Shape and Illumination from Shading using the Generic Viewpoint Assumption
The Generic Viewpoint Assumption (GVA) states that the position of the viewer or the light in a scene is not special. Thus, any estimated parameters from an observation should be stable under small perturbations such as object, viewpoint or light positions. The GVA has been analyzed and quantified in previous works, but has not been put to practical use in actual vision tasks. In this paper, we show how to utilize the GVA to estimate shape and illumination from a single shading image, without the use of other priors. We propose a novel linearized Spherical Harmonics (SH) shading model which enables us to obtain a computationally efficient form of the GVA term. Together with a data term, we build a model whose unknowns are shape and SH illumination. The model parameters are estimated using the Alternating Direction Method of Multipliers embedded in a multi-scale estimation framework. In this prior-free framework, we obtain competitive shape and illumination estimation results under a variety of models and lighting conditions, requiring fewer assumptions than competing methods.

This paper proposes a method for estimation of shape and illumination from shading by using the generic view assumption proposed in [9]. The authors formulate a cost function that consists of a data term and a regularization term based on the generic viewpoint assumption that depends on both shape and illumination. The cost is minimized with respect to these unknowns using a message passing variant for alternating direction method of multipliers. The experimental results on the MIT/Berkeley intrinsic images database show that the method performs close to the prior art method by Barron and Malik, but it does not outperform it.The idea of using the generic viewpoint assumption (GVA) directly in the cost function for shape and illumination from shading is novel, to the best of my knowledge. Therefore, the idea presented in the paper is original. The addressed problem is also a very significant one in computer vision. However, the authors have not made their case to convince the reader why incorporating the GVA actually makes sense and why they expect it to outperform previous work. Particularly, they should explain why using GVA makes more sense than using natural shape statistics priors (e.g. shape smoothness). GVA states that the viewpoint is typically not in a special relation to the object, thus small variations in the viewpoint (or light source) will induce small variations in the object appearance. In that case, one can say that invariance to such small variations under GVA relies a lot on the natural statistics of the scene, such as smoothness. Hence, using GVA as a prior could indirectly assume shape smoothness as well. However, the smoothness then might be enforced only with respect to the viewpoint change considered in the GVA term in the cost function (in this paper only with respect to rotations). Could this interpretation explain the unusual streaks in the shape reconstruction results and the dependence of their orientation on the viewpoint? I think it is very important to discuss this issue in the paper, and justify why the GVA prior is better than the smoothness prior. Even though the authors state that their GVA is not a prior, looking at the cost function it seems to me that it is a prior.The clarity of the paper should be significantly improved. Besides my comment related to the GVA assumption above, the authors need to put more effort into explaining the mathematical formulation of the GVA term in the cost function, given in the Eq.14. It is not clear at all how the authors arrive to this formulation from Eq.9-13. Moreover, how they obtain Eq.11-13 is not clear either. The supplemental material only provides the derivation of the linearization formula. There is also a typo in the supplemental in two equations that are not enumerated (please enumerate them!) and are between Eq.5 and Eq.6 - it should be h here instead of f. Overall, the mathematical derivation of the cost function in Eq.15 is not clear at all, in addition to the unclear motivation of using this cost. The obtained results do not justify the method either. Numerical results show that the proposed method does not outperform state of the art, which makes one wonder why would someone use the proposed method. Visual comparisons are difficult to interpret since the proposed method gives shapes with strange artifacts. These are some streaks, whose orientation seems to be dependent on the viewpoint. These streaks are visible on the 3D shape renderings, but not in the rendered image from a specific viewpoint. This makes the reader wonder how would the rendered image look like from another viewpoint?In detail:Sec. 3. "We found it to be highly accurate for the models in our experiments" - what about the models not presented in the paper?Sec. 4.1 - Authors need to be more careful with the language to make sure the reader understands that this was done in [9]. E.g. line 180: "We get the …" - Actually it has been obtained in [9]In supple. mat. Eq.6 uses a variable 'x'. How is that obtained?Sec.6 What is the mask and how it affects the results?Sec.6. Why do you do a DC shift?


Bregman Alternating Direction Method of Multipliers
The mirror descent algorithm (MDA) generalizes gradient descent by using a Bregman divergence to replace squared Euclidean distance. In this paper, we similarly generalize the alternating direction method of multipliers (ADMM) to Bregman ADMM (BADMM), which allows the choice of different Bregman divergences to exploit the structure of problems. BADMM provides a unified framework for ADMM and its variants, including generalized ADMM, inexact ADMM and Bethe ADMM. We establish the global convergence and the O(1/T ) iteration complexity for BADMM. In some cases, BADMM can be faster than ADMM by a factor of O(n/ ln n) where n is the dimensionality. In solving the linear program of mass transportation problem, BADMM leads to massive parallelism and can easily run on GPU. BADMM is several times faster than highly optimized commercial software Gurobi.

The paper under review considers a generalization of the ADMM algorithm, named BADMM, where the quadratic penalty term is replaced by some Bregman divergence terms. Various convergence results (on the iterates, and on the objective values in an ergodic sense) are given. Moreover, the performance of BADMM is evaluated on a high dimensional linear program coming from a mass transportation problem. Promising results are obtained from an empirical point of view. The problem faced in the paper is interesting and deserves further investigation. The proof of convergence relies on different tools with respect to the ones tipically used for the ADMM algorithm. Nevertheless, I have one main concern about the proof of the main results. It seems to me that the optimality conditions stated in (29) for the lagrangean function of (1) refer to the unconstrained case (i.e. X=R^{n1} and Z=R^{n2}) (and indeed the normal cones of the two sets do not appear in the formulation). The same mistake is made also in equations (30)-(31), when the optimality conditions corresponding to (3) and (4) are derived. Then, in Theorem 1, the iterates are shown to converge to a point (x*,z*,y*) satisfying (29). Therefore, it seems to me that the proof of convergence given in this paper holds only for the unconstrained case. Convergence of the algorithm for the examples with explicit constraints given in the paper is not in principle proved. The organization of the paper could be improved. In particular, I think that the informal presentation at the beginning of pag 4 is hard to follow. FOr instance the definition of h as "the problematic term which need to be linearized" is not completely clear to me (maybe exampe 1 could be anticipated to guide the reader).Minor comments: 1) X and Z should be closed (otherwise the projection could be not well-defined)2)p.3, line 111: "since \phi is convex" should be replaced by "since \phi is strictly convex"3) p. 4: according to the definition of Bregman divergence given at the beginning of the section, the method described here works only if $\varphi_x$ is continuously differentiable and strictly convex (and not only convex as stated after eq. (15))4) p.6, line 311: I don't understand what $\tau=O(\rho)$ means here. Since in the previous result $\tau$ is a constant multiplied by \rho this is already satisfied.5) p. 8 Figure 1 (c) : I don't clearly see here that BADMM is faster here.  The authors in their reply stated that the constraints can be explicitly added and the proofs work also in this case. I suggest to add them to fix the error.


