score. On the other hand there are many other ways of reducing number of parameters of a neural network, so if the evaluation claim is "minimisation of number of weights given small accuracy drop" than one should compare against exactly these approaches, such as: network prunning, even methods like "optimal brain surgeon" from 90s; micro-architectures which were found explicitely to minimise this constraint (like MobileNets etc.).  - significance of these results are quite limited as the empirical evaluation shows limited benefits (or at least the proper evaluation metric, a number authors want to optimise, is unclear to the reviewer) and the theoretical results, while valuable, don't seem strong enough to consider it as a purely math paper.  Minor remarks: - please fix language errors/typos, such as: Table 2 caption "has perplexity is", using "low rank" and "low-rank" (please pick one),


Generating Informative and Diverse Conversational Responses via Adversarial Information Maximization
Responses generated by neural conversational models tend to lack informativeness and diversity. We present a novel adversarial learning method, called Adversarial Information Maximization (AIM) model, to address these two related but distinct problems. To foster response diversity, we leverage adversarial training that allows distributional matching of synthetic and real responses. To improve informativeness, we explicitly optimize a variational lower bound on pairwise mutual information between query and response. Empirical results from automatic and human evaluations demonstrate that our methods significantly boost informativeness and diversity.

The authors present several modified GAN architectures and losses for tackling response generation in a single-turn conversational setting. In particular, the authors propose a particular architecture and loss for the discriminator, an additional mutual information component to the loss (using a variational approximation to MI and an approximate backward model), and finally a "dual" objective, which aims to treat the forward and backward models symmetrically. The authors apply their approach to two social-media style datasets, and evaluate in terms of BLEU, ROUGE, some embedding-based metrics from previous work, some diversity-targeting metrics, as well as with a human user study. Their approaches improve over baseline seq2seq, conditional GAN, and the MMI model of Li et al. (2016) in essentially all metrics.  Strengths: -  The authors carry out a large number of experiments with a large number of evaluation metrics (including human evaluation), and their approach generally outperforms the baselines.  - The experimental comparison between cGAN, AIM, and DAIM effectively ablates at least some of the novel architectural and loss components introduced by the authors. - The authors suggest several modifications to GAN-style generation models that appear to be helpful.  Weaknesses: - It would have been much better if the authors had compared their approaches with previously published results on established datasets. For instance the datasets of Li et al. (2016) could presumably have used. Even if, as in footnote 1, there are concerns about some of the other datasets, some results on these datasets could have at least been included in an appendix in order to better establish how the proposed approaches measure against previously published results. - While some of the novel architectural and loss components are effectively ablated (as above), the authors claim additional benefits of their approach that are not backed up theoretically or empirically, such as that the cosine-similarity based discriminator is superior to other discriminator architectures, and that learning with DPG is preferable to other approaches.  Finally, there are some relatively small presentation-related issues: - Line 81: if Z is added to H0 element-wise this isn't a Hadamard product (which would multiply element-wise) - Line 83: it's a bit strange to claim you aren't using a standard LSTM unit just because you take the (soft) argmax of the output distribution rather than sample; as far as I can tell the LSTM architecture hasn't changed at all. -  The claims throughout of proposing a "learning framework" seem overblown; this isn't a new framework, but a modified loss and architecture.


A Bayes-Sard Cubature Method
This paper focusses on the formulation of numerical integration as an inferential task. To date, research effort has largely focussed on the development of Bayesian cubature, whose distributional output provides uncertainty quantification for the integral. However, the point estimators associated to Bayesian cubature can be inaccurate and acutely sensitive to the prior when the domain is high-dimensional. To address these drawbacks we introduce Bayes-Sard cubature, a probabilistic framework that combines the flexibility of Bayesian cubature with the robustness of classical cubatures which are well-established. This is achieved by considering a Gaussian process model for the integrand whose mean is a parametric regression model, with an improper prior on each regression coefficient. The features in the regression model consist of test functions which are guaranteed to be exactly integrated, with remaining degrees of freedom afforded to the non-parametric part. The asymptotic convergence of the Bayes-Sard cubature method is established and the theoretical results are numerically verified. In particular, we report two orders of magnitude reduction in error compared to Bayesian cubature in the context of a high-dimensional financial integral.
This paper argues that the perceived performance gap between probabilistic and non-probabilistic methods should be reconsidered. To this end, we consider a non-parametric Bayesian regression model augmented with a parametric component. The features in the parametric component, that is the pre-specified finite set of basis functions, will be denoted π. Then, an improper prior limit on the regression coefficients (see [48,33] and [42,Sec. 2.7]) is studied. This gives rise to Bayes-Sard cubature 1 (BSC), which differs at a fundamental level to standard BC, in that the functions in π are now exactly integrated. The extension is similar, though not identical, to that proposed in 1974 by Larkin [28] and in 1991 by O'Hagan [35], and non-probabilistic versions have appeared independently in [3,9] in the context of interpolation with conditionally positive definite kernels and optimal approximation in reproducing kernel Hilbert spaces. For other recent work, see also [40,Sec. 2.4]. Our contributions therefore include (i) establishing a coherent and comprehensive Gaussian process framework for BSC; (ii) rigorous study of convergence and conditions that need to be established on π; (iii) empirical experiments that demonstrate improved accuracy in high dimensions and robustness to misspecified kernel parameters compared to BC; and (iv) the important observation that, when the dimension of the function space π matches the number of cubature nodes, the BSC method can be used to endow any cubature rule with a meaningful probabilistic output.

