Loss Functions for Multiset Prediction
We study the problem of multiset prediction. The goal of multiset prediction is to train a predictor that maps an input to a multiset consisting of multiple items. Unlike existing problems in supervised learning, such as classification, ranking and sequence generation, there is no known order among items in a target multiset, and each item in the multiset may appear more than once, making this problem extremely challenging. In this paper, we propose a novel multiset loss function by viewing this problem from the perspective of sequential decision making. The proposed multiset loss function is empirically evaluated on two families of datasets, one synthetic and the other real, with varying levels of difficulty, against various baseline loss functions including reinforcement learning, sequence, and aggregated distribution matching loss functions. The experiments reveal the effectiveness of the proposed loss function over the others.

The paper proposes a novel method for multiset prediction, which is to predict, for each class, the number of instances of that class present in the example.  As in previous work, the problem is reduced to training a policy to predict a possibly-repeating sequence of labels.  The main novel proposal in this work is to train the policy to minimize the KL divergence between the expert policy and the model policy, which avoids the need to define an arbitrary order in which to predict the sequence (as in other sequence-based methods), and also sidesteps the optimization difficulties of the RL-based approach.  Experiments show that this method substantially outperforms existing methods on the task of multiple-instance prediction for images.  Pros: 1. The proposed method is simple, well-motivated and carefully designed, and performs well in practice 2. The task seems like a good abstraction for a number of practical applications, and the proposed method solves it very well 3. Focused experiments systematically motivate the method, validate hypotheses, and demonstrate the real-world usefulness and substantial advantages of the method over existing methods 4. Paper is clearly written overall  Cons: 1. The novelty and generality of the technique deployed here may be a bit on the low side 2. One relevant baseline may be missing: using a graphical model over the instance counts of different classes  Overall, I believe the paper makes a compelling case for the proposed method.  It is simple and substantially outperforms what seem to be reasonably strong baselines for the task on real-world problems.  The method is well-motivated, and the paper does a good job of articulating the careful consideration that went into designing the method, and why it might be expected to outperform existing approaches.  The experiments are also well-designed, focusing on answering the most important and interesting questions.  I could also imagine this work having significant impact, because many interesting tasks could be formulated in terms of multiset prediction.  I believe the paper does a commendable job of categorizing the different possible approaches to this problem, explaining the advantages of the proposed method, and empirically demonstrating those advantages.  The proposed method avoids the arbitrary-permutation-dependence of some other sequential prediction approaches, and avoids having to do RL over a long time horizon, as in RL-based methods.  I appreciated how these advantages were clearly articulated and then validated experimentally with targeted experiments.  I did have a doubt with regard to the “one-step distribution matching” baseline—this was tried in the experiments, and the paper cited the “lack of modeling of dependencies among the items” as a potential explanation for its poor performance, but I found this a bit unsatisfying.  I think it should be possible to define a graphical model where each node counts the number of instances of a particular class, and cliques model correlations between counts of different classes.  The node and clique potentials could then be learned so as to maximize the data likelihood.  Since this model may be non-trivial, and I do not have a citation for it, I do not see the lack of this baseline as an egregious oversight, however.  I also noticed that although the lack of a need to perform RL is claimed as a benefit of this method over [25], I think you could argue that the proposed method could be thought of as an approximation of a more natural method that would also require RL.  Specifically, the “most natural” version of the multiset loss function would be marginalized over all possible policy roll-outs.  However, it seems that in practice, the method just samples one roll-out, and optimizes the resulting loss with that roll-out fixed.  The resulting loss gradient is therefore biased, because it does not take into account how the sampled roll-out changes as the policy parameters change.  To un-bias the gradient, one would again have to resort to policy gradient.  If it turns out that neglecting the bias is fine in practice, then that is fine; however, it should probably be acknowledged.  On the other hand, I would like to point out that the choice to sample past states from the policy instead of the expert is a subtle but smart choice, and the paper both includes a citation as to why this is superior, and demonstrates empirically that this choice indeed outperforms the naive approach of sampling past states from the expert when evaluating the loss.  In terms of novelty, I would say that might be one of the weaker aspects of the work, since this is technically a rather straightforward method.  However, I think there is nonetheless significance in carefully and systematically designing a simple method to perform well for a given task, especially taking subtle considerations such as that mentioned above into account.  In summary, I think the clarity and simplicity of the method, combined with the compelling experimental results shown here, will make this work interesting to a significant cross-section of the NIPS audience.  POST-REBUTTAL COMMENTS  I think the paper should acknowledge the connection to previous methods (mentioned by reviewer 1) that employed a KL loss for similar problems.  Mentioning the potential applications to computer vision problems up-front may also help motivate the problem better, because 'multisets' may sound too abstract to many readers.  As for the issue of potential bias in the gradient, I am still a little unclear on this.  It seems like there are two ways to interpret this method: as an RL method, or as an online learning problem (e.g., learning to search).  I am more familiar with the former, but I vaguely understand that there is a regret-based analysis where the bias issue I brought up doesn't directly factor in, or may appear in some other guise.  Ideally, it would also be nice to have some clarity on this issue, though it may be too tangential for this submission.


Group Equivariant Capsule Networks
We present group equivariant capsule networks, a framework to introduce guaranteed equivariance and invariance properties to the capsule network idea. Our work can be divided into two contributions. First, we present a generic routing by agreement algorithm defined on elements of a group and prove that equivariance of output pose vectors, as well as invariance of output activations, hold under certain conditions. Second, we connect the resulting equivariant capsule networks with work from the field of group convolutional networks. Through this connection, we provide intuitions of how both methods relate and are able to combine the strengths of both approaches in one deep neural network architecture. The resulting framework allows sparse evaluation of the group convolution operator, provides control over specific equivariance and invariance properties, and can use routing by agreement instead of pooling operations. In addition, it is able to provide interpretable and equivariant representation vectors as output capsules, which disentangle evidence of object existence from its pose.

While previous work on capsules [1,2,3] identifies equivariance of the routing process as a desirable property, these methods do not guarantee equivariance. The goal if this paper is to create capsule networks with built-in equivariance.  The paper contains several interesting ideas, but lacks sufficient theoretical motivation and experimental support for the proposed architectural innovations. Several more or less independent changes are proposed (equivariant routing, pose normalization layers, spatial aggregation, combination with group convolution), and although each addition is motivated by a plausible sounding line of reasoning, ultimately the proposed innovations don't seem innevitable, and no rigorous ablation study is performed.  Although section 2 is very clearly written, I found it hard to understand section 3. It is not clear to me why simply summing the vectors in Fig 2b would be a problem (the result would be equivariant). Figure 2c seems like a very unnatural way to represent the data.   It seems like a lot of complexity in this paper can be removed by working with representations of G instead of G itself. Specifically, if the pose vectors (which is a misnomer if they are group elements) are taken to be vectors in a vector space V in which a (unitary) representation of G is defined, then M and delta can be simply defined as the vector mean and inner product, and the required properties will follow automatically (and this works for any group, not just SO(2)). The issue identified in section 3, where each vector is seen to rotate and move to a new place, can then be understood very simply as in [4] via the notion of induced representation.  I find it strange that the authors write "Since we take expressiveness from the trainable pose transformations to ensure equivariance and invariance, it is not to be expected that the proposed capsule networks using the proposed routing algorithms will achieve the same classification accuracies as their original counterparts" If these networks are not expected to work better, then what is the point? In general we would expect equivariant networks to work better on data with the appropriate invariances, as demonstrated in many previous works. A more likely explanation for why the network is not working well yet is that it has become a bit too complicated, using too many components that deviate far from the existing engineering best practices (i.e. CNNs with relus, batchnorm and skip connections, etc.).  For comparison with related work, results in MNIST-rot would be nice to see. This dataset has only 12k training samples. The reported number of 98.42% (obtained from 60k training samples, if I understand correctly) is not really competitive here (SOTA is 0.7% error [5]). Results on non-MNIST datasets would also be very welcome.  [1] Hinton et al. 2011, Transforming Auto-encoders [2] Sabour et al. 2017, Dynamic Routing Between Capsules [3] Hinton et al. 2018, Matrix Capsules with EM Routing [4] Cohen et al. 2016, Steerable CNNs [5] Weiler et al., 2017, Learning Steerable Filters for Rotation Equivariant CNNs   -------------------- Post author response edit:  Thank you for the clear headed author response. Although there is a lot to like about this paper, I will maintain my score because I think that the current evidence does not support the effectiveness of the method.   I still do not really understand the point about "pose normalization". I look forward to a future version of the paper where this is clarified.  Regarding representations of G, I should have been clear that the concept I had in mind is that of a "linear group representation" (https://en.wikipedia.org/wiki/Group_representation), not a parameterization of G. Indeed, the fact that a Lie group G is a manifold (whose points we cannot easily add / average) was the motivation for mentioning group representations. If instead of viewing poses as elements g in G, you view them as vectors v in V (where V is the vector space of a group representation), then one can average pose vectors v without any difficulty. Several papers in the equivariant networks literature now take this approach.