A Multi-World Approach to Question Answering about Real-World Scenes based on Uncertain Input
We propose a method for automatically answering questions about images by bringing together recent advances from natural language processing and computer vision. We combine discrete reasoning with uncertain predictions by a multiworld approach that represents uncertainty about the perceived world in a bayesian framework. Our approach can handle human questions of high complexity about realistic scenes and replies with range of answer like counts, object classes, instances and lists of them. The system is directly trained from question-answer pairs. We establish a first benchmark for this task that can be seen as a modern attempt at a visual turing test.

This paper describes a dataset and system for answering natural language questions about a depth/RGB image, which uses multiple segmentations to capture uncertainty in the scene understanding when computing answers.Quality=======This is an extremely difficult task which requires understanding natural language forms of queries, segmenting and categorising the depth image, understanding the scene layout in three dimensions (including some understanding of support) and bringing all these pieces together.  The state of the art in each part individually is not currently close to having good accuracy - one concern is that it is premature to try and tie these systems together to solve an even harder problem.  The worry is that errors will just accumulate from system to system - although it certainly helps that some uncertainty in the segmentation is communicated though samples (multiple worlds).  This concern seems borne out by the fact that the overall system is giving results only slightly better than always picking the same label all the time (7.86% vs 4.4%).  I wonder how much better the system is doing than a colour/word histogram-based straw man?  With just 4 examples (Fig 6) It's hard to tell the kinds of mistakes the system is making and which piece of the system is the cause, but the fact that it is getting the type wrong (reporting a colour in answer to "what is behind the television?") suggests that there's room for improvement in the question-answering part alone.  The WUPS evaluation metric seems to have some issues - the fact that humans doing so badly (61% at 0.9) seems more likely to be an issue with the metric than with the humans.  I'm not quite sure what the sentence "Despite our instructions the answers are subject to... human judgement" is implying! It might be interesting to explore an evaluation metric that says whether a human thinks the automatically-given answer is correct or not - or at least use this to validate the WUPS metric.Clarity=======Overall acceptably clear, but with a lot of missing details which require reading [1] or are just not present e.g. the definition of the 'sampling strategy' used to produce segmentation samples.  The figures could use refinement e.g. the segmentation images lack a key, the text in Fig 6 is hard to read.  The authors should also say how the examples in Fig 6 were selected (at random? are these typical?).  The introduction could use some references for the methods being referred to as could the second sentence of section 3.Originality & significance==========================The question/answer dataset which augments the existing NYU depth/RGB image dataset is a useful contribution.  Given the extreme difficulty of the task and the issues with the individual components, the contribution of combining them is mainly to get a straw man accuracy number.Typos: Pg 2 "[4] objects" - words missingBottom of pg 4 "words"->"worlds"Refs: many capitalization issues.


Distributed Balanced Clustering via Mapping Coresets
Large-scale clustering of data points in metric spaces is an important problem in mining big data sets. For many applications, we face explicit or implicit size constraints for each cluster which leads to the problem of clustering under capacity constraints or the "balanced clustering" problem. Although the balanced clustering problem has been widely studied, developing a theoretically sound distributed algorithm remains an open problem. In this paper we develop a new framework based on "mapping coresets" to tackle this issue. Our technique results in first distributed approximation algorithms for balanced clustering problems for a wide range of clustering objective functions such as k-center, k-median, and k-means.

The paper describes an approach to distributed (balanced) clustering using the notion of a coreset, a concept introduced and studied in theoretical computer science in the areas of approximation algorithms and computational geometry. Starting from a recent work of Indyk et al. (PODS’14) the authors introduce the idea of “mapping coresets” which is basically a coreset together with a mapping from the the original space to the coreset points. Basically the proposed clustering algorithm works as follows: first the input data set is partitioned into several chunks arbitrarily. Then, for each chunk, a coreset is computed together with a mapping of the original points in the chunk to those in the coreset. Next, clustering is performed over the union of all the coresets and the solution found is finally mapped back to the original data points. After a long list of definitions the authors provide some theoretical properties and show connections to MapReduce and streaming clustering algorithms.The writing of the paper is quite dense and technical, and it is not easy to read. Also, the authors presuppose familiarity with coresets and its properties and with results from  approximation algorithms. Indeed, almost all references come basically from the theoretical computer science area (STOC, FOCS, SODA, etc.).All in all the contribution is quite incremental. The idea of using coresets in distributed clustering has been used before extensively, although the idea introduced here of mapping coresets and the application to balanced clustering looks novel. The connection with MapReduce and streaming clustering algorithm is interesting but I'm not sure this will appeal to the NIPS community.A major weakness of the paper, however, is the experimental evaluation which aimed to show the scalability of the proposed algorithm. Indeed, the authors applied their implementation of the algorithm on just two (admittedly very large) graphs, so the overall conclusions are questionable.