The paper develops a new integration method which follows from a Gaussian process (GP) modeling of the integrand. The author starts by defining the posterior of the GP model, which appears as an approximation of the integrand. Fixing some parameters in the GP models, the author recovers the standard Bayesian cubature method (rk 2.3). The originality of their proposal, the Bayes-Sard cubature (BSC) method, comes from considering a limiting case in the GP model (which characterizes the most uninformative prior). The estimate given by the BSC method is the integral of the mean of the resulting posterior Gaussian process. It is a linear integration rule and another nice property is that it integrates perfectly the functions lying in some linear space pi (chosen by the user). The paper is reasonably organized and the ideas are well explained (with good examples). On top of that the paper surveys nicely many results by putting in light new links between some existing methods.   Here are some points/questions that might help to improve the paper: - The main contribution of the paper seems more methodological than theoretical but too few experiments are given in the end to validate the approach.  - The proposed method depends on a linear space pi (a notation which I find a bit exotic for a linear subspace). It is not clearly stated that the integrals of functions in pi should be known for the method to work. This being said, there might be some link with the control variates method as detailed for instance in the archived paper arXiv:1801.01797. In section 2.4 of the previous reference, the authors obtain a formulation with cubature weights of control variates (which integrates perfectly the functions in a linear space that correspond to your pi). In the present paper, the author gives some weights that, as well, are integrating perfectly the functions in pi. In Th 2.9 the weights are claimed to be unique. Does it means that both methods coincide? (the statement on uniqueness might require more details). - The statements of the theorems are too vague and it is sometimes difficult to understand their meaning. For instance, ‘’in the limit’’ is not clear while a standard equation would do the job. Especially, in Th 2.7, where one cannot know what means ‘’in the limit’’ without checking the proof. Another example is ‘’consider an n points cubature rule’’. This has not been defined. - Even if interesting, the convergence analysis is not the very point of the paper (as it follows from known results). It would be preferable to furnish some remarks on the rate and perhaps to compare with other methods (in place of theoretical consideration that would perfectly fit the supplementary material). - Section 2.1 results from classical techniques from the GP literature. It should be mentioned from the beginning (for the non expert reader). - page 3. line 105. As the meaning of the remark coincides with the definition of s and k (line 97), it seems to me redundant. - page 3. line 112. The remark should be at the beginning of section 2.1.3. - remark 2.13. It is said that the supplementary material ‘’elaborates’’ on assumptions (i) and (ii) whereas it just gives some definitions. I was disappointing to see no further explanation on the assumptions.


Why Is My Classifier Discriminatory?
Recent attempts to achieve fairness in predictive models focus on the balance between fairness and accuracy. In sensitive applications such as healthcare or criminal justice, this trade-off is often undesirable as any increase in prediction error could have devastating consequences. In this work, we argue that the fairness of predictions should be evaluated in context of the data, and that unfairness induced by inadequate samples sizes or unmeasured predictive variables should be addressed through data collection, rather than by constraining the model. We decompose cost-based metrics of discrimination into bias, variance, and noise, and propose actions aimed at estimating and reducing each term. Finally, we perform case-studies on prediction of income, mortality, and review ratings, confirming the value of this analysis. We find that data collection is often a means to reduce discrimination without sacrificing accuracy.

Summary/Contribution This paper shows that disparities in many fairness measures can be decomposed into “bias” (loss caused by deviating from the best feasible classifier), “variance” (loss caused by randomness in the dataset), and “noise” (the loss of the best feasible classifier). In doing so it illuminates some important issues that need to be considered when attempting to improve group fairness measures. For example, many people suspect that high error rates (either FPR or FNR) for a minority group is at least partially due to a lack of minority data. This work shows that these error rates can persist even with plentiful data (ie when the contribution of “variance” to the error rate differences is zero).   Crucially, this paper recognizes that “existing approaches for reducing discrimination induced by prediction errors may be unethical or impractical to apply in settings where predictive accuracy is critical, such as in healthcare or criminal justice,” and proposes concrete means to improve algorithms without bearing this unacceptable cost.  Weaknesses: The biggest weakness of this paper is its use of the word “discrimination” to refer to differences in cost functions between groups. The authors provide no justification for why differences in (for example) zero-one loss should be termed “discriminatory,” evoking injustice and animus in the reader’s mind. A classifier that tries to predict who will become an NFL quarterback will have a worse zero-one loss for men than women (since no woman has ever played in the NFL), but this is absolutely not discrimination. I’d give this paper an "overall score" of 8 if they used a more value-neutral term (such as “disparities” or “differences”) instead of “discrimination”.  The authors also suggest a method for determining where to expend effort to produce better models, which looks at subgroups where error rates differ by protected characteristics. For example, they find that their model seems to make far fewer errors on Hispanic cancer patients than cancer patients of other races. I’d be interested to see whether this effect was due to differences in base rates within the subgroups. One group might be easier to classify simply because their base rate is closer to zero or one, but this doesn’t necessarily suggest the existence of extra features to reduce noise (and therefore the accuracy gap).   Clarity: This paper is well written and the math is clear.  Originality: This paper is clearly original, although other papers have hinted at similar high-level results.  Significance: This paper contains some valuable insights that could be readily applied to existing machine learning workflows, a rare achievement for FATML papers. However, I suspect the practical impact will be small since many problems have lots of data (so bias and variance are small) and no good way to get additional predictive features (so noise can't be reduced).  Response to author rebuttal: I was disappointed to see the authors push back about the use of "discrimination" to describe differences in cost functions. "However, in the NFL example, if differences in error rates were related to race, there might be cause for concern--depending on how the classifier is used. Drawing on terminology from prior work, we use “discrimination” as we consider applications in which decisions based on error-biased classifiers may be considered unfair, such as healthcare, employment and criminal justice—similar to how a human making consistent race-dependent errors could also be considered discriminatory." This is all true, differences in error rates *might* be discriminatory, but they also might not be. This is why we need to be extremely precise with our language. Previous papers have been careless with the word "discriminatory", but this does not mean this (otherwise careful and important) paper should follow their example. The title of the paper does not give me confidence that the discussion in the revised paper about when, exactly, differences in cost functions are discriminatory will be sufficiently nuanced.