Proximal Graphical Event Models
Event datasets involve irregular occurrences of events over the timeline and are prevalent in numerous domains. We introduce proximal graphical event models (PGEMs) as a representation of such datasets. PGEMs belong to a broader family of graphical models that characterize relationships between various types of events; in a PGEM, the rate of occurrence of an event type depends only on whether or not its parents have occurred in the most recent history. The main advantage over state-of-the-art models is that learning is entirely data driven and without the need for additional inputs from the user, which can require knowledge of the domain such as choice of basis functions and hyper-parameters. We theoretically justify our learning of parental sets and their optimal windows, proposing sound and complete algorithms in terms of parent structure learning. We present efficient heuristics for learning PGEMs from data, demonstrating their effectiveness on synthetic and real datasets.

This paper deals with event model learning from an event dataset, by considering that the probability of an event depends on the occurrence of some other event (the "parent" events) in the recent history.  The Proximal graphical even model proposed in this paper is an extension of the Graphical event models of the literature, where the authors have added the explicit definition of the time window the parent events must occur to "generate" each target event. The authors proposes one learning algorithm decomposed in several steps : learning the windows for already known parents, then identifying the optimal parent set by a forward-backward algorithm. optimizing the windows for multiple parents simultaneously is one hard problem, so the authors proposed 2 heuristics, one simple one where each parent is treated independently, and another one where a block coordinate ascent strategy is used over the parent set. Experiments are performed with synthetic datasets where the more complex strategy doesn't seem to give better results than the first (independent) strategy. This last strategy is then used with real datasets and gives interesting results compared to competitive solutions.  Some questions or comments: - why considering instantaneous events in your event datasets where process mining algorithms can deal with events defined in time windows. Is it possible to extend GEM and PGEM in this context ? - GEM deal with "transitions" between events, but how do you deal with the "initial" distribution of events ?  - why considering the last time between an event and the end of the sequence in the set t_{xx} ??? in a "process" point of view, it should be the time between x and the "END" state ?  - in your PGEM definition, you restrict yourself with the occurence of one parent event in only one time window, could you define the occurence of B with a presence of A in one time window and the absence of A in another one ??? (so considering that A could be present twice in the parent list of B, with 2 different time windows ?)  - 3.1, equation 1. The log likelihood is defined for every value \lambda. \hat\lambda is the argmax of this log likehood rwrt \lambda. What your are defining in eqn 1 is the optimal value of the logL.  - line 170 : typo : the computation still NEED? ...."  - theorem 6 : is your assumption over 2^|U| realistic ?  - line 197 : can RUN algo.2 ?


Bias and Generalization in Deep Generative Models: An Empirical Study
In high dimensional settings, density estimation algorithms rely crucially on their inductive bias. Despite recent empirical success, the inductive bias of deep generative models is not well understood. In this paper we propose a framework to systematically investigate bias and generalization in deep generative models of images. Inspired by experimental methods from cognitive psychology, we probe each learning algorithm with carefully designed training datasets to characterize when and how existing models generate novel attributes and their combinations. We identify similarities to human psychology and verify that these patterns are consistent across commonly used models and architectures.

* Summary:  This paper provides an empirical study of the generalization properties of deep implicit generative models. Previous works have mostly focused on the mathematical generalization properties of such networks [Arora et al., ICML17], while previous empirical studies lacked the rigorous methodology of this paper.  This paper introduces a methodology inspired by neuroscience to probe such models, by using toy datasets with specified high-level features. For instance, for a dataset of images made of small dots, the number of dots and the colors of the dots in each image are such features, which can be easily assessed. The paper investigates the differences between the distribution of such features in the dataset and their distribution in the generated dataset, across different models (VAE/GAN), architectures (fully connected / convolutional) and datasets.  The patterns identified by the authors are the following: - Single features are generalized in a sort of convolutional way: the distribution "impulse response" of the algorithm to an input dirac distribution (parametrized by a real value, e.g. radius of circles in an image or proportion of red) behaves akin to a linear filter. When there are multiple diracs, the convolution effects still holds, with an enhancement effects for intermediate values when the diracs are close. This behaviour is close to previous neuroscientific findings. - Features are independent: modifying many other features does not change the distribution reponse of the algorithms when studying a single feature. - When multiple combinations of features are part of the dataset, the distribution responses keep the combinations in the original distribution (high recall), but generalize to new combinations when the number of combinations grows (precision decreasing).   * Opinion:  This is a paper of very good quality. Writing is very clear. I think that the value of this paper does not solely lie in its empirical findings - some of which are surprising and may spark debate - but also in the experimental methodology it proposes to assess the properties of generative models. This methodology would be a very significant contribution to help understand generalization for deep neural networks, provided it is reproducible in a proper fashion.  * Questions :  - Do the authors plan to release the experimental code along with the toy dataset (l.146)? At least, knowing the training scheme of all networks would be very helpful.  - A weak point of the paper is the lack of discussion of the sizes of the datasets with respect to the sizes of the models. How many layers are used, how many channels/dimensions per layer? It is not sure that these values are adequate measures of the capacity of networks, but reporting them would help anyway.  - The findings in sec 5 concerning the generalization growing with the number of combinations in the original distribution is very interesting. Is using absolute values (l. 229-257) for such combinations really relevant? Did the authors observe the same thresholds for varying architectures' sizes?  - In Figures 9B and 9D, there are significant variations in the core set of generated combinations: for instance, in D, green.red/cone.sphere has 7, while red.red/cylinder.cone has 38. Yet the input distribution seems to be evenly distributed among all combinations. What could explain such a discrepancy? Is it due to a small sample size due to the fact that the shapes were evaluated by human judgement (and there were only 3 judges, cf l.118)? In this case, are the values in the last column really significant? Is it consistent across all architectures and algorithms, or are there differences?  - I find very surprising that all results are consistent with both fully-connected networks and convolutional ones and VAE/GAN. There may be hidden biases in the methodology or the datasets in this case. What about other generative algorithms, such as PixelCNN?


IntroVAE: Introspective Variational Autoencoders for Photographic Image Synthesis
We present a novel introspective variational autoencoder (IntroVAE) model for synthesizing high-resolution photographic images. IntroVAE is capable of selfevaluating the quality of its generated samples and improving itself accordingly. Its inference and generator models are jointly trained in an introspective way. On one hand, the generator is required to reconstruct the input images from the noisy outputs of the inference model as normal VAEs. On the other hand, the inference model is encouraged to classify between the generated and real samples while the generator tries to fool it as GANs. These two famous generative frameworks are integrated in a simple yet efficient single-stream architecture that can be trained in a single stage. IntroVAE preserves the advantages of VAEs, such as stable training and nice latent manifold. Unlike most other hybrid models of VAEs and GANs, IntroVAE requires no extra discriminators, because the inference model itself serves as a discriminator to distinguish between the generated and real samples. Experiments demonstrate that our method produces high-resolution photo-realistic images (e.g., CELEBA images at 1024 2 ), which are comparable to or better than the state-of-the-art GANs.

Update:  I raised my score by two points because the rebuttal and reviews/comments revealed more differences that I originally noticed with respect to the AGE work, in particular in terms of the use of the KL divergence as a discriminator per example, and because the authors promised to discuss the connection to AGE and potentially expand the experimental section.  I remain concerned that the resulting model is not a variational auto-encoder anymore despite the naming of the model (but rather closer to a GAN where the discriminator is based on the KL divergence), and about the experimental section, which reveals that the method works well, but does not provide a rich analysis for the proposed improvements.  ---  The paper proposes an approach for adversarial learning in the context of variational auto-encoders. Rather than using a separate discriminator network, the work proposes a learning objective which encourages the encoder to discriminate between real data and generated data: it guides the approximate posterior to be close to the prior in the real data case and far from the prior otherwise. The approach is illustrated on the task of synthesizing high-resolution images, trained on the CelebA-HQ dataset.  First, high-quality image generation remains an important area of research, and as a result, the paper's topic is relevant to the community. Furthermore, the results are very good, comparable to state of the art, despite not using a discriminator network.  However, I believe the paper does not position itself strongly with respect to the cited work, AGE [34]. The authors highlight the following differences: "design of inference models, the training objects, and the divergence computations," but without detail. To me, the approaches seem quite similar: in both cases, the objective relies on decreasing the divergence between the posterior and the prior for real data, and increasing it for generated data; in both cases the chosen divergence measure is a KL divergence, and the reference (prior) distribution is a Gaussian; etc.. There are slight differences such as the use of an upper bound (m) on the divergence between the generated data posterior and the prior, but a discussion of why they might be needed is missing. Could you discuss this in your rebuttal?  A major point made in the write-up is that previous methods based on encoder-decoder architectures (without discriminators), including AGE, have obtained weaker results and that the submission is the first to generate high-resolution images. This result is promising, but I think it should come with an understanding of the differences to the previous works, highlighting which modifications have caused the improvement. Otherwise, the improvement could be attributed to better hyper-parameter tuning. Instead, an empirical comparison with the cited work, AGE, is not provided at all.  Other comments: * In lines 127-132, the use of E(x) to denote the KL divergence loss, as well as referring to E as the inference (encoder) model creates confusion. Same with E* later.  Summary: The current work presents good image synthesis results for an adversarially trained VAE architecture with no discriminator. However, the approach appears very similar to previous work, making it less relevant for the NIPS community.