Improved Multimodal Deep Learning with Variation of Information
Deep learning has been successfully applied to multimodal representation learning problems, with a common strategy to learning joint representations that are shared across multiple modalities on top of layers of modality-specific networks. Nonetheless, there still remains a question how to learn a good association between data modalities; in particular, a good generative model of multimodal data should be able to reason about missing data modality given the rest of data modalities. In this paper, we propose a novel multimodal representation learning framework that explicitly aims this goal. Rather than learning with maximum likelihood, we train the model to minimize the variation of information. We provide a theoretical insight why the proposed learning objective is sufficient to estimate the data-generating joint distribution of multimodal data. We apply our method to restricted Boltzmann machines and introduce learning methods based on contrastive divergence and multi-prediction training. In addition, we extend to deep networks with recurrent encoding structure to finetune the whole network. In experiments, we demonstrate the state-of-the-art visual recognition performance on MIR-Flickr database and PASCAL VOC 2007 database with and without text features.

This paper proposes a modality reconstruction criterion (given the othermodalities) for training the top level of a multi-modal architecture (withthe lower levels pre-trained by unsupervised learning on a per-modalitybasis, and a separate path for each modality, like in previous multi-modalmodeling with the DBM).The mathematical results are pretty straightforward and unsurprising, andone would think that this methodology is less "powerful" than the maximumlikelihood training, of say DBMs (which have a similar architecture). Yetthe comparative experimental results are impressive and beat the DBMconsistently across many benchmarks. The fact that the whole thing isfine-tuned like in the MP-DBM may be part of the explanation (and it wouldbe good to test it, i.e., what happens without the fine-tuning part?).One thing I don't like, besides the fact that the training criterion is nottrying to model the marginals, is that the conditionals are approximated bya factorial distribution, which seems like a very strong assumption. Isuspect that the reason it seems to work so well is that the tasks involvechoosing one value of a modality given the value observed for the other. Soin a sense we are not even interested in the posterior distribution butmore in the MAP, and a unimodal factorial posterior is then a reasonableway to focus on an estimated MAP. I bet that sampling from one modalitygiven the other would not give so nice results (unlike the case ofthe DBM). But maybe that's ok, and if we really want to solve thekinds of problems in the benchmark, one is really better off trainingin this MAP-like manner than in the full probabilistic mode that DBMs enjoy. So I think that although the ideas in this paper are simple on thesurface, the very surprisingly good results and the questions theseraise are very interesting and worth publishing. I would modify thepaper accordingly, trying to focus the attention, the discussion,and maybe extra experiments, in trying to understand *why* theproposed approach works better than the multi-modal DBM.Toy experiments on MNIST: Note that CD is not recognized to be aparticularly good way of training RBMs in a generative modeling perspective, soyou should really try to train them by PCD/SML instead. And you can'treally call CD-training "maximum likelihood" because it is quite far fromit. PCD/SML is closer to maximum likelihood.Spell out 'GT' in Figure 2.


Multi-View Perceptron: a Deep Model for Learning Face Identity and View Representations
Various factors, such as identity, view, and illumination, are coupled in face images. Disentangling the identity and view representations is a major challenge in face recognition. Existing face recognition systems either use handcrafted features or learn features discriminatively to improve recognition accuracy. This is different from the behavior of primate brain. Recent studies [5,19] discovered that primate brain has a face-processing network, where view and identity are processed by different neurons. Taking into account this instinct, this paper proposes a novel deep neural net, named multi-view perceptron (MVP), which can untangle the identity and view features, and in the meanwhile infer a full spectrum of multi-view images, given a single 2D face image. The identity features of MVP achieve superior performance on the MultiPIE dataset. MVP is also capable to interpolate and predict images under viewpoints that are unobserved in the training data.

This paper presents a novel way to do multi-view representation of faces using a neural-net like model with deterministic and probabilistic units. The network is trained to recover the identity and view. It can be used to synthesize a new view as well. Generally, the paper does a good job at disentangling the contributing factors to the success of the method, and the results seem quite good.I wish the authors presented more evidence for why they chose to design their model they way they did. For one, it is not clear that a non-deterministic approach is really needed in this case -- could they have done a model that is fully feed-forward with deterministic neurons? It would have certainly avoided the need to variational/importance sampling inference.Quality: generally, a good paper with an interesting and well-grounded model, evaluated well on a competitive benchmark and Clarity: The paper is well-written and easy to read, for most of the part.Originality: in some sense, the approach is comparable to the work of Geoff Hinton and collaborators, who use stacks of Restricted Boltzmann Machines, where the top RBM can have the label as a sideSignificance: this is likely to be of interest to the facial recognition community, but also to other researchers who work on problems where a hybrid deterministic and generative approach may be a good solution.Comments and questions:- How did the authors come up with the structure in Figure 2? What are the insights behind the design choices made?- The authors should define q(h) at line 165- Is the MCEM method crucial to the model presented? More analysis on why this particular optimization method was used is in order since MCEM is not exactly a widely used method in the community.- For inference: how big is S at line 235? How expensive is inference generally? Some numbers and O() notation results would be good.- Is LDA necessary to get the best results? How do the results look like without LDA?- I don't think the authors should be using the tangent with how the brain works, except very sparsely. There is not much evidence that the presented method is particularly close to how humans do facial recognition or view point interpolation. - Did the authors try their approach on the Labeled Faces in the Wild benchmark? If yes, do they have results to report?


Online Decision-Making in General Combinatorial Spaces
We study online combinatorial decision problems, where one must make sequential decisions in some combinatorial space without knowing in advance the cost of decisions on each trial; the goal is to minimize the total regret over some sequence of trials relative to the best fixed decision in hindsight. Such problems have been studied mostly in settings where decisions are represented by Boolean vectors and costs are linear in this representation. Here we study a general setting where costs may be linear in any suitable low-dimensional vector representation of elements of the decision space. We give a general algorithm for such problems that we call low-dimensional online mirror descent (LDOMD); the algorithm generalizes both the Component Hedge algorithm of Koolen et al. (2010), and a recent algorithm of Suehiro et al. (2012). Our study offers a unification and generalization of previous work, and emphasizes the role of the convex polytope arising from the vector representation of the decision space; while Boolean representations lead to 0-1 polytopes, more general vector representations lead to more general polytopes. We study several examples of both types of polytopes. Finally, we demonstrate the benefit of having a general framework for such problems via an application to an online transportation problem; the associated transportation polytopes generalize the Birkhoff polytope of doubly stochastic matrices, and the resulting algorithm generalizes the PermELearn algorithm of Helmbold and Warmuth (2009).