Total stochastic gradient algorithms and applications in reinforcement learning
Backpropagation and the chain rule of derivatives have been prominent; however, the total derivative rule has not enjoyed the same amount of attention. In this work we show how the total derivative rule leads to an intuitive visual framework for creating gradient estimators on graphical models. In particular, previous "policy gradient theorems" are easily derived. We derive new gradient estimators based on density estimation, as well as a likelihood ratio gradient, which "jumps" to an intermediate node, not directly to the objective function. We evaluate our methods on model-based policy gradient algorithms, achieve good performance, and present evidence towards demystifying the success of the popular PILCO algorithm [5].

In this paper, the authors investigate the application of a total gradient theorem to the evaluation of gradient of expectations in probabilistic computation graphs. By combining the total gradient rule with other known gradient estimators (reparametrization and score function estimator), they derive new estimators, in particular in the context of policy gradient for reinforcement learning. They use these new estimators to explain the empirical success of PILCO.  Though I found the exposition a bit lacking, I found the paper overall very interesting (the Gaussian shaping gradient in particular); both because the problem of estimating gradients of expectations is fundamental (and therefore new estimators are highly valuable) and for the careful analysis in the experimental section.  - I felt that what the authors really wanted to present was derivative of marginal distribution with respect to other marginal distributions, but because this would have been mathematically cumbersome, introduced 'virtual' parameters \xi, even though the distribution for which \xi are parameters are never actually specified, and it in the vast majority of PCGs, there would be no known distribution with parameters \xi corresponding to the true marginal distribution. This leads to a total stochastic gradient theorem that takes a strange form, since it involves variables which are both underspecified and never actually computed.  I understand why this was done, but this makes this entire section read a bit strangely. - Theorem 1 - even if it follows from the total derivative rule, deserves a short proof (and the total derivative rule, a reference). - The second and third section don't tie very well together, since one section (section 3) relates gradient of distribution parameters to others, and the other (section 2), is instead about computing gradients of expectations. Of course, the parameters of a distribution can often be written as expectation of sufficient statistics (a fact used by the Gaussian Shaping gradient), but this is never made clear and the sections are not connected enough. For that matter, it's not clear how does the policy gradient (eq 5) actually relates to a total gradient theorem (what is the critic a gradient of?). The connection between (5) and (6) being different estimators of the same computation graph was already known (see for instance [2]).  The connection between path-relative partial gradient and reparametrization is also only implicit in the text.  - Section 5.2 was confusingly written. As I understand, the first half total gradient theorem is applied with variables x_m, and the first part of the gradient is estimated by making a gaussian assumption and noting that the parameters of the marginal gaussian can be written as expectation of sufficient statistics; at which point the score function estimator is applied to compute the expectation gradient.   - For the PCG framework, aren't properties 1 and 2 implying properties 3 and 4?  Minor:  - I didn't feel the introduction of a new framework was necessarily warranted- as stochastic computation graphs were also introduced as factor graphs and the problem of interest (gradient of expectation) was the same. The SCG framework did not explicitly call for sampling the graph forward, though it is true that the methods introduced call for sampling - but practically, so do the methods in this paper. Both frameworks define distributions over variables, identify the relevant problem as an intractable deterministic distribution, and neither paper actually offers fully deterministic computation on those distributions as practical algorithms. The main difference is the explicit focus on computing marginal distributions in the PCG framework. - Given you give variables meaningful names in the PCG for model-free RL, it would be simpler overall not to index the parameters variables \xi, but perhaps to use a notation like \xi(x), \xi(u), etc. \xi(x_m) would be much easier to parse than \xi_m, since that notation could refer to the sufficient statistics of any m-indexed variable. - Hunch: the gaussian shaping gradient could be related to policy gradients for average-cost MDPs [1], since in both cases , the gradient of the expected value is written as gradient of marginal distributions times rewards (instead of gradient of conditional distribution times returns in the classical PG theorem). The settings are different and no Gaussian approximation is made, but this felt related.  [1] Simulation-Based Optimization of Markov Reward Processes, Marbach and Tsitsiklis.  [2] Stochastic Value Gradients, Heess et. Al