A Structured Prediction Approach for Label Ranking
We propose to solve a label ranking problem as a structured output regression task. In this view, we adopt a least square surrogate loss approach that solves a supervised learning problem in two steps: a regression step in a well-chosen feature space and a pre-image (or decoding) step. We use specific feature maps/embeddings for ranking data, which convert any ranking/permutation into a vector representation. These embeddings are all well-tailored for our approach, either by resulting in consistent estimators, or by solving trivially the pre-image problem which is often the bottleneck in structured prediction. Their extension to the case of incomplete or partial rankings is also discussed. Finally, we provide empirical results on synthetic and real-world datasets showing the relevance of our method.

This paper presents an interesting approach to the label ranking problem, by first casting it as a Structured Prediction problem that can be optimized using a surrogate least square methodology, and then demonstrating an embedding representation that captures a couple of common ranking loss functions -- most notable being the Kendall-Tau distance.  Overall I liked the paper and found a decent mix of method, theory and experiments (though I would have liked to see more convincing experimentation as further detailed below). In particular I liked the demonstration of the Kendall tau distance and Hamming distances to be representable in this embedding formulation/  That said I had a few concerns with this work as well:  - Specifically the empirical results were not very convincing. While this may not have been a problem for a theory-first paper, part of the appeal of an approach like this it is supposed to work in practice. Unfortunately with the current (some what limited) set of experiments I am not entirely convinced.  For example: This only looked at a couple of very specific (and not particularly common loss functions) with the evals only measuring Kendall Tau. Instead metrics like MAP and NDCG are the more standard metrics typically used these days. Absence of any of those metrics or other standard metrics was quite concerning.  Coupled with the result that indicated that optimizing the specific metric does not always lead to the best results on other metrics is why more eval metrics would have helped paint a clearer picture.  Furthermore as the authors themselves point out: top-k rankings are a primary focus in most applications and towards this end the paper does not exactly provide a solution for this more practical problems or even discuss variants to tackle it. Furthermore there are no metrics or evals either on this important setting.  The datasets used in these evals also are not the most common or standard from the IR perspective and I would have liked to see more standard ranking datasets be used for the evaluation.  Lastly I would have liked to see more competitive baselines that capture performance of the different previous works in this field that may not be label-ranking based. This may help contrast this approach versus other methodologies. Would also be great to understand running time for the different methods compared.  ----  POST-AUTHOR FEEDBACK EDIT: Thank you to the authors for their response. I appreciate you taking time to clarify some of my concerns.  Regarding my main concern about the evaluation: Unfortunately I don't think I felt that was adequately addressed. I shoulder some of the blame for not not being more detailed so let me try to convey my thoughts in more detail below:  - The authors mention that their approach is specific  to label ranking and not LTR and other related problems. However I think that reduces the appeal of the paper since label ranking is a far less common problem than LTR with a lot more niche applications. If the sole focus was label ranking then I'd like the authors to have explained what problems can only be tackled by label ranking approaches and not by approaches from LTR or multi-class classification approaches.  - In particular the latter (multi-class classification) could easily be used as well to produce a "ranking" over the different labeled class. What I don't see is an evaluation justifying the approach for the niche cases multi-class classification cannot handle as well (say where there is a relationship among the labels).  - Lastly when I referred to previous approaches, I was thinking about the works by Thorsten Joachims and collaborators for example. I failed to see any mention of how well something like a structual SVM would do on this problem.  I feel the paper would be a lot stronger if it discussed (and ideally compared) against these existing approaches.


Boosting Black Box Variational Inference
Approximating a probability density in a tractable manner is a central task in Bayesian statistics. Variational Inference (VI) is a popular technique that achieves tractability by choosing a relatively simple variational approximation. Borrowing ideas from the classic boosting framework, recent approaches attempt to boost VI by replacing the selection of a single density with an iteratively constructed mixture of densities. In order to guarantee convergence, previous works impose stringent assumptions that require significant effort for practitioners. Specifically, they require a custom implementation of the greedy step (called the LMO) for every probabilistic model with respect to an unnatural variational family of truncated distributions. Our work fixes these issues with novel theoretical and algorithmic insights. On the theoretical side, we show that boosting VI satisfies a relaxed smoothness assumption which is sufficient for the convergence of the functional Frank-Wolfe (FW) algorithm. Furthermore, we rephrase the LMO problem and propose to maximize the Residual ELBO (RELBO) which replaces the standard ELBO optimization in VI. These theoretical enhancements allow for black box implementation of the boosting subroutine. Finally, we present a stopping criterion drawn from the duality gap in the classic FW analyses and exhaustive experiments to illustrate the usefulness of our theoretical and algorithmic contributions.

In the submission, the authors aim at developing a black-box boosting method for variational inference, which takes a family of variational distributions and finds a mixture of distribution in a given family that approximates a given posterior distribution well. The main keyword here is black-box; white-box, restricted approaches exist. In order to achieve their aim, the authors formulate a version of the Frank-Wolfe algorithm, and instantiate it with the usual KL objective of variational inference. They then derive a condition on the convergence of this instantiation that is more permissive than the usual smoothness and is based on the reformulation of the bounded curvature condition (Theorem 2). They also show how the constrained optimization problem included in the instantiation of Frank-Wolfe can be expressed in terms of a more intuitive objective, called RELBO in the submission. Finally, the authors propose a criterion of stopping the algorithm (Lemma 4). The resulting black-box algorithm is tested with synthetic data, Bayesian logistic regression, and Bayesian matrix factorization, and these experiments show the promise of the algorithm.  I am not an expert on boosting, but I enjoyed reading the submission and found the results interesting. I particularly liked the fact that the RELBO can be understood intuitively. I have a few complaints though, mostly about presentation. Someone like me (who is familiar with variational inference but not boosting nor Frank-Wolfe) might have appreciated the submission more if the authors had explained in more detail what the LMO objective attempts to do intuitively and how the formula at the bottom of page 5 is derived from the definition of LMO in equation (6), and the authors had described how one should implement the stopping criterion. I also struggled to follow the discussion right after Theorem 2, and I couldn't quite see where the delta relaxation in (7) is used in the authors' algorithm. Finally, the held-out test likelihood for Bayesian matrix factorization does not seem to show that Boosted BBVI beats BBVI, but the text (329-330) says it differently. This made me very confused.  * equation (3), p3: p(x,z) ===> p(z|x) * What do you mean by L-smooth? * boldface q0 in Algorithm 1 ===> q^0 * second display, p6: D^KL(s || ...Z) ===> D^KL(s || .../Z)


FD-GAN: Pose-guided Feature Distilling GAN for Robust Person Re-identification
Person re-identification (reID) is an important task that requires to retrieve a person's images from an image dataset, given one image of the person of interest. For learning robust person features, the pose variation of person images is one of the key challenges. Existing works targeting the problem either perform human alignment, or learn human-region-based representations. Extra pose information and computational cost is generally required for inference. To solve this issue, a Feature Distilling Generative Adversarial Network (FD-GAN) is proposed for learning identity-related and pose-unrelated representations. It is a novel framework based on a Siamese structure with multiple novel discriminators on human poses and identities. In addition to the discriminators, a novel same-pose loss is also integrated, which requires appearance of a same person's generated images to be similar. After learning pose-unrelated person features with pose guidance, no auxiliary pose information and additional computational cost is required during testing. Our proposed FD-GAN achieves state-of-the-art performance on three person reID datasets, which demonstrates that the effectiveness and robust feature distilling capability of the proposed FD-GAN. ‡ ‡
: The image encoder in the FD-GAN is trained to learn robust identity-related and poseunrelated representations with assistance of pose-guided image generator and discriminators. During inference, it does not need pose information and additional computational cost.
Generative adversarial network (GAN) is gaining increasing attention for image generation. Recently, some works exploited GANs' potential on aiding current person reID algorithms. Zheng et al. [3] proposed a semi-supervised structure which learns generative images with label smoothing regularization for outliers (LSRO) regularization. PTGAN [4] was proposed to bridge the domain gap between separate datasets. In addition to image synthesis, GAN can be used for representation learning as well. In this work, we propose a novel identity-related representation learning framework for robust person re-identification.
The proposed Feature Distilling Generative Adversarial Network (FD-GAN) maintains identity feature consistency under pose variation without increasing the complexity of inference (illustrated in Figure 1). It adopts a Siamese structure for feature learning. Each of the branch consists of an image encoder and an image generator. The image encoder embeds person visual features given the input images. The image generator generates new person images conditioned on the pose information and the input person features by the encoder. Multiple discriminators are integrated in the framework to distinguish inter-branch and intra-branch relations between generated images by the two branches.
The proposed identity discriminator, the pose discriminator, and the verification classifier together with a reconstruction loss and a novel same-pose loss jointly regularizes the feature learning process for achieving robust person reID. With the adversarial losses, identity-irrelevant information, such as pose and background appearance, in the input image is mitigated from the visual features by the image encoder. More importantly, during inference, additional pose information is no longer needed and saves additional computational cost. Our method outperforms previous works in three widely-used reID datasets, i.e. Market-1501 [5], CUHK03 [6] and DukeMTMC-reID [7] datasets.
Overall, this paper has the following contributions. 1) We propose a novel framework, FD-GAN, to learn identity-related and pose-unrelated representations for person re-identification with posevariation. Unlike existing alignment or region-based learning methods, our framework does not require extra auxiliary pose information or increase the computational complexity during inference. 2) Although person image generation is an auxiliary task for our framework, the generated person images by our proposed method show better quality than existing specific person-generation methods.
3) The proposed FD-GAN achieves state-of-the-art re-identification performance on Market-1501 [5], CUHK03 [6], and DukeMTMC-reID [7] datasets.