The paper considers online learning of combinatorial decision problems.A new method LDOMD is introduced, which generalizes the Component Hedgealgorithm of Koolen et al. [14] for 0/1-polytopes and the method ofSuehiro et al. [15] for polytopes associated with submodular functions.In Theorem 3, a general regret bound is established for LDOMD, which isclaimed to be optimal for 0/1-polytopes. Some new polytopes areconsidered, but, with the possible exception of the transportationpolytope, they appear to be minor generalizations of the polytopes of[14] and [15]. Thus, the main contribution of the paper appears to be aunification of the results of [14] and [15].*** Changes after author response ***[Deleted claim that Thm 3 is suboptimal, which was incorrect, as theauthors pointed out in their response.]The provided unification is satisfying, but does not seem to lead tomany new applications. The exception might be the transportationpolytope, which the authors argue is "truly novel and non-trivial".On the whole, I would judge the paper as borderline. I am not sure thatthe transportation polytope is technically a very large step forward,but it does appear practically important. This tips the balance towardsaccept.*** End of changes after author response ***Other remarks:Since both [14] and [15] give bounds in terms of L* instead of T, itshould be discussed that the weakening to T is still sufficientlyinteresting.Sections 3.1,3.2: It seems unfair to apply Hedge to the whole class cal{C}          instead of only the subset with ||phi(c)||_1 <= m, which would          give a better bound that would be easier to compare to the          bound for LDOMD.line 196: although true, it is actually not so easy to see that F is          1/m-strongly convex, and, since x^1 is not explicitly          specified, it is also not that obvious that B_F(phi(c),x^1) <= m log(d/m).


Extremal Mechanisms for Local Differential Privacy
Local differential privacy has recently surfaced as a strong measure of privacy in contexts where personal information remains private even from data analysts. Working in a setting where the data providers and data analysts want to maximize the utility of statistical inferences performed on the released data, we study the fundamental tradeoff between local differential privacy and information theoretic utility functions. We introduce a family of extremal privatization mechanisms, which we call staircase mechanisms, and prove that it contains the optimal privatization mechanism that maximizes utility. We further show that for all information theoretic utility functions studied in this paper, maximizing utility is equivalent to solving a linear program, the outcome of which is the optimal staircase mechanism. However, solving this linear program can be computationally expensive since it has a number of variables that is exponential in the data size. To account for this, we show that two simple staircase mechanisms, the binary and randomized response mechanisms, are universally optimal in the high and low privacy regimes, respectively, and well approximate the intermediate regime.