Bayesian Structure Learning by Recursive Bootstrap
We address the problem of Bayesian structure learning for domains with hundreds of variables by employing non-parametric bootstrap, recursively. We propose a method that covers both model averaging and model selection in the same framework. The proposed method deals with the main weakness of constraint-based learning-sensitivity to errors in the independence tests-by a novel way of combining bootstrap with constraint-based learning. Essentially, we provide an algorithm for learning a tree, in which each node represents a scored CPDAG for a subset of variables and the level of the node corresponds to the maximal order of conditional independencies that are encoded in the graph. As higher order independencies are tested in deeper recursive calls, they benefit from more bootstrap samples, and therefore are more resistant to the curse-of-dimensionality. Moreover, the re-use of stable low order independencies allows greater computational efficiency. We also provide an algorithm for sampling CPDAGs efficiently from their posterior given the learned tree. That is, not from the full posterior, but from a reduced space of CPDAGs encoded in the learned tree. We empirically demonstrate that the proposed algorithm scales well to hundreds of variables, and learns better MAP models and more reliable causal relationships between variables, than other state-of-the-art-methods.

This manuscript proposes B-RAI, an extension of the Recursive Autonomy Identification (RAI) algorithm of Yehezkel & Lerner (JMLR, 2009), which is itself a constraint-based algorithm for Bayesian network structure learning. The idea of B-RAI is to use bootstrapping within each each RAI-substep in order to create a space of possible CDPAG (BN equivalence classes) solutions, for each of which a score is computed. So B-RAI belongs  actually to the class of hybrids between constraint-based and score-based structure learning. The proposed approach has the advantage to cover both model averaging and model selection in the same framework.  In summary, this is interesting work that could be useful to other researchers. The studied problem is important, and the results of benchmark studies look promising. The manuscript is generally written well.   I have a few comments/questions, though:  [1] The difference of B-RAI to RAI could be stated more explicitly early on (end of intro). Within Section 3, it is not easy to see where description of the old method ends and where the novel content starts. I had to look in the JMLR paper from 2009 to clarify some aspects.  [2] The article employs BDeu as scoring function, but does not fully specify the prior: What is the chosen equivalent sample size (ESS)? This information is essential for reproducing the results.  [3] If I understand correctly, the algorithm does not sample CPDAGs from the (full) posterior, but samples only CPDAGs that survive initial independence tests (and are thus included in the graph generating tree) according to their posterior probability. If this is so, it could be stated more explicitly, especially in the abstract.  [4] For the model selection part, I miss a comparison with the globally optimal (CP)-DAG according to BDeu (with same ESS, see comment [2]) for the problem sizes (Child, Insurance, Mildew, Alarm, perhaps also Barley) where it can be computed with modern solvers (e.g. GOBNILP, CPBayes, URLearn).   [5] For the model selection I also miss an evaluation of the solution's quality in terms of structural similarity to the ground-truth (measured by structural Hamming distance, for instance). It might be a more informative criterion than the log probability of MAP models, which is pretty hard to interpret (is a difference small or large?).  [6] Very minor stylistic comments regarding the reference list: Please be consistent in using either full conference names or abbreviations (one "IJCAI" appears), and use of initial caps in paper/journal/conference titles. "Bayesian" instead of "bayesian", etc.  [7] Another presentation issue: In Fig. 4, showing both the barplots and the numbers is a bit redundant. If the precise numbers are really important, a plain table might be a better way to present the results. Otherwise one could add a y-axis just to the leftmost plots (which then pertains to the entire row).  ################## After rebuttal:  Thank you for the detailed response, in particular clarifying [5]. Perhaps it's possible to add some result pertaining [4] to the final version [if completed until then], although it is not that critical, just a nice-to-have.


Learning a High Fidelity Pose Invariant Model for High-resolution Face Frontalization
Face frontalization refers to the process of synthesizing the frontal view of a face from a given profile. Due to self-occlusion and appearance distortion in the wild, it is extremely challenging to recover faithful results and preserve texture details in a high-resolution. This paper proposes a High Fidelity Pose Invariant Model (HF-PIM) to produce photographic and identity-preserving results. HF-PIM frontalizes the profiles through a novel texture warping procedure and leverages a dense correspondence field to bind the 2D and 3D surface spaces. We decompose the prerequisite of warping into dense correspondence field estimation and facial texture map recovering, which are both well addressed by deep networks. Different from those reconstruction methods relying on 3D data, we also propose Adversarial Residual Dictionary Learning (ARDL) to supervise facial texture map recovering with only monocular images. Exhaustive experiments on both controlled and uncontrolled environments demonstrate that the proposed method not only boosts the performance of pose-invariant face recognition but also dramatically improves high-resolution frontalization appearances.