This paper describes a GAN approach to addressing a common and important problem in person re-identification: inter- and intra-view pose variation. The technique, in extreme synthesis, uses a generative model to implicitly marginalize away pose- and background-dependent information in the feature representaiton to distill a representation that is invariant to both, but still discriminative for person identities. Pose is represented as the spatial configuration of landmarks, and during training person images conditioned on a randomly selected pose are generated from image encodings. These generated images are fed to multiple adversarial discriminators that determine if the generated image is real/false, if the pose in a real/fake image is accurate, and if two feature embeddings correspond to the same person. Experimental results are given on multiple, important benchmark datasets and show significant improvement over the state-of-the-art.   Clarity, quality, and reproducibility: The clarity of exposition is quite good. The authors do a good job of describing a complicated combination of modules and losses, with in my opinion the right degree of precision and level of detail. There are some minor typos and grammar errors throughout, but not to distraction. The quality of the technical exposition and experimental evaluation is similarly high, and I appreciated how each component and loss term is methodically and incrementally presented in section 3.3.  I feel like the results of the paper would be challenging to reproduce, however this is mainly due to the large number of moving parts and not to lack of clarity or missing details.  On a more critical note, and related to reproducibility, generative adversarial architectures with just a *single* adversarial loss are notoriously unstable during training. The proposed system has five terms in the loss, and three phases of (what appears to be) carefully crafted training schedule. Was this training pipeline, with its myriad hyperparameters, derived on a validation re-identification dataset?  More insight into the behavior of the system at training time would be a useful contribution. Also, some ablation analysis showing the incremental contributions each loss would lend credibility to the need for each of the adversarial and identity modules and losses.  Novelty: This work uses the idea of generative adversarial models and applies it in a novel and clever way to learn identity discriminative feature representations that are robust to pose and background variations -- probably the two most significant challenges in person re-identification. This type of adversarial invariance learning has not been applied in person re-identification, and I am unaware of similar approaches in other applications (other than DR-GAN for pose-invariant face recognition, included in the comparative evaluation). The authors do an excellent job of positioning their work in the context of the state-of-the-art and analyzing the advantages of their approach.  Significance and fit with NIPS: The experimental results on multiple, modern, and large scale re-identification benchmarks show a significant improvement over the state-of-the-art. Though the proposed system is based on multiple known techniques, the combination is novel and well thought-out. This paper is fundamentally an architecture engineering paper, but an extremely well-executed one. It is likely to have significant impact in the person re-identification community, and could potentially contribute insights to adversarial invariant feature learning in the broader NIPS world.  Some specific comments and questions:   1. Figures 2 and 3 are gorgeous and do a good job of explaining the     complexities of the components. However their size has been     reduced to the limits of printed legibility (likely due to space).  Line 19: widely --> wide Line 103: regularizes --> regularize Line 113: same person's another image --> another image of the same person Line 210: integratie --> integrate  POST REBUTTAL: The rebuttal addressed my main concerns (and I was already quite positive). The clarifications about training and crossvalidation, plus the additional ablation table, make the paper even stronger.


PointCNN: Convolution On X -Transformed Points
We present a simple and general framework for feature learning from point clouds. The key to the success of CNNs is the convolution operator that is capable of leveraging spatially-local correlation in data represented densely in grids (e.g. images). However, point clouds are irregular and unordered, thus directly convolving kernels against features associated with the points will result in desertion of shape information and variance to point ordering. To address these problems, we propose to learn an X -transformation from the input points to simultaneously promote two causes: the first is the weighting of the input features associated with the points, and the second is the permutation of the points into a latent and potentially canonical order. Element-wise product and sum operations of the typical convolution operator are subsequently applied on the X -transformed features. The proposed method is a generalization of typical CNNs to feature learning from point clouds, thus we call it PointCNN. Experiments show that PointCNN achieves on par or better performance than state-of-the-art methods on multiple challenging benchmark datasets and tasks.

Paper summary: - This work proposes a new neural network layer to perform convolution-like operations on unordered point cloud data. The main crux of the technique is the transformation of given unordered points into a canonical representation using a learned matrix multiplication and then a standard convolution is applied on those canonically represented points. Wide range of experiments on classification and segmentation tasks validate the use of the proposed technique in comparison to existing techniques.   Strengths: - Simple yet generic technique for processing point cloud data with unordered points. - Applications on both classification and segmentation on a wide range of datasets. - Very good performance compared to existing state-of-the-art techniques.   Weaknesses: - A main weakness of this work is its technical novelty with respect to spatial transformer networks (STN) and also the missing comparison to the same. The proposed X-transformation seems quite similar to STN, but applied locally in a neighborhood. There are also existing works that propose to apply STN in a local pixel neighborhood. Also, PointNet uses a variant of STN in their network architecture. In this regard, the technical novelty seems limited in this work. Also, there are no empirical or conceptual comparisons to STN in this work, which is important. - There are no ablation studies on network architectures and also no ablation experiments on how the representative points are selected. - The runtime of the proposed network seems slow compared to several recent techniques. Even for just 1K-2K points, the network seem to be taking 0.2-0.3 seconds. How does the runtime scales with more points (say 100K to 1M points)? It would be good if authors also report relative runtime comparisons with existing techniques.   Minor corrections: - Line 88: "lose" -> "loss". - line 135: "where K" -> "and K".   Minor suggestions: - "PointCNN" is a very short non-informative title. It would be good to have a more informative title that represents the proposed technique. - In several places: "firstly" -> "first". - "D" is used to represent both dimensionality of points and dilation factor. Better to use different notation to avoid confusion.   Review summary: - The proposed technique is sensible and the performance on different benchmarks is impressive. Missing comparisons to established STN technique (with both local and global transformations) makes this short of being a very good paper.   After rebuttal and reviewer discussion: - I have the following minor concerns and reviewers only partially addressed them.  1. Explicit comparison with STN: Authors didn't explicitly compare their technique with STN. They compared with PointNet which uses STN. 2. No ablation studies on network architecture. 3. Runtimes are only reported for small point clouds (1024 points) but with bigger batch sizes. How does runtime scale with bigger point clouds?  Authors did not provide new experiments to address the above concerns. They promised that a more comprehensive runtime comparison will be provided in the revision. Overall, the author response is not that satisfactory, but the positive aspects of this work make me recommend acceptance assuming that authors would update the paper with the changes promised in the rebuttal. Authors also agreed to change the tile to better reflect this work.


Attention in Convolutional LSTM for Gesture Recognition
Convolutional long short-term memory (LSTM) networks have been widely used for action/gesture recognition, and different attention mechanisms have also been embedded into the LSTM or the convolutional LSTM (ConvLSTM) networks. Based on the previous gesture recognition architectures which combine the threedimensional convolution neural network (3DCNN) and ConvLSTM, this paper explores the effects of attention mechanism in ConvLSTM. Several variants of ConvLSTM are evaluated: (a) Removing the convolutional structures of the three gates in ConvLSTM, (b) Applying the attention mechanism on the input of ConvLSTM, (c) Reconstructing the input and (d) output gates respectively with the modified channel-wise attention mechanism. The evaluation results demonstrate that the spatial convolutions in the three gates scarcely contribute to the spatiotemporal feature fusion, and the attention mechanisms embedded into the input and output gates cannot improve the feature fusion. In other words, ConvLSTM mainly contributes to the temporal fusion along with the recurrent steps to learn the long-term spatiotemporal features, when taking as input the spatial or spatiotemporal features. On this basis, a new variant of LSTM is derived, in which the convolutional structures are only embedded into the input-to-state transition of LSTM. The code of the LSTM variants is publicly available 2 .