The paper claims to make a contribution to local differential privacy.  Unfortunately, I didn't sufficiently understand the text to confidently interprete and summarize the content.The quality of the paper was not sufficient to let me understand its main message.  In particular, the writing is quite vague and unclear.The paper describes some related work, but not being able to interprete the fine details of the contribution, I couldn't assess the originality and significance.The following are detailed comments in order of occurrence in the text:The abstract is a bit vague wrt. the topic and contribution of the paper.  It says "We address a general problem of utility maximization under local differential privacy." but doesn't specify what this "general problem of utility maximization" is.   The rest of the abstract is therefore over the top of my head upon first reading.The authors define local privacy as when "individuals disclose their personal information (e.g. voluntarily on social network sites).", but if individuals disclose data to the world, what is then the problem of privacy?The authors discuss that "differential privacy has been extended to local privacy" and use in their formal definition "privatized views Y_i" without explaining what are privatized views (remember from the previous comment that the data is already public).  These "view" (usually inputs to the viewer) are also called "outputs" in the next sentence.  In this definition, it is also not clear why exactly two distributions (P_0 and P_1) are considered.  The sentence "We consider Q’s satisfying the privacy conditions," is unclear in not specifying what is the "privacy condition" (is it the differential privacy discussed later in the definition?).  The formula of the definition looks a common one, so I guess the problem is mainly in the formalization and wording.This definition of differential privacy uses Q for a conditional probability distribution, where the conditions are on one single x_i and n-1 different y_j's.  Formula (2) uses Q with conditioning on n x_i's.  The number of conditionings is the same, but it is unclear how they map to each other.  Moreover, the "privatization" formulation suggests that the x_i and y_j are not necessarily elements of the same domain.The introduction further states that the power to discriminate data from P_0 from data from P_1 depends on the marginals M_\nu.  However, it seems there are other ways to discriminate, e.g. by just considering the distribution of the values of X_i for some i (everyone knows at least one X_i).Line 110: "Q the minimized the error" -> "Q that minimizes the error" It is unclear why Equation (4) introduces f-divergence and then (5) specializes to KL-divergence (which the paper says is a special case).Line 175: and marginal of the privatized output -> ungrammaticalSection 2 starts saying "We first give a formal definition of the staircase mechanisms," but I don't find such formal definition before theorem 2.1.  Theorem 2.1 is not proved in the main paper and does not refer to the supplementary material.  The proof in the supplementary material seems to use staircase notion (which as I said don't seem to be provided before that point).After this point, the technical content gets increasingly confusing.The paper has an usual structure, has no conclusion section, does not outline the structure at the end of the introduction.The paper does not provide experimental results, examples, illustrations, figures, or other attempts at making the content somewhat easier to digest.-------------------------------------------Additional comments after the author's rebuttal.W.r.t. Comment 3, Authors say: "the authors say: We provide in lines 121-157, a summary of our contributions in the context of existing literature."I reread now this part, and try to comment based on what I understand from the paper, the discussion with other reviewers and the author's response:* Line 122: In fact, the authors are not solving an optimization problem under local differential privacy constraints, but they are optimizing privatization mechanisms under local differential privacy constraints.  Taking the sentence literally, one (of the several) possible semantics for this sentence in isolation would be that we are given a privatized view and the data analyst should try to find the best possible value for some (model) parameter.  The second part of the sentence (resulting in a family of optimal mechanisms) is inconsistent with the first part.  * Terms such as "large class", "family", "important", ... are rather vague, and will need to be instantiated to the concrete contribution at some point (which does not happen in the part 121-157).  It is (especially here) unclear why "optimization problem" gets the specification "large class of", as the only optimization problem the authors are solving is Equation (5), while "large class" strengthens the wrong semantics that it concerns a (not yet explained) other class of optimization problems.  I guess that "large class" does not refer to optimization problems but to a large class of probability distributions P_\nu, large classes of privatization schemes Q, etc.* Line 124: Next, the reader stumbles upon "the differential privacy area, where the basic mechanisms have been few".  What is a basic mechanism?  It could refer to privatization mechanisms, but why are they called basic (rather than privatization) then?  A much simpler and less confusing formulation would be "... to the differential privacy area where allmost no results are known on the optimality of privatization mechanisms." (if at least this is what the authors mean).* Somehow, the reader also needs to realize that the "extremal" from the title is a synonym for the "optimal" in this paragraph.  Avoiding the use of synonyms often avoids confusion.* Line 125 mentions a linear program over "the alphabet |\mathcal{X}|.  Probably the "alphabet size" is meant (|.| gives a number).  By the way, in line 64, \mathcal{X} was not introduced (and the reader learns here that it is called "alphabet").  Up to here, the reader may think that \mathcal{X} is an uncountably infinite set (e.g. vector space).  This impression is strengthened by the usage of integrals in the formulas up to here.* Line 126-128 seems to revoke the original stronger claim that optimal mechanisms can be found using this paper.  It now seems to hard to compute, and the paper will only give optimal mechanisms in certain "regimes", which usually means something like "the optimality result holds for the extremes (e.g. 0 and infinity), and the more you are in the middle between these extremes, the large is the suboptimality.".   Still, later in lines 144-146, the text compares with related work and says that this other work only provides "near-optimality" while this paper does better.* line 129 announces bounds on differential privacy: Suddenly, it is not local anymore. What exactly is lower bounded?  In terms of what is the lower bound given?  The statement is quite vague.* In "recovering some known results.", what is "recover"?  It sounds as this "recovering" is not giving new results, but repeating what has been published earlier?  Or do you mean that you adapt existing bounds to a new setting where they originally did not yet apply?* In Line 129, The sentence "As a motivating example, we provide optimal mechanisms" is again confusing.  I thought that already line 123 announced optimal mechanisms?  So are the optimal mechanisms a motivating example for the motivating mechanisms?  What is the difference?* Ine line 134, it is unclear what "a converse to the optimization problem" means, the following phrase (and show ...) does not disambiguate this completely.In conclusion, even though the authors indeed provide in the mentioned lines a summary of their contributions, it is vague, and the text provides many opportunities to the average reader (who does not have author responses and fellow reviewers) for getting confused.  In allmost all cases, simple reformulations exist which make the text clearer, more precise, less ambiguous and less confusing.W.r.t. Comment 6:  Authors say: "The specific quoted phrase is embedded in a larger sentence. Reading the entire sentence, local privacy DOES NOT mean that individuals reveal their personal information, but instead local privacy is required IN THE CONTEXT where individuals reveal their personal information. Local differential privacy is when users first privatize their personal data (X_i's) and then release privatized views (Y_i's) to a data collector. Therefore, the data collector never observes the X_i's but instead has access to the Y_i's." It indeed often happens that the authors write sentences which have certain grammatical features which do not allow an interpretation consistent with other sentences or parts of sentences.  In this case, the quoted phrase IS NOT embedded in a larger sentence which may let the reader suspect he is being misled.  In particular, the complete sentence is "The need for data privacy appears in two different contexts: one in the data collection scenario, as in when individuals disclose their personal information (e.g. voluntarily on social network sites).".  Later, the paper says that this first scenario is local differential privacy.  It is true that there are other sentences in the paper which describe local differential privacy better, but why then first give a wrong description?My specific comment refers amongst others to the fact that the example is clearly not a good one.  Users providing their information on a social network site do not privatize their information in some complicated way.  They do not know the (one or more) data analysts who will analyze the data, and hence even if they would apply a privatization scheme, they would not be able to use the content in this paper to select an optimal privatization scheme.  Even if we ignore the specific ill-chosen example, it can't be denied that the paper assumes that there is only one data analyst willing to test only one hypothesis.  In practice, this is not realistic.  Data is published, potentially in some privatized way, but then usually a data analyst will have more then a binary question.Authors say: "7A) Local differential privacy has been studied in the literature. Our notations, definitions, and problem statement have been chosen to be consistent with recent prior papers on the subject (which we cite in our paper). Specifically, the terms "privatized views", "privatized outputs", and "privatization mechanism" are chosen to be consistent with their use in [10]."Ideally, a paper is self-contained as should not require from the reader that he digs into a lot of other literature to grasp the main message.Even if the authors choose to not define terms already used in the literature, why then let the reader guess for a long time and not simply start by saying that the concepts and notations in this paper are defined formally in [10] ?More generally, several boosting sentences such as "We first give a formal definition ..." let the reader expect a certain level of rigorousness, and cause the reader to think his missed something in this paper while he is not able to find it.  If you don't plan to give a formal definition, or if you give it in supplementary materials, ... my advice is to simply tell this to the reader.Still, it is my belief (now understanding things better), that there are simple ways to convey most of this essential information to the reader without using significantly more space.  Even if a clearer explanation would require more space, I feel it is worth moving one or two technical derivations to the supplementary materials.Authors say: "7B) Binary hypothesis testing is a canonical statistical inference problem with a wide range of applications. As is evident from [10] and this paper, understanding the fundamental limits to private binary hypothesis testing is a challenging problem. The more general problem of private M-ary hypothesis testing is also interesting, but is outside of the scope of this paper."I agree with that.  But then, this is an interesting point of discussion and possible future work.  Why not have a short "conclusion and future directions" section where you outline the limitations of the current paper and remaining open questions?w.r.t. comment 16, I feel that examples, discussions and illustrations don't necessarily require figures.    Well-written sentences often can help a lot.