The paper proposes a face frontalization method based on a combination of existing methods of dense correspondence-based texture estimation and warping. An adversarial network was also trained in assisting the improve the texture map learning. The proposed method was evaluated via face recognition and verification tasks.  Face frontalization is important specifically for applications in the wild with no pose and other conditional constraints. The topic is relevant to the NIPS audience. The paper reads good and is easy to follow. However, there are many weaknesses in the paper. I will list them as follows.  Major comments: ===============  - Since face recognition/verification methods are already performing well, the great motivation for face frontalization is for applications in the wild and difficult conditions such as surveillance images where pose, resolution, lighting conditions, etc… vary wildly. To this effect, the paper lacks sufficient motivation for these applications.  - The major drawback is the method is a collection of many existing methods and as such it is hard to draw the major technical contribution of the paper. Although a list of contributions was provided at the end of the introduction none of them are convincing enough to set this paper aside technically. Most of the techniques combined are standard existing methods and/or models. If the combination of these existing methods was carefully analyzed and there were convincing results, it could be a good application paper. But, read on below for the remaining issues I see to consider it as application paper.  - The loss functions are all standard L1 and L2 losses with the exception of the adversarial loss which is also a standard in training GANs. The rationale for the formulation of these losses is little or nonexistent.  - The results for face verification/recognition were mostly less than 1% and even outperformed by as much as 7% on pose angles 75 and 90 (see Table 1). The exception dataset evaluated is IJB-A, in which the proposed model performed by as much as 2% and that is not surprising given IJB-A is collected in well constrained conditions unlike LFW. These points are not discussed really well.  - The visual qualities of the generated images also has a significant flaw in which it tends to produce a more warped bulged regions (see Fig. 3) than the normal side. Although, the identity preservation is better than other methods, the distortions are significant. This lack of symmetry is interesting given the dense correspondence is estimated.   - Moreover, the lack of ablation analysis (in the main paper) makes it very difficult to pinpoint from which component the small performance gain is coming from.  - In conclusion, due to the collection of so many existing methods to constitute the proposed methods and its lack of convincing results, the computational implications do not seem warranted.  Minor comments: ===============  - Minor grammatical issue need to be checked here and there.  - The use of the symbol \hat for the ground truth is technically not appealing. Ground truth variables are usually represented by normal symbols while estimated variables are represented with \hat. This needs to be corrected throughout for clarity.


Nonparametric learning from Bayesian models with randomized objective functions
Bayesian learning is built on an assumption that the model space contains a true reflection of the data generating mechanism. This assumption is problematic, particularly in complex data environments. Here we present a Bayesian nonparametric approach to learning that makes use of statistical models, but does not assume that the model is true. Our approach has provably better properties than using a parametric model and admits a Monte Carlo sampling scheme that can afford massive scalability on modern computer architectures. The model-based aspect of learning is particularly attractive for regularizing nonparametric inference when the sample size is small, and also for correcting approximate approaches such as variational Bayes (VB). We demonstrate the approach on a number of examples including VB classifiers and Bayesian random forests.

The idea: You want to do Bayesian inference on a parameter theta, with prior pi(theta) and parametric likelihood f_theta, but you're not sure if the likelihood is correctly specified. So put a nonparametric prior on the sampling distribution: a mixture of Dirichlet processes centered at f_theta with mixing distribution pi(theta). The concentration parameter of the DP provides a sliding scale between vanilla Bayesian inference (total confidence in the parametric model) and Bayesian bootstrap (no confidence at all, use the empirical distribution).  This is a simple idea, but the paper presents it lucidly and compellingly, beginning with a diverse list of potential applications: the method may be viewed as regularization of a nonparametric Bayesian model towards a parametric one; as robustification of a parametric Bayesian model to misspecification; as a means of correcting a variational approximation; or as nonparametric decision theory, when the log-likelihood is swapped out for an arbitrary utility function.  As for implementation, the procedure requires (1) sampling from the parametric Bayesian posterior distribution and (2) performing a p-dimensional maximization, where p is the dimension of theta. (1) is what you need to do in parametric Bayesian inference anyway, and (2) will often be a convex optimization problem, provided that your log-likelihood or your utility function is concave. You have to do (1) and (2) a bunch of times, but it's parallelizable.  The illustrations of the method are wide-ranging and thoughtful. Section 3.2 shows that the method can be used to correct a variational Bayes logistic regression model; the corrected VB samples look like MCMC samples from the actual Bayesian posterior but are faster to generate than the MCMC samples. Section 3.3 explores how posterior predictive samples from this method could be passed as pseudo-data to an outside analyst who is not permitted to access the data directly. This is an interesting idea, though I'm not sure how it would compare to simple noise addition (or whatever other methods are used in the privacy literature).  A quibble with the wording of lines 112-113 ("unlike MCMC, there are no issues or need for checking convergence..."), as the method does require sampling from the parametric Bayesian posterior, and this will often require checking convergence and using a burn-in phase, etc.  In practice I think I'd struggle with choosing c, the DP concentration parameter, but when doing parametric Bayesian inference (c=infinity), it could be good practice to redo the inference under various finite values of c as a form of sensitivity analysis. The nice thing is that you can use the same set of posterior draws across all values of c, which is a real time-saver.  In summary, this is a well-written paper that presents several potential applications of a simple, good idea. I recommend acceptance.