SUMMARY:  This paper proposes a pipeline combining Res3D-3DCNN, convLSTM, MobileNet-CNN hybrid architecture for performing gesture recognition.  In particular, it explores the integration of pooling and neural attention mechanisms in ConvLSTM cells.  Four convLSTM variants are compared, which place pooling and attention mechanisms at different locations inside the cell. The pooling leads to a somewhat novel LSTM/convLSTM hybrid architecture.  Finally, an attention-inspired gating mechanism is proposed, with some differences to the formulation in [5].  The proposed architecture is evaluated on the Jester and ISOGD data sets and achieves state-of-the-art on the RGB-only setting of IsoGD.  QUALITY:  In the LSTM gates, fully connected weight matrices and matrix multiplication are used. Are there good reasons for doing this? In the original LSTM paper [3], a two vector Hadamard product is proposed (section II.A on the forward pass) instead of matrix multiplication. It will be of interest to compare the matrix-matrix or matrix-vector Hadamard-products in the gates. Following [3] it could also be interesting to explore gating based on output values instead of the cell state. The proposed max-pooling approach should allow this given that same padding was used in the convolutions, so that the spatial resolution inside and outside of the cell should remain the same.  Published attention mechanisms have thus far been based on the notion of probability distributions, e.g. in [r6], [r7] or even the cited [5] on which the current attention mechanism is based.  However, the proposed "attention" mechanism in equation (22) breaks the probabilistic interpretation by using a max instead of a sum operation.  The explanation given in 158-159 is not very clear, why using a max (and not a sum) will distribute the scores between 0-1.   Experimentation wise, all proposed modifications have been tested.  Additionally a comparison of the attention weights used in variants (c) and possibly a classical soft attention formulation as described in equation (18) would have been interesting in order to enable readers to asses the newly proposed mechanism from eq. (22). Overall the results are state of the art and suffice to support that the authors successfully reduced the number of convLSTM parameters though it is hard to asses the modified attention mechanism proposed by the authors.  In particular, looking at the supplementary material results, it looks as if (since the subjects are all stationary and the only movement in the scene is relevant to the hand gesture) that a simple flow detection would suffice.  To prove that the attention mechanism is actually working, one would need a baseline comparing against optical flow / movement detection.  Also is there some border effects in the attention?  There seem to be very strong response in the bottom edge of the scene for almost all samples?  Some comparisons to other methods are missing, e.g. the experimental results on the Jester-Data set are not compared to  state-of-the-art; they are better than [r4] but worse than [r2].  [r2] reports an accuracy of 96.33% on the Jester V1 data set (using flow and RGB) while [r1] reports an accuracy of 80.96% on the IsoGD-Data set.  The paper provides a comparison only to [8], and only to the RGB results, which are significantly worse (51.31% / 58.65% for RGBD).  Finally, some statistical analysis would make the results more convincing.           CLARITY: The paper is relatively easy to read and follow, though some important details are omitted, e.g.  What are the performance metrics being used for evaluation? What variant of gradient descent is used?  ORIGINALITY:  Attention has been shown to be beneficial in vision problems.  The pooling approach is somewhat interesting.   Additional related works on gesture recognition are given below in [r1, r2].  Other related works to convLSTM is [r5] which presents a convGRU; an interesting aside is [r3], which found that recurrent dropout may be applied on past state values during gate and candidate value computation. This means that for an RNN to function, past states must not be available in their original values at the gates.  This may be why GlobalAveragePooling can be regarded as an interesting choice in the convLSTM case when computing gate values.    SIGNIFICANCE:   The main contribution of the paper is the experimentation; the paper tests four variants of LSTMs to test the effects of attention in LSTMs.  It is found that spatial convolutions in the LSTM gates do not contribute to spatiotemporal feature fusion; furthermore, attention mechanisms embedded into the input and output gates also do not improve the feature fusion.  As such, the authors make a recommendation for a new cell architecture which reduces the number of required weights, leading to smaller memory footprints and less training time. Such a cell may also be interesting for those working in action recognition and video understanding.  The work adds to the body of literature for anyone working on integrating CNNs and recurrent architures.  EXTRA REFERENCES:  [r1] Gesture Recognition: Focus on the Hands by Pradyumna Narayana and J. Ross Beveridge in CVPR 2018 [r2] Motion Fused Frames: Data Level Fusion Strategy for Hand Gesture Recognition by Okan Köpüklü and Neslihan Köse and Gerhard Rigoll in CVPR Workshops 2018 [r3] Recurrent Dropout without Memory Loss by Stanislau Semeniuta, Aliaksei Severyn, Erhardt Barth in Proceedings of COLING 2016 [r4] Temporal Relational Reasoning in Videos by Bolei Zhou and Alex Andonian and Antonio Torralba  https://arxiv.org/pdf/1711.08496.pdf [r5] Deep Learning for Precipitation Nowcasting: A Benchmark and A New Model by Xingjian Shi et al. in (NIPS 2017) [r6] Listen, Attend and Spell by Chan, William and Jaitly, Navdeep and Le, Quoc V. and Vinyals, Oriol in 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) [r7] Dzmitry Bahdanau, Kyunghyun Cho, and Yoshua Bengio.  Neural Machine Translation by Jointly Learning to Align and Translate. In ICLR 2015.


To Trust Or Not To Trust A Classifier
Knowing when a classifier's prediction can be trusted is useful in many applications and critical for safely using AI. While the bulk of the effort in machine learning research has been towards improving classifier performance, understanding when a classifier's predictions should and should not be trusted has received far less attention. The standard approach is to use the classifier's discriminant or confidence score; however, we show there exists an alternative that is more effective in many situations. We propose a new score, called the trust score, which measures the agreement between the classifier and a modified nearest-neighbor classifier on the testing example. We show empirically that high (low) trust scores produce surprisingly high precision at identifying correctly (incorrectly) classified examples, consistently outperforming the classifier's confidence score as well as many other baselines. Further, under some mild distributional assumptions, we show that if the trust score for an example is high (low), the classifier will likely agree (disagree) with the Bayes-optimal classifier. Our guarantees consist of non-asymptotic rates of statistical consistency under various nonparametric settings and build on recent developments in topological data analysis.

This paper proposes a "trust" score that is supposed to reliably identify whether a prediction is correct or not. The main intuition is that the prediction is more reliable if the instance is closer to the predicted class than other classes. By defining alpha-high-density-set, this paper is able to provide theoretical guarantees of the proposed algorithm, which is the main strength of this paper. This paper proceeds to evaluate the "trust" score using a variety of datasets. One cool experiment is to show that the "trust" score estimated from deeper layers than lower layers.  My major concern about this paper lies in the motivation behind the proposed score. Trust is certainly an important problem for our research community to work on. But I find this paper abuses this term, "trust". In general, trust should involve some notion of humans/users/agents. One definition in Lee and See, 2004 [1] of trust is "the attitude that an agent will help achieve an individual’s goals in a situation characterized by uncertainty and vulnerability". It is concerning that the "trust" score in this paper does not involve any consideration of the end user. For instance, the score will fall in any range and it is unclear that users or experts can determine whether they should trust the classifier based on this score.   A percentile adaptation could help alleviate this issue, which is how this paper conducts the evaluation. However, although the percentile adaptation seems to make the proposed score more interpretable, it carries very different information from calibration: the proposed score only guarantees that instances with high "trust" scores should be more likely to be correct, but the 90 percentile in "trust" score does not necessarily lead to 90% accuracy. This further shows that it can be challenging for any agent to make sense of the proposed "trust" score, even though the precision-percentile curves look nice.  Another difference from calibration that this paper emphasizes is that the ordering preserving property, but this property seems to be a limitation of the current calibration approach. The goal of calibration is that instances with a certain confidence score lead to the same accuracy. So a calibrated classifier may not optimize this precision-percentile curve. Again, I do not find the notion of "trust" score in this paper well motivated. This paper would have been stronger if it can articulate the notion of "trust" and its motivation and difference with confidence with the subject of trusting in mind.  Some relatively minor concerns about the experiment that requires clarification/explanation:  1) How is the percentile computed? Based on the description, it seems that the percentile is determined based on the test set, which seems rather strange. It would be natural to determine the percentile based on the training set.  2) The interpretation of percentile seems to be different from the normal interpretation. Does the highest trust score fall in the 100 percentile or the 0 percentile?  3) What are the chosen alphas? It seems that how well this metric behaves is highly dependent on the geometry space. One can also build a modified nearest-neighbor classifier based on the proposed score. How is the performance of the proposed score in the experiments related to the performance of that modified nearest-neighbor classifier?  4) Interpretable machine learning seems to be an area that is clearly related, but not really cited in the references. For instance, Why should I trust you?: Explaining the Predictions of Any Classifier by Ribeiro, Singh, and Guestrin; Examples are not Enough, Learn to Criticize! Criticism for Interpretability by Kim, Khanna, and Koyejo.  Also, references are not sorted alphabetically.  [1] John D. Lee and Katrina A. See, "Trust in Automation: Designing for Appropriate Reliance", in Human Factors.  I have read the rebuttal. I think that this paper is onto something interesting, but it fails to articular what the proposed ranking is for and how it is superior/complementary to calibration from a human perspective. I would caution against calling this trust.


Stochastic Composite Mirror Descent: Optimal Bounds with High Probabilities
We study stochastic composite mirror descent, a class of scalable algorithms able to exploit the geometry and composite structure of a problem. We consider both convex and strongly convex objectives with non-smooth loss functions, for each of which we establish high-probability convergence rates optimal up to a logarithmic factor. We apply the derived computational error bounds to study the generalization performance of multi-pass stochastic gradient descent (SGD) in a non-parametric setting. Our high-probability generalization bounds enjoy a logarithmical dependency on the number of passes provided that the step size sequence is square-summable, which improves the existing bounds in expectation with a polynomial dependency and therefore gives a strong justification on the ability of multi-pass SGD to overcome overfitting. Our analysis removes boundedness assumptions on subgradients often imposed in the literature. Numerical results are reported to support our theoretical findings.