Semi-supervised Learning with Deep Generative Models
The ever-increasing size of modern data sets combined with the difficulty of obtaining label information has made semi-supervised learning one of the problems of significant practical importance in modern data analysis. We revisit the approach to semi-supervised learning with generative models and develop new models that allow for effective generalisation from small labelled data sets to large unlabelled ones. Generative approaches have thus far been either inflexible, inefficient or non-scalable. We show that deep generative models and approximate Bayesian inference exploiting recent advances in variational methods can be used to provide significant improvements, making generative approaches highly competitive for semi-supervised learning.

This paper builds on the recently introduced variational autoencoder (VAE) framework of Kingma and Welling (2014) and of Rezende et al. (2014) to introduce two separate semi-supervised learning models. The first (called M1) is a VAE version of self-taught learning (Raina et al., 2007), while the second (M2) blends a standard discriminative model with a conditionalgenerative VAE that models the input data given the class label. I am  conflicted about this paper. On the positive side I find the VAE a very interesting and important modeling framework and I find the idea of extending this framework to the semi-supervised domain to be both natural and sensible. I would expect this to be the first in a long series of papers exploring this direction. On the negative side, the specific two proposed approaches seem fairly straightforward. This isn't a strong criticism but it does impact the novelty of the paper.  It would have been better if the experiments really focused on the differences between the two, in order to give the reader some idea of their differential abilities, but that wasn't really the case as they were only really compared directly in one set of experiments limited to the MNIST hand-written digits database. More seriously, there are a large number of similar methods thatare not discussed and not compared empirically. In particular there are many papers not cited discussing learning in the self-taught learning framework (including the original self-taught learning paper of Raina et al. (2007)) which is essentially identical to the proposed M1 approach. Other missing citations and comparisons are discussed below inmore specific comments on the experiments.The empirical evaluation of the proposed approach is based on three types of experiments:1 - Benchmark Classification: The first is a basic comparison of the proposed approach in a semi-supervised version of the MNIST hand-written digits database. These results are based entirely on the experiments of Rifai et al. (2011) where the authors have simply added the results for the proposed approach. This isn't really a problem, except that they neglect to provide all of the results from Rifai et al. (2011). While they include the results for 100, 600 and 1000 labeled examples. They do not provide results for either 3000 or 5000 (all) labeled examples. Why do they neglect to provide these 2 numbers? I think it's important to see how the proposed methods (M1 and M2) work in the larger labeled set regime. 2 - Conditional Generation: The second set of experiments explore the ability of the model to separately model label content and other more stylistic variations in two datasets: SVHN (street-view house numbers) and the NORB object dataset. Here the authors provide a set of qualitative results -- sampled images with variable "style" and "content" (label info). These results aremildly compelling in that they capture -- for SVHN -- the color information of both the background and foreground but do not seem to capture the font style. There are also several papers discussing the separation of style and content that are either cited nor compared. These include: Tenenbaum and Freeman (2000), "Separating Style and Content with Bilinear Models";  Grimes and Rao (2005) "Bilinear sparse coding for invariant vision"; Rifai et al (2012) "Disentangling factors of variation for facial expression recognition"; Desjardins et al. (2012) "Disentangling Factors of Variation via Generative Entangling" and Reed et al. (2014) "Learning to Disentangle Factors of Variation with Manifold Interaction"3 - Image Classification: The third set of experiments explore semi-supervised classification with SVHN and NORB image datasets. The authors state that there are no published results on these datasets in the semi-supervised setting so they compare to their own results using nearest neighbors and Transductive SVM. While I know of no results on these twodatasets in the semi-supervised regime, there are plenty of results on other image classification datasets with published results in the semi-supervised regime. Examples include: CIFAR-10 object recognitiondataset, Caltech-101, and the STL-10 dataset. Experiments with these dataset can be found in the following four papers (among others):Dai and Van Gool (2013) "Ensemble Projection for Semi-supervised Image Classiﬁcation" Goodfellow et al. (2012) "Large-Scale Feature Learning With Spike-and-Slab Sparse Coding"Coates et al. (2011) "An Analysis of Single-Layer Networks in Unsupervised Feature Learning"Coates and Ng (2011) "Selecting receptive fields in deep networks"


Pre-training of Recurrent Neural Networks via Linear Autoencoders
We propose a pre-training technique for recurrent neural networks based on linear autoencoder networks for sequences, i.e. linear dynamical systems modelling the target sequences. We start by giving a closed form solution for the definition of the optimal weights of a linear autoencoder given a training set of sequences. This solution, however, is computationally very demanding, so we suggest a procedure to get an approximate solution for a given number of hidden units. The weights obtained for the linear autoencoder are then used as initial weights for the inputto-hidden connections of a recurrent neural network, which is then trained on the desired task. Using four well known datasets of sequences of polyphonic music, we show that the proposed pre-training approach is highly effective, since it allows to largely improve the state of the art results on all the considered datasets.

Quality and originality: The paper is well written. The introduction motivates the general problem. Section 2 is very easy to read, providing both explanation and necessary linear algebra.  and does a good job of supporting the proposed model. I see two important issues in the paper. First is the motivation of the importance of pre-training. The authors are convincing here. The second is whether they authors’ particular version of pre-training for RNNs is the right one. Rather they show that they can outperform a particular RNN approach which uses no pre-training. Here it’s a bit more confusing, as they compare only to the results from a single paper on music data.  Furthermore there’s some confusion as to how much better the proposed model works compared to the one from Sperduti in 2007 (the “conceptual framework” extended here by the authors).  Does the new model actually work better than the Sperduti one on music data? Or is it just that the theoretical approach is reworked? The authors address this directly in the closing paragraph of Section 1, but I wish they had spent more time pulling apart their contributions from those of previous work on pre-training. Furthermore, I wish they had at least implemented Sperduti’s method in the experiments section.Clarity and Significance: It’s not clear why the authors chose to use music datasets. No analyses of the performance of the musical performance of the models is given, nor do we get any musical examples.  This adds some confusion to the paper: is this about sequence prediction in general or about music sequence prediction? I presume it’s about sequence prediction in general, but would have appreciated either some non-music benchmarks or some more exploration of the music space. Of course space is an issue. However I would have preferred that the lemmas and some of the algorithmic details be moved out to supporting material, with more time spent exploring how pre-training does anything other than raise accuracy.