Data center cooling using model-predictive control
Despite the impressive recent advances in reinforcement learning (RL) algorithms, their deployment to real-world physical systems is often complicated by unexpected events, limited data, and the potential for expensive failures. In this paper, we describe an application of RL "in the wild" to the task of regulating temperatures and airflow inside a large-scale data center (DC). Adopting a data-driven, modelbased approach, we demonstrate that an RL agent with little prior knowledge is able to effectively and safely regulate conditions on a server floor after just a few hours of exploration, while improving operational efficiency relative to existing PID controllers.

This paper applies model predictive control (MPC) for data center cooling, i.e. regulating air temperature and air flow on server room/floor by controlling blower speeds and water flow at air handling units (AHUs). The dynamic model for the MPC is assumed to be a linear autoregressive model and its parameters are learned from randomized exploration over controls. The performance of the approach is evaluated by field experiments at a data center (DC), discussed and compared with the classical/traditional PID control.  Pros - This is a very practical topic which has great potentials for real-world applications. It is exciting to see the field experiments have been performed (I believe the field experiment is expensive) and the results are promising.   - This paper is clearly written, well-organized. The high presentation quality makes this paper an enjoyable read.  Cons - The theory/methodology contribution is limited. The paper is more of a demonstration that we can applying existing techniques to a DC for substantial improvements. - I don't like the comparison of computation time with cvxpy in Section 4.3, line 185. The computation time largely depends on programming language, computing hardware, and many details in implementing the optimization library. Besides, given the cooling is a slow process, I'm curious if we can increase our step to be more than 30s.  Other Questions/Comments  The proposed approach relies on little or no prior knowledge. For an operating DC which has historical recordings, will these historical data somehow help with the model learning, if we want to upgrade its cooling from PID to MPC? I was thinking this because I believe obtaining its historical data is not expensive/difficult.   Regarding the CAT/DP sensors. For "failed sensors", could you please add comments on the sensors' failing rates? For "measurement redundancy", how close are the measurement/readings from nearby sensors? I was thinking the adverse impacts of the failed sensor to the control and whether it is beneficial to build a model which contains every sensor's reading.  In Fig2, could you please add some explanations/descriptions for the model structure on shared parameters among local models. Is there any symmetry in the structure? I was thinking, (assuming the AHU are located on a 2*6 matrix, zero-based), why AHU_0_0's (top row, leftmost) red arrow points to the right, while AHU_0_5's (top row, rightmost) red arrow also points to the right? Why Column_4 is different from Columns 0/1/2/3 in that its red arrows point to the right?    In the exploration stage (Section 4.2), for the safety considerations, are you only limiting the size of control step? Are you also monitoring the temperatures at critical points?   In the experiments analysis, the entering water temperature (EWT) is quite different between Model3 and Model1/2. Could you please comment on how will EWT impact the cooling? Is EWT a big impact to cooling efficiency? How difficult is it to make EWT consistent for all experiments, thus that we have a fairer comparison?  ======= Phase 2 ========= I have read the response from authors. Thanks for the explanations!


Deep State Space Models for Time Series Forecasting
We present a novel approach to probabilistic time series forecasting that combines state space models with deep learning. By parametrizing a per-time-series linear state space model with a jointly-learned recurrent neural network, our method retains desired properties of state space models such as data efficiency and interpretability, while making use of the ability to learn complex patterns from raw data offered by deep learning approaches. Our method scales gracefully from regimes where little training data is available to regimes where data from large collection of time series can be leveraged to learn accurate models. We provide qualitative as well as quantitative results with the proposed method, showing that it compares favorably to the state-of-the-art.