The paper presents a high probability analysis of SGD for non-smooth losses, with weak assumptions on domain and gradients. It presents many different results, some of them are very interesting while some others are nice to have but not surprising at all.  In details:  - Section 3.1 presents high probability convergence rates for convex smooth functions. The core trick is to show that the iterates of SGD are (almost) bounded with high probability for square summable stepsizes. This result is not surprising at all: classic results on SGD already proved convergence with probability 1 even under weaker assumptions (i.e. non-convex functions with well-behaved gradients, see for example [6]) and through the same reasoning. The high probability bounds are nice to have, but nothing earth-shattering.  - Section 3.2 has similar results for strongly convex functions. These are even less suprising: changing the proof of [17] to make it work for smooth losses is a simple excercise that many of us have already done on their own. The high probability bounds for strongly objective functions are well-known, even in the composite mirror descent algorithm. Also, despite the claims in lines 274-275, removing the boundedness assumption on the gradients to obtain high probability bounds is trivial: It is enough to add a projection step into the ball where the optimal solution lives, that is always known using f(0, z_t)+r(0) and the strong convexity constant that you assumed to know. Indeed, this is how the Pegasos software was analyzed and implemented, [Shalev-Shwartz et al. ICML'07] (not cited). The projection step results in empirical faster convergence, better resistance to mispecified stepsizes, and even with better constants in the convergence rate. So, not using a projection step is actually a very bad idea. Overall, this is also a nice to have result, but not too strong.  - Section 4 presents the application of these results to prove generalization bounds for a multiple pass procedure that minimizes the unregularized empirical error. The obtained convergence rate matches the one obtained in Theorem 3 in [Orabona, NIPS'14] (not cited) with worst constants, yet here the authors don't assume bounded gradients and run multiple passes. I found this result very interesting, probably the most important one in the paper. As said, a way to achieve this rate without tuning stepsizes was known, but the fact that SGD achieves this rate after multiple passes, with a very weak dependency on the number of passes, is somehow suprising to me and it improves the result obtained with the stability analysis of SGD.  Overall, in my opinion the result presented in Section 4 warrants the publication of this paper. Also, it would be nice to see less overselling about the bounded gradients business.


Virtual Class Enhanced Discriminative Embedding Learning
Recently, learning discriminative features to improve the recognition performances gradually becomes the primary goal of deep learning, and numerous remarkable works have emerged. In this paper, we propose a novel yet extremely simple method Virtual Softmax to enhance the discriminative property of learned features by injecting a dynamic virtual negative class into the original softmax. Injecting virtual class aims to enlarge inter-class margin and compress intra-class distribution by strengthening the decision boundary constraint. Although it seems weird to optimize with this additional virtual class, we show that our method derives from an intuitive and clear motivation, and it indeed encourages the features to be more compact and separable. This paper empirically and experimentally demonstrates the superiority of Virtual Softmax, improving the performances on a variety of object classification and face verification tasks.

The paper proposes a simple technique for improved feature learning in convolutional neural networks. The technique consists of adding a “negative” virtual class to CNN training on classification tasks with the softmax loss function. The authors evaluate their approach on a range of computer vision datasets, (CIFAR10/100/100+, LFW, SLLFW, CUB200, ImageNet32) and find that it outperforms simple baselines on all of them, and outperforms more complicated state-of-the-art techniques on most of them. The authors also present an analysis from a few different standpoints as to why their method is effective.  Strengths:  - The technique proposed by the authors is extremely simple to implement (just a one line change in existing code would suffice, as far as I can tell).  - Their technique performns well across a range of datasets, often outperforming more complicated approaches.   Weaknesses:  - I am not entirely convinced by any of the analysis presented in the paper. Section 5.1 seems to particularly lack rigor, as it ignores most of the terms when studying an objective being optimized. The authors acknowledge this, but have still included this analysis in the paper. The analysis in Section 5.2 also make a number of approximations (these are more reasonable, however).  - The paper would benefit from some minor edits in English style/grammar. For example, in line 16-17: “While, many research works take” -> omit the “while”.   In the end, I feel that the simplicity of the method, coupled with its strong performance on a large number of datasets merits an acceptance. However, the paper could be greatly improved with a better / more rigorous analysis of why it works well.   Other comments:  - Figure 2: What exact visualization technique is being used here? Would be good to mention that in the figure caption.  - The authors criticise L-softmax and A-softmax for requiring an annealing-like training procedure, but this method itself has a very specific learning rate schedule for experiments on CIFAR and Face Verification.


Nonparametric Bayesian Lomax delegate racing for survival analysis with competing risks
We propose Lomax delegate racing (LDR) to explicitly model the mechanism of survival under competing risks and to interpret how the covariates accelerate or decelerate the time to event. LDR explains non-monotonic covariate effects by racing a potentially infinite number of sub-risks, and consequently relaxes the ubiquitous proportional-hazards assumption which may be too restrictive. Moreover, LDR is naturally able to model not only censoring, but also missing event times or event types. For inference, we develop a Gibbs sampler under data augmentation for moderately sized data, along with a stochastic gradient descent maximum a posteriori inference algorithm for big data applications. Illustrative experiments are provided on both synthetic and real datasets, and comparison with various benchmark algorithms for survival analysis with competing risks demonstrates distinguished performance of LDR.

The paper proposes a survival regression method for competing risks based on generalizing exponential distributions by using scale mixtures with gamma variables, giving Lomax distributions for the competing event times. This is further extended so that each competing event time can be divided into latent causes, basically using the same racing "trick" (taking minimum of the latent times) and gamma process. This allows some non-linearity in the covariate associations to the event times or hazards, since min-function is non-linear. A Gibbs sampling algorithm for full posterior inference and a MAP estimation algorithm are detailed in the Appendix. Experiments on synthetic data and real data are presented, showing good performance compared to some alternatives.  The paper introduces an interesting parametric method for competing risk survival regression. Overall, it is well-written and clear. I'm not sure if it brings anything drastically new to survival analysis, but the methodology seems reasonable and possibly useful. The way to decompose a risk into latent causes seems especially interesting contribution.  Main comments for possible improvements of the paper: (1) It's not really true that one can't tell how covariates affect the survival in Gaussian process models, although, of course, with flexible non-linear models and/or high-dimensional covariates it gets more difficult. For low-dim. example, see Joensuu et al. Risk of recurrence of gastrointestinal stromal tumour after surgery: an analysis of pooled population-based cohorts, Lancet Oncology, 2012. It would have been nice to have GP model(s) included in the results. (2) It's not very clear what is the benefit of the Lomax distribution for the sub-event times rather than any other parametric assumption (except over the exponential model, which has only a single parameter and leads to a constant baseline hazard model). It it mainly computational convenience in the availability of Gibbs sampling scheme? (How important is this when we now have probabilistic programming languages that are usually relatively efficient for (at least well-identifiable continuous parameter) regression models?) (3) The relation of the proposed approaches to previous literature could be more clearly delineated. Is is so that the Exponential racing is previously published but Lomax racing (and Lomax delegate racing) is original to this paper? No previous approaches to find latent causes of survival are discussed. (4) The interpretation of latent components is not easy/unambiguous as evident in the text as they are varyingly discussed as accounting for non-linearities or for subtypes of a competing risk.  Minor comments: * Non-monotonic covariate effects don't necessarily break the PH assumption, but rather the linearity assumption? * I found the discussion around Equation 3 somewhat confusing; it tries to explain the data augmentation way of computing missing information/censored data, but didn't seem very clear. * Intuitively (so could be wrong...), with a model that takes min. over linear components, one would think that two equally weighted components would be reasonable in the Synthetic data 2, since the risk functions are symmetric? * typo: p.4, line 169: "Lamax" * Is the code available or will it be made available?  Update after author feedback: This seems an interesting contribution for competing risks analysis and the author seem to acknowledge the main concerns of the reviewers in their response. (As a clarification to my point (4) above, if I remember correctly I meant something like that it's probably not really identifiable from data if there is "real" non-linearity of covariate effects or if the non-linearity arises from a combination of multiple linear latent causes. This might be important when interpreting the model inferences.)


Learning towards Minimum Hyperspherical Energy
Neural networks are a powerful class of nonlinear functions that can be trained end-to-end on various applications. While the over-parametrization nature in many neural networks renders the ability to fit complex functions and the strong representation power to handle challenging tasks, it also leads to highly correlated neurons that can hurt the generalization ability and incur unnecessary computation cost. As a result, how to regularize the network to avoid undesired representation redundancy becomes an important issue. To this end, we draw inspiration from a well-known problem in physics -Thomson problem, where one seeks to find a state that distributes N electrons on a unit sphere as evenly as possible with minimum potential energy. In light of this intuition, we reduce the redundancy regularization problem to generic energy minimization, and propose a minimum hyperspherical energy (MHE) objective as generic regularization for neural networks. We also propose a few novel variants of MHE, and provide some insights from a theoretical point of view. Finally, we apply neural networks with MHE regularization to several challenging tasks. Extensive experiments demonstrate the effectiveness of our intuition, by showing the superior performance with MHE regularization.