An Autoencoder Approach to Learning Bilingual Word Representations
Cross-language learning allows one to use training data from one language to build models for a different language. Many approaches to bilingual learning require that we have word-level alignment of sentences from parallel corpora. In this work we explore the use of autoencoder-based methods for cross-language learning of vectorial word representations that are coherent between two languages, while not relying on word-level alignments. We show that by simply learning to reconstruct the bag-of-words representations of aligned sentences, within and between languages, we can in fact learn high-quality representations and do without word alignments. We empirically investigate the success of our approach on the problem of cross-language text classification, where a classifier trained on a given language (e.g., English) must learn to generalize to a different language (e.g., German). In experiments on 3 language pairs, we show that our approach achieves state-of-the-art performance, outperforming a method exploiting word alignments and a strong machine translation baseline.

This paper proposes to learn bilingual word vector representations through an autoencoder.The novelty of this approach is to not rely on word-level alignments. It only requires aligned sentences.An autoencoder model is used to reconstruct the bag-of-words representation of aligned sentences, within and between languages.Two different variations are proposed. The first one is based on binary bag-of-words (i.e. words present or not) and the second considers the frequency of each word. The authors demonstrate the quality of these representations for the task of cross-language document classification, where they have been able to reach state-of-the-art performance.I like the idea to learn cross-lingual word representations while not relying on word-level alignment.This offers a clear advantage compared to other approaches.Furthermore, the method using binary bag-of-words reconstruction is quite simple and give the best overall results. And I like simple methods.However, the authors introduce a training with merged bags-of-words that it is not very clear to me.They said that they merged adjacent sentences to perform mini-batch training and speed up the process. But they don't say how they define sentences as adjacent.This model is also vocabulary-dependent. The vocabulary size in the experiment is relatively small (between 35,000 and 50,000). Would this method be scalable with a larger vocabulary?I am also surprised to see that the tree-based model performs significantly worse (less than 10-14%) for EN/DE, DE/EN, EN/FR and FR/EN pairs, while it performs much better for EN/ES (more than 10%).How do the authors explain such variation?That makes me think that the tree-based model is not properly trained.In my opinion, it remains too many open questions in the experiment section.The authors compared their results to Hermann and Blunsom's paper. Hermann and Blusom also proposed a method to learn multilingual distributed representations without word alignment.They showed in their paper the usefulness of adding training data to increase the overall performance.However the training size is never mentioned in this paper. The authors only said that the corpus contains roughly 2 million parallel sentences. Did they train the word representations with all of them? In this case, it would make the training data twice larger than the Hermann and Blunsom's training dataset and explain why they achieve better performance.Or it could be due to the fact that the authors fine-tuned the monolingual embeddings on RCV1/RCV2.To make a fair comparison, it would be nice to run experiments with the same number of training sentence pairs and without fine-tuning.The authors also said that they consider only documents which were assigned exactly one of the 4 top level categories in the topic hierarchy.This makes a 4-class classification problem. How is it possible to have a majority class accucary smaller than 25% for EN/FR, EN/ES and ES/EN pairs? Results for the other models are also not described in enough detail.For Klementiev's model with EN/DE language pairs, the authors report the results from the paper. But is it the same test set?What classifier is used with the MT's model?My intuition would be to use the translated words to construct a document representation with the model described in section 3.2.But I am not sure this is the case here, because the authors again report results from Klementiev et al. for EN/DE and DE/EN pairs. Authors also said that their embeddings are meaningful because they can generalize well even at low data sizes. It is however only true for EN/DE pairs, as we can see that the accuracy is still increasing with 10,000 training documents for DE/EN pairs.Finally, I think that the authors should mention the paper "Multilingual Distributed Representations without Word Alignment" from Hermann and Blunsom in the related work section.As their method looks very similar to the one proposed in this paper, it seems to me important to mention what are the differences and the benefits of the method compared to theirs. -- After reading authors' comments: we still believe there are too many imprecisions in the experimental setup for a NIPS paper.


Gaussian Process Volatility Model
The prediction of time-changing variances is an important task in the modeling of financial data. Standard econometric models are often limited as they assume rigid functional relationships for the evolution of the variance. Moreover, functional parameters are usually learned by maximum likelihood, which can lead to overfitting. To address these problems we introduce GP-Vol, a novel non-parametric model for time-changing variances based on Gaussian Processes. This new model can capture highly flexible functional relationships for the variances. Furthermore, we introduce a new online algorithm for fast inference in GP-Vol. This method is much faster than current offline inference procedures and it avoids overfitting problems by following a fully Bayesian approach. Experiments with financial data show that GP-Vol performs significantly better than current standard alternatives.