This paper proposes introducing deep neural networks to output the time-varying parameters of a linear state-space model (SSM), preserving the analytical tractability of SSM (e.g. Kalman filtering equations, in the case of a Gaussian likelihood) with increased flexibility coming from time-varying SSM parameters. In the paper, an LSTM maps from the covariates to the set of SSM parameters, and the LSTM captures time-series effects in the parameters.  Overall, the paper is very well written and quite easy to follow. The review of SSM is adequate, and the connection with the proposed approach is well made and intuitive. As to the technical contribution itself, the DeepState method of incorporating deep neural networks within a SSM appears novel, and worthy of study within the important topic of time series forecasting. Important connections to the recent literature, such as Fraccaro et al. (2017), Johnson et al (2016) and Krishnan et al. (2017) are provided, and helpful.  I have three main questions & comments for this review.  First, as stated on lines 125-130, the main use of the LSTM is to non-linearly map from covariates to SSM parameters (sharing this mapping across all time series). An obvious question is why are past observations of a given time series not also provided as adjunct to the covariates, not unlike the treatment within DeepAR. Are there identifiability issues to doing so? This should merit some discussion in the paper.  Second, the experimental evaluation first seeks to recover known generative parameters on synthetic data, which it appears to successfully carry out. Sadly, the evaluation on real datasets is somewhat disappointing, with a comparison against only two multi-series datasets. The evaluation metric is limited to the quantile loss, which is considers all time-steps over the prediction horizon to be independent of one another — whereas the proposed method (as stated on line 83) aims at making predictions over complete future trajectories. It would have been nice to report some measure of the predictive likelihood of this distribution over complete trajectories (using, e.g., some form of kernel density estimation to smooth over the Monte Carlo predictions). Moreover, the loss function QL is a normalized variant of the well-known pinball loss, but a citation would nonetheless be in order. Separately, the set of comparison models leaves to be desired and does not allow appreciating the contribution to performance of the different model components. It is not clear whether the auto.arima and ets model have access to the covariates that DeepState and DeepAR have. Since DeepState extends well-known SSMs, it should test against two simple baselines: (1) a standard fixed-parameter Linear Dynamical System (LDS) that does not use covariates, and (2) one that does use them linearly. Moreover, it would be helpful to run a modicum of ablation studies, e.g. removing the recurrence in the neural network, and varying the dimensionality of the hidden state h_t (which does not appear to be reported).  Third and finally, the section 4.3 is interesting and relevant, but seems to have been hastily written and does not really fit within the rest of the manuscript. In particular, none of the experiments make use of the approach, which would be best suitable in contexts where the time series consist of non-negative observations, with possibly fat tails.  Overall, I think the paper proposes a fruitful line of inquiry, but remains in too early a state to recommend acceptance at NIPS. [Update: I think the authors' rebuttal was helpful, including running additional experiments, and with the proposed changes I have updated by score to a 6.]   Detailed comments:  * Line 52: efffects ==> effects * Line 61: dependent ==> depend * Line 77: acronym LDS (presumably Linear Dynamical System) is not defined * Line 88: are the covariates always assumed to be non-stochastic, even over the prediction range? * Eq. (2): it’s not clear why the innovation \epsilon_t is assumed to be a scalar, which forces the random disturbance to the latent state to be strictly along g_t. In many state-space models, the transition dynamics is assumed to have noise dimension to be equal to the latent space dimension, so this discrepancy should be explained.  * Line 114: the dynamics is ==> the dynamics are * Footnote 3: the the ==> the * Equation 8: should be more careful about notation, in particular indicating that the integration is carried out wrt variables u and l. * Line 238-240: notation overload with \tau used to denote forecast horizon and evaluation quantile. * References [8] and [9] are identical. * Add to to background work on linear state space models, this paper of relevance: Chapados, N., 2014. Effective Bayesian Modeling of Groups of Related Count Time Series. In International Conference on Machine Learning (pp. 1395-1403).


Diffusion Maps for Textual Network Embedding
Textual network embedding leverages rich text information associated with the network to learn low-dimensional vectorial representations of vertices. Rather than using typical natural language processing (NLP) approaches, recent research exploits the relationship of texts on the same edge to graphically embed text. However, these models neglect to measure the complete level of connectivity between any two texts in the graph. We present diffusion maps for textual network embedding (DMTE), integrating global structural information of the graph to capture the semantic relatedness between texts, with a diffusion-convolution operation applied on the text inputs. In addition, a new objective function is designed to efficiently preserve the high-order proximity using the graph diffusion. Experimental results show that the proposed approach outperforms state-of-the-art methods on the vertex-classification and link-prediction tasks.

The main idea of this paper is to use the diffusion convolutional operator to learn text embedding that takes into account the global influence of the whole graph. It then incorporates the diffusion process in the loss function to capture high-order proximity. In contrast, previous works either neglect the semantic distance indicated from the graph, or fails to take into account the similarities of context influenced by global structural information. The author then conducts experiments on the task of multi-label classification of text and link prediction and shows that the proposed model outperforms the baselines.   Strength: The high level idea of of this paper is good, and the method is novel. The diffusion convolutional operator is a good idea to softly incorporate the global factor of the whole graph.   Weakness:  The major quality problem of this paper is clarity. In terms of clarity, there are several confusing places in the paper, especially in equation 9, 10, 11, 12.   1) What is s_{i,j} in these equations? In definition 1, the author mentions that s_{i,j} denotes edge weights in the graph, but what are their values exactly in the experiments?  Are they 0/1 or continuous values?   2) How is the diffusion map computed for structural embedding in 10 and 12? Is it using equation 1 only with the learned structural embedding and without text embedding?  3) Why is the diffusion convolution operator only applied to text embedding? Can it also be applied to structural embedding?  On the other hand, if the author wants to capture global information in the graph as claimed between line 191 and line 194, why not directly use the diffusion map in equation (1) on text embedding instead of applying the diffusion convolution operator in 4.2? It's confusing to me the relationship between equation (1) and equation (5), (6) and (7) in section 4.2. In other words, there are two methods that could capture the global information: equation (1), and equation (5)(6)(7). Equation (1) is applied to structural embedding in equation (10) and (12); equation (5)(6)(7) are applied to textual embeddings. The author should explain why they do so.   4) I wonder whether the structural embedding is really necessary in this case, since in the learning process, the structural embedding just involves a embedding table lookup. The author does not explain the point of using a structural embedding, especially in such a way. What if just use diffusion text embedding? I don't see any experimental results proving the effectiveness of structural embedding in Table 1.   5) What's the motivation of each part in equation (8)? For example, what's the motivation of maximizing the probability of textual embedding of vertex i conditioned on the diffusion map of structural embedding of vertex j in equation (12)?   6) In line 135, the author says "Initially the network only has a few active vertices, due to sparsity." How is "active vertices" defined here?   7) In 5.2, when the author trains the SVM classifier, do they also fine-tune the embeddings or just freeze them? There are many existing CNN and RNN based neural classifier for text classification. What if just use any of those off-the-shelf methods on the text embedding without the diffusion process and fine-tune those embedding? This is typically a strong baseline for text classification, but there is no corresponding experimental results in Figure 5.   8) In line 234, how those objective function weights obtained? Are they tuned on any development set? Has the author tried only using a subset of those objectives? It's not clear how important each of those four objectives is.   9) In line 315, the author attributes the result of Table 3 to "both structure and text information". However, the fact that the method picks vertex 3 is due to diffusion convolution operator, as explained in line 313.  Does the "structure" here mean the diffusion convolution operator or the structural embedding?