[Summary] The over-parameterization nature of neural networks has an undesirable consequence that many units become highly correlated after model training. To reduce the redundancy in representation, this paper extends some recent work on diversity regularization in neural networks by proposing the so-called hyperspherical potential energy defined on the Euclidean distance or the angular distance, which, when minimized, helps to increase the diversity of the input weights of different neurons and hence reduce the redundancy. The regularized loss function contains two regularization terms corresponding to the hidden units and the output units, respectively.  [Quality] Note that only the normalized weight vectors lie on the surface of the unit hypersphere. The unnormalized weight vectors generally do not. However, what actually contributes to the computation by each unit (neuron) in the neural network is the unnormalized weight vector. So two normalized weight vectors that are close to each other on the surface of the hypersphere may not actually be close when we consider the unnormalized weight vectors. How does this discrepancy affect the technical soundness of the proposed method?  [Clarity] It is a bit misleading to say “the diversity of neurons” or “the neurons are more diverse”. I think by “neuron” you actually mean “the input weights of the neuron”.  Figure 2 shows an example with only two neurons. Suppose there are many more neurons. How can we ensure that the virtual neurons all reside in the same half-space like that in Figure 1?  It is said in Section 3.7 that previous methods based on orthogonality/angle-promoting regularization model diversity regularization at a more local level while the proposed method based on MHE regularization achieves it in a more top-down manner. I don’t understand what it means by “local level” and “top-down manner” here. Please elaborate.  [Originality] There exist some previous works taking the orthogonality/angle-promoting regularization approach. The novelty of this work is in the MHE regularization terms.  [Significance] The empirical results generally look promising.  The theoretical analysis in Section 4 seems to imply that reducing the hyperspehical energy and hence increasing the diversity is good as it is closely related to improvement in generalization (Section 4.2). However, from the objective function in equation (4), it should be noted that the interplay between data fitting and hyperspherical energy minimization is crucial to achieving good performance. Among other things, finding the proper regularization parameters \lambda_h and \lambda_o is essential. Figure 3 shows the sensitivity analysis for CIFAR-100 with the CNN-9 network model by varying the value of the hyperparameters (I suppose it means both hyperparameters have the same value). What is not known is whether the hyperparameters are sensitive to the dataset and model used. Does changing either the dataset or the model require substantial effort in finding the right values for the hyperparameters?   There are some language errors, e.g., L9: “as even as possible” L26: “that principled guides” L28: “Another stream of works seek to” L37: “geodesic distances … plays” L80: “class-imbalance” L116: “equivalent to optimize” L145: missing “.” after “redundancy” L218: “uniformly distribution” L267: “Results is given” L268: “both … outperforms” L278: “Both … performs” L298: “the our” L302: “can yields” L359: “complementary”, not “complimentary” L364: “as describe”; “MHE complete” Please proofread the paper more thoroughly.  [Post-rebuttal comments]  I have read the author feedback and the other two reviews.  Regarding my comment on using unnormalized weight vectors, I do know the recent research on decoupling intra-class variation from inter-class variation [22-25]. My concern is that MHE (not angular-MHE) does not just focus on the angle when formulating the objective function. The formulation for angular-MHE is more correct. However, in the experiments, A-MHE is not consistently better than MHE. Deeper analysis and understanding of this is necessary.  For my other questions, the author has generally provided satisfactory answers.  I have increased my overall score from “5” (marginally below the acceptance threshold) to “6” (marginally above the acceptance threshold), but I don't think I am ready to vote for anything higher than “6”.


Bayesian Inference of Temporal Task Specifications from Demonstrations
When observing task demonstrations, human apprentices are able to identify whether a given task is executed correctly long before they gain expertise in actually performing that task. Prior research into learning from demonstrations (LfD) has failed to capture this notion of the acceptability of an execution; meanwhile, temporal logics provide a flexible language for expressing task specifications. Inspired by this, we present Bayesian specification inference, a probabilistic model for inferring task specification as a temporal logic formula. We incorporate methods from probabilistic programming to define our priors, along with a domain-independent likelihood function to enable sampling-based inference. We demonstrate the efficacy of our model for inferring specifications with over 90% similarity between the inferred specification and the ground truth, both within a synthetic domain and a real-world table setting task.

Summary: The authors extend Bayesian concept learning to infer Linear Temporal Logic (LTL) specifications from demonstrations. The concept space is that of a finite subset of all possible well formed formulas of LTL constrained to a conjunction between three well founded structures for capturing tasks (Global satisfaction, Eventual completion, Temporal ordering). The authors propose three different priors on the structure of the Temporal ordering (Linear chain, Set of linear chains, Forest of sub-tasks) which allow for efficient sampling of candidate formulas. The posteriors using the different priors have different explanatory power of the observed data. The explanatory power depends on how well the observed task adheres to the structure of the respective prior, which further provides insights on which temporal order structure structure that is more suitable for a specific demonstrated task. The authors propose a likelihood (likelihood odds ratio) which they evaluate together with the priors on both toy data and a real world task scenario with good results.   Strengths: I really like the interaction between Bayesian machine learning and temporal logics in the paper. The paper reminds me of the first part of Chapter 3 about Bayesian concept learning in [1] where they show the elegance and power of Bayesian machine learning for learning from only positive demonstrations, although under much simpler circumstances. This is a direction I would like to see more of within the ML community. This paper is original to the best of my knowledge in the sense that the concept space is a finite subset of well formed formulas of a Modal logic (LTL) consisting of three proposed, for the problem well founded, structures as well as the proposal of three distinctly different but suitable priors used for the inference which are also empirically investigated.  I deem the contributions significant and novel. The contributions are important for advancing this line of research into both the integration of ML and logics as well as opening up for future valuable contributions to the reinforcement and learning from demonstration communities.  The paper is clearly written and have a fair presentation of both the probabilistic aspects of Bayesian machine learning and of Linear Temporal Logic (LTL). Everything is not easy to understand at first, but it is rather due to the many important technical details across the applied Bayesian inference and the temporal logic than anything else. The approach makes sense, is reasonable and the experimentation is suitable.  The Algorithm listings help a lot and increase clarity of the paper.  The paper seem to be technically correct and the quality of the paper is in my opinion high.  The experiments are explained in detail and seem to be reproducible with access to the data.   Weaknesses: For an audience which is less familiar with Bayesian machine learning, such as from other parts of the ML field or from the fields of more logic based AI, some parts of the paper can be made clearer. One example is the likelihood odds ratio in equation (7) which is not explicitly shown how it is used as a likelihood (e.g. in the relation to Bayes theorem). I understand why it is sufficient to state it as is, with the context of Bayesian model selection in mind, but it might not be self-evident for a wider audience.   Other comments: It is my understanding that the three priors can be made into a single prior (e.g. with a probability of 1/3 to draw a sample from either of them). What would be the reason for doing this versus how you do it in the paper where you keep them separate as three different inferences?  Some figures are very small. Especially Figure 1, but also Figure 2 and Figure 4. Figure 1 can be made bigger by limiting the plotting to y >= -2.  The caption of Figure 2 seem to be inconsistent (e.g. "Scenario 1" and "Scenario 2 L(\phi)")  [1] Murphy, K. P., Machine Learning - A probabilistic Perspective, 2012, The MIT Press.   --- Thank you for your detailed author feedback.


GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration
Despite advances in scalable models, the inference tools used for Gaussian processes (GPs) have yet to fully capitalize on developments in computing hardware. We present an efficient and general approach to GP inference based on Blackbox Matrix-Matrix multiplication (BBMM). BBMM inference uses a modified batched version of the conjugate gradients algorithm to derive all terms for training and inference in a single call. BBMM reduces the asymptotic complexity of exact GP inference from O(n 3 ) to O(n 2 ). Adapting this algorithm to scalable approximations and complex GP models simply requires a routine for efficient matrix-matrix multiplication with the kernel and its derivative. In addition, BBMM uses a specialized preconditioner to substantially speed up convergence. In experiments we show that BBMM effectively uses GPU hardware to dramatically accelerate both exact GP inference and scalable approximations. Additionally, we provide GPyTorch, a software platform for scalable GP inference via BBMM, built on PyTorch.

Summary ========================  The authors propose a generic inference algorithm for GP regression that attempts to exploit the advantages of modern GPU based architectures to perform fast matrix multiplications. They proposed a modification of PCG (preconditioned conjugate gradient descent) to solve “Ab = c” that computes simultaneously the solution for multiple r.h.s vectors it computes, at the same time, the tri-diagonalization of the matrix w.r.t. the r.h.s vectors. Based on these outputs, the author propose efficient estimates of the three main quantities needed for computing the marginal log-likelihood: the projection of the output using the inverse of the kernel matrix , the log-determinant of the kernel matrix and the trace of the kernel matrix times its derivative. In the experimental section they show a significant speed-up with respect to state-of-the-art inference methods for scalable GP regression and improvements in terms of accuracy due to the better stability of the proposal.   Details =========================  The paper is focused on scalable inference method for GP regression (although the authors claim the method can be easily extended to other scenarios, e.g. classification). The main idea is to take advantage of modern GPUs and its high performance to perform fast matrix multiplications. To do so, they cleverly modify PCG to solve several r.h.s. vectors simultaneously where the matrix is the kernel matrix of the training set. More specifically, they solve for the output variable "y" and a set of random i.i.d vectors sampled from a standard multivariate gaussian. The random vectors are used to approximate the log determinant term of the kernel matrix in the log-marginal likelihood. In addition, the method outputs the tri-diagonalizations of the kernel matrix w.r.t. the random vectors, that are used to compute the trace term in the log-marginal likelihood. In addition, they propose preconditioning to reduce the number of sequential steps.  One of the selling points of the algorithm is that it is black-box: the user only have to define a matrix multiplication operator for the kernel and its derivative. However, the paper focused on regression. It is true that it can be easily extended to other problems like classification, but in that case the algorithm needs specific inference algorithms for the problem at hand and it could be argued that it is not that black-box anymore.   In the experimental section the authors perform a wide set of experiments where they show how their method outperforms the baselines in the majority of the scenarios in terms of speed, and in some cases, in terms of accuracy. For the improvement in terms of accuracy the authors hypothesis is that it is related to the better stability of their method, although further research is encouraged. Overall, it is a strong well-written paper with nice theoretical and practical contributions.  Minor: Should not be K instead of T at the beginning of eq. (6)?