Predictive Uncertainty Estimation via Prior Networks
Estimating how uncertain an AI system is in its predictions is important to improve the safety of such systems. Uncertainty in predictive can result from uncertainty in model parameters, irreducible data uncertainty and uncertainty due to distributional mismatch between the test and training data distributions. Different actions might be taken depending on the source of the uncertainty so it is important to be able to distinguish between them. Recently, baseline tasks and metrics have been defined and several practical methods to estimate uncertainty developed. These methods, however, attempt to model uncertainty due to distributional mismatch either implicitly through model uncertainty or as data uncertainty. This work proposes a new framework for modeling predictive uncertainty called Prior Networks (PNs) which explicitly models distributional uncertainty. PNs do this by parameterizing a prior distribution over predictive distributions. This work focuses on uncertainty for classification and evaluates PNs on the tasks of identifying out-of-distribution (OOD) samples and detecting misclassification on the MNIST and CIFAR-10 datasets, where they are found to outperform previous methods. Experiments on synthetic and MNIST and CIFAR-10 data show that unlike previous non-Bayesian methods PNs are able to distinguish between data and distributional uncertainty.

The authors develop prior networks, an approach to identifying misclassification on in and out of distribution examples. The work largely builds upon Malinin et al, 2017, adapting their method to the Dirichlet case. The experiments are simple but lack controls and may be too simple to validate the method. Overall: Quality: There do not appear to be any obvious errors. There is no model uncertainty in this paper as a dirac is used for the model prior, so why spend time talkimg about it? Clarity: The presentation at times seems convoluted and several confusing terms are introduced for apparently the same thing, even where standard terms exist for these in statistics. Some of the explanation is unclear and needs refinement. Originality: It is a fairly straightforward adaptation of Malinin et al, 2017 to the Dirichlet case (using a net for the concentration parameter instead of the variance). Significance: The experimental evaluation is weak. (See comments below) Comments: Intro: The epistemic/aleatoric uncertainty terms are not useful. It has been related to the explained/unexplained variance in the law of total variance, which differs from reducible/irreducible uncertainty in general. Model/data/distributional uncertainty are much clearer notions, are well defined, and are analogous to terms in statistical learning theory. It's worth noting that variantional methods have also been applied to (1), most recently see Graves, 2011, and Blundell et al, 2015, Kingma et al, 2015, Louizos and Welling, 2016. Eq (2)/(3): this explanation needs improving. 1) Instead of P(y=w_c), why not use capital letters for the random variables and lower case (with subscripts if you like) for their values? 2) eq (3) should include the conditional for each P(y = w_c) term: they are not marginals, it's just a vector of the terms in the sum of eq (2). Line 94 talks about decision boundaries, but there are not any defined in text or the figures (you need to specify a loss over choices to identify the boundary). I'm also not sure aim to have increasingly varied decision boundaries far from training data, how is this justified? Section 3: it seems sensible to mention that what is proposed is a hierarchical Bayesian model, in the sense there are now three layers: the likelihood, the per-data prior distribution and the global prior distribution. This idea has been extensively explored in non-neural bayesian models (e.g., LDA). (7) and (8) were a surprise. They effectively eliminate the whole hierarchy that was introduced in Section 3. It makes the whole story about Bayesian inference a bit overboard: in fact, there is very little to do with Bayes here. Indeed, it's not stated explicitly that I could see, but p(w_c|mu) = mu_c and so, fact, everything simplifies to eq (12) which shows that essentially the prediction is just a softmax over a neural network applied to the inputs in eq (13). Whereas Malinin et al, 2017 use (14) to fit Gaussians, this work use it to fit categorical data. That appears to be the main distinction to prior work. This work gives no further justification to this heuristic (they appear to set the coefficient trading off between these two tasks to one without justification). Certainly it looks like parameter estimation by this approach will be biased, but what other properties does it possess? The experiments consist of an experiment on a toy Gaussian discrimination task and on MNIST vs OMNIGLOT out of distribution discrimination. It's not unremarkable that PN worked on the toy task (but it is not really a strong scientific test; there's no baseline, maybe the task is too easy). The MNIST vs OMNIGLOT tasks is concerning. Performance of the baseline models is already high on these tasks, and no error bars are included, hence we do not know if the task is simply too easy and there is no difference in performance between the proposal and other obvious approaches.