Maximum Causal Tsallis Entropy Imitation Learning
In this paper, we propose a novel maximum causal Tsallis entropy (MCTE) framework for imitation learning which can efficiently learn a sparse multi-modal policy distribution from demonstrations. We provide the full mathematical analysis of the proposed framework. First, the optimal solution of an MCTE problem is shown to be a sparsemax distribution, whose supporting set can be adjusted. The proposed method has advantages over a softmax distribution in that it can exclude unnecessary actions by assigning zero probability. Second, we prove that an MCTE problem is equivalent to robust Bayes estimation in the sense of the Brier score. Third, we propose a maximum causal Tsallis entropy imitation learning (MCTEIL) algorithm with a sparse mixture density network (sparse MDN) by modeling mixture weights using a sparsemax distribution. In particular, we show that the causal Tsallis entropy of an MDN encourages exploration and efficient mixture utilization while Shannon entropy is less effective.

************************* Summary: ************************* This work introduces a new variant of imitation learning, MCTEIL, that replaces the common approach of maximizing the causal entropy within recent imitation learning approaches with maximizing the causal Tsallis entropy. This allows learning unimodal and multi-modal policies from demonstrations. The work is trained in an adversarial way, similar to GAIL [1], and is compared to behavior cloning, GAIL, and a baseline that is introduced in the paper, soft GAIL.  ************************* Quality: ************************* The approach appears sound, although I did not check the math too heavily. The approach is well-supported with several theoretical proofs. There is no discussion about the weaknesses of the approach.   ************************* Clarity: ************************* The paper is well-written and there were few typos.   One disadvantage is that there were no hyper-parameters or architectural details included for the experiments, and so it is unlikely that the results can be reproduced. However, it is useful that the pseudo-code was provided.   ************************* Originality: ************************* The main contribution to this work is that it describes how to incorporate causal Tsallis entropy into GAIL. This seems like an interesting formulation, however, it is unclear because this paper does not have a related works section. There are a few relevant works mentioned throughout the paper, but they either 1) are directly relevant to describing the background or 2) only mentioned briefly to state why they are not used as baselines. As such, it is unclear how much this work differs from other papers. For example, there are a couple works that were published in NIPS last year, InfoGAIL [2], and Multi-modal imitation learning [3], that learn multi-modal behaviors from demonstrations. The paper states that there are no comparisons with InfoGAIL because it uses a single Gaussian for the policy. However, InfoGAIL uses latent codes to capture multiple modalities. Additionally, the paper claims the latter work was excluded because it focuses on multi-task settings, but the experiments in that paper include both single and multi-task results. As such, it appears that these works should have been included in the comparisons, or at least warranted further discussions.  ************************* Significance: ************************* It is useful to learn multi-modal policies, in particular because they provide alternatives to difficult policies to achieve, and additionally can highlight different preferences among experts. This paper has nice theoretical foundations, and the pseudo-code is pretty clear, so it would be easy to make a couple of adjustments to GAIL if researchers are interested in using MCTEIL. However, because this paper does not compare against relevant works, it is difficult to assess how significant it is.   Additionally, the paper needs more analysis of the results. Why does MCTEIL outperform in Half-Cheetah and Reacher, but not the other environments? Furthermore, there were only 3 averaged runs, so it is unclear how significant the results are.   ************************* Typos ************************* Line 39: modeling expert’s -> modeling the expert’s  Line 109: to the expected -> with the expected  ************************* References: ************************* [1] Ho, Jonathan, and Stefano Ermon. "Generative adversarial imitation learning." Advances in Neural Information Processing Systems. 2016.  [2] Li, Yunzhu, Jiaming Song, and Stefano Ermon. "InfoGAIL: Interpretable Imitation Learning from Visual Demonstrations." arXiv preprint arXiv:1703.08840 (2017).  [3] Hausman, Karol, et al. "Multi-modal imitation learning from unstructured demonstrations using generative adversarial nets." Advances in Neural Information Processing Systems. 2017.  Update: I have read through the reviews and the author's response.  I still think it is necessary to have discussions in the paper relating the work to other relevant literature, but I am willing to change my review to weak accept, given the theoretical contributions and commitment to include the relevant works and experiments in the paper.


Complex Gated Recurrent Neural Networks
Complex numbers have long been favoured for digital signal processing, yet complex representations rarely appear in deep learning architectures. RNNs, widely used to process time series and sequence information, could greatly benefit from complex representations. We present a novel complex gated recurrent cell, which is a hybrid cell combining complex-valued and norm-preserving state transitions with a gating mechanism. The resulting RNN exhibits excellent stability and convergence properties and performs competitively on the synthetic memory and adding task, as well as on the real-world tasks of human motion prediction.
Complex-valued representations have begun receiving some attention in the the deep learning community but they have been applied only to the most basic of architectures [1,10,36]. For recurrent networks, complex representations could gain more acceptance if they were shown to be compatible with more commonly used gated architectures and also competitive for real-world data. This is exactly the aim of this work, where we propose a complex-valued gated recurrent network and show how it can easily be implemented with a standard deep learning library such as TensorFlow. Our contributions can be summarized as follows 2 :
• We introduce a novel complex-gated recurrent unit; to the best of our knowledge, we are the first to explore such a structure using complex number representations.
• We compare experimentally the effects of a bounded versus unbounded non-linearity in recurrent networks, finding additional evidence countering the commonly held heuristic that only bounded non-linearities should be applied in RNNs. In our case unbounded non-linearities perform better, but must be coupled with the stabilizing measure of using norm-preserving state transition matrices.
• Our complex gated network is stable and fast to train; it outperforms the state of the art with equal parameters on synthetic tasks and delivers state-of-the-art performance one the real-world application of predicting poses in human motion capture using fewer weights.

Summary of approach and contributions: The authors resurrect the pioneering work of Hirose on complex valued neural networks in order to provide a new RNN based on a complex valued activation/transition function and a complex argument gating mechanism. In order to obtain a differentiable function that is not constant and yet bounded, the authors step away from holomorphic functions and employ CR calculus. The authors show experimental improvements on two synthetic tasks and one actual data set.  Strengths of the paper: o) Moving away from strict holomorphy and using CR calculus to apply complex valued networks to RNNs is interesting as a novel technique. I think that the authors should spend more time explaining how phases can be easily encoded in the complex domain and therefore why such complex representations can be advantageous for sequential learning. o) The paper is cleanly written and the architectural changes simple enough that they can be written in a few lines of a standard deep learning package such as tensorflow. o) The study of Hirose vs modReLU and the impact of learning transition matrices on the Stiefel Manifold is interesting as it gives additional evidence helping compare two radically different approaches to maintaining stability in a RNN. Such a study fits nicely within recent architectural developments in the field of RNNs.  Weaknesses of the paper: o) The authors rely on CR calculus to differentiate the complex functions they employ and, more importantly, design an architecture where key mechanisms (equation (7) and (13)) could have a similar construction with real numbers and additional numbers of dimensions. For instance (13) is analogous to a bilinear gating mechanism which has been employed studied in https://arxiv.org/pdf/1705.03122.pdf for sequential learning. I believe that in order to isolate the effect of learning complex valued values it would be necessary to compare the performance of the proposed architecture with a real valued competitor network that would employ the same family of non-linearities, in particular bi-linear gates as in (13). o) The authors provide very few insights as to why a complex valued representation could be better for sequential learning. I believe that even simple elements of signal processing could expose in a paragraph theoretical elements that would help consider the source of experimental improvement as coming from a complex valued representation. o) The experiments themselves are not most convincing. It seems surprising that no neural translation or neural language understanding benchmark is featured in the paper. The only real-work task should feature the size of the networks involved in numbers of parameters and MB as well as a comparison of computational complexity. Without such elements, it is not certain that better results could be achieved by a larger real valued network.  Overall the paper appears original and well written but could really benefit from more substantial theoretical and experimental insights designed to isolate the role of complex values in the network from non-linearity design changes.  The author's feedback has better convinced me that complex values play a fundamental positive role in the architecture. I indeed am familiar with the ease of use of complex representations and their expressiveness in the field of time series and the addition of sequential tasks will help that point clearer. In that respect, I appreciate that the authors will add new experimental results to make their experimental claim more robust with TIMIT and WMT data. I revised my rating accordingly.