This paper proposes a new nonparametric volatility model.The contribution of the paper relies on the application of Gaussian process prior to stochastic volatility models. The inference approach is based on SMC and is a straightforward application of the Liu and West's APF algorithm.The literature review lacks of some important references and the empirical comparison is not complete. My major concerns are the following:\begin{enumerate}\item The authors proposed a new stochastic volatility (SV) model, but in the introduction and in the paper there is no reference (e.g., Taylor (1987), Jacquier, Polson, Rossi (1994, 2004) to this class of models.\item A comparison is proposed between GP-Vol and GARCH models, but the increased flexibility of a SV over the GARCH family has already been proved in the literature by many parts. See e.g. Fridman and Harris (1998). Thus I would strongly suggest the inclusion of a comparison between a standard SV model and the proposed GP-Vol model.\item The author proposed a new nonparametric model, but no references is give to the recent advances in Bayesian nonparametric which make use of flexible prior processes such as Dirichlet processes (e.g., see Bassetti, Casarin, Leisen (2014), Griffin (2011), Griffin and Steel (2011)). \end{enumerate}References:\begin{itemize}\item Jacquier, E., Polson, N., Rossi, P., 1994. Bayesian analysis of stochastic volatility models (with discussion). Journal of Business and Economic Statistics 12 (4), 371-417.\item Jacquier, E., Polson, N., Rossi, P., 1994. Bayesian analysis of stochastic volatility models with fat-tails and correlated errors. Journal of Econometrics 122, 185-212.\item Fridman, M., Harris, L., 1998. A maximum likelihood approach for non-Gaussian stochastic volatility models.Journal of Business and Economics Statistics 16 (3), 284-291.\item Bassetti, F., Casarin, R., Leisen, F. (2014), Pitman-Yor Process Prior for Bayesian Inference, Journal of Econometrics, 180, 49-72. \item J. E. Griffin. Inference in infinite superpositions of non-Gaussian Ornstein-Uhlenbeck processesusing Bayesian nonparametic methods. Journal of Financial Econometrics, 1:1-31, 2011.\item J. E. Griffin and M. F. J. Steel. Stick-breaking autoregressive processes. Journal of Econometrics, 162:383-396, 2011.\end{itemize}


Generalized Unsupervised Manifold Alignment
In this paper, we propose a Generalized Unsupervised Manifold Alignment (GU-MA) method to build the connections between different but correlated datasets without any known correspondences. Based on the assumption that datasets of the same theme usually have similar manifold structures, GUMA is formulated into an explicit integer optimization problem considering the structure matching and preserving criteria, as well as the feature comparability of the corresponding points in the mutual embedding space. The main benefits of this model include: (1) simultaneous discovery and alignment of manifold structures; (2) fully unsupervised matching without any pre-specified correspondences; (3) efficient iterative alignment without computations in all permutation cases. Experimental results on dataset matching and real-world applications demonstrate the effectiveness and the practicability of our manifold alignment method.

This paper proposes an unsupervised method for aligning manifold structures of different datasets and finding correspondence between objects in different datasets. The proposed method is a combination of three objective functions: 1) geometry matching term, 2) feature matching term, and 3) geometry preserving term. In the learning procedures, matching objects and estimating projection matrices are alternately performed so as to maximize the objective function. In the experiments, the authors demonstrate the effectiveness of the proposed method comparing with unsupervised manifold alignment methods.The proposed method is the combination of three related methods as described below. Therefore, the novelty of the proposed method is limited. However, it is interesting to combine related frameworks to solve unsupervised manifold alignment, which is a very difficult problem. The proposed method achieved the good performance in the experiments.The geometry preserving term in the objective function is the same as that of unsupervised manifold alignment methods as described in the paper. The geometry matching term in the objective function is related to unsupervised object matching methods, such as kernelized sorting and least square object matching. Especially equation (3) is the same as that of convex kernelized sorting. Discussion on these unsupervised object matching methods should be added. The feature matching term is related to CCA (canonical correlation analysis) based unsupervised matching methods, such as matching CCA and many-to-many matching latent variable models. These methods find linear projection matrices and object correspondence.[kernelized sorting] Quadrianto, et al, Kernelized sorting, IEEE TPAMI, 2010[least square object matching] Yamada and Sugiyama, Cross-domain object matching with model selection, AISTATS, 2011[convex kernelized sorting] Djuric, et al, Convex kernelized sorting, AAAI, 2012[matching CCA] Haghighi, Learning bilingual lexicons from monolingual corpora, ACL, 2008[many-to-many latent variable model] Iwata et al, Unsupervised Cluster Matching via Probabilistic Latent Variable Models, AAAI, 2013In the face pose experiments, it seems that the similarity between different datasets can be calculated. So, it might be able to solve this task with (supervised) manifold alignment methods. Please clarify it is a task for unsupervised methods.


Optimizing Energy Production Using Policy Search and Predictive State Representations
We consider the challenging practical problem of optimizing the power production of a complex of hydroelectric power plants, which involves control over three continuous action variables, uncertainty in the amount of water inflows and a variety of constraints that need to be satisfied. We propose a policy-search-based approach coupled with predictive modelling to address this problem. This approach has some key advantages compared to other alternatives, such as dynamic programming: the policy representation and search algorithm can conveniently incorporate domain knowledge; the resulting policies are easy to interpret, and the algorithm is naturally parallelizable. Our algorithm obtains a policy which outperforms the solution found by dynamic programming both quantitatively and qualitatively.

This is an application paper that attacks the problem of managingturbine speeds of four dams in Quebec. The goal is to maximize energyproduction (equivalent to maximizing turbine speeds) subject tovarious ecological and operational constraints. Interestingly, a full dynamical model for this problem isavailable. However, this is a continuous state, continuous action,discrete time (weekly-time-step) problem, so applying standard DPmethods to solve the problem requires discretization. This in turnleads to non-smooth policies (i.e., turbine rates jump around becauseof discretization), that are hard to explain (and undesirable fornon-represented operational reasons) to the operators.Instead of DP, this paper pursues a PSR approach in which theexisting simulator (a custom auto-regressive model) and historicaldata are combined to create a dynamical model. One relevant statevariable (month of year) is observable, so the authors incorporatethis variable into the PSR via the methods of [8]. The learn PSRswith and without water input forecasts. Constraints are incorporated by a mix of penalty terms, fixing thepolicy in certain time periods, and partitioning the state space intotwo time periods and learning a separate policy for each time period. The results evaluate performance on many dimensions including (a)total energy produced, (b) frequency with which constraints areviolated, and (c) severity with which constraints are violated.(a) and (c) are improved but at a slight cost of (b). In addition, thepolicies are qualitatively much nicer. Quality: The paper is well written and the material is reasonablyself-contained, with appropriate references to prior work.  The newapproach is compared to a state-of-the-art solution developed by theQuebec water management organization, which is exactly the rightbaseline. The fact that they are able to significantly improve uponthe DP policy is very interesting and has wider lessons for all of uswho work on applied reinforcement learning methods.  In particular,the need for explanable/visualizable policies is not sufficientlyappreciated in the research community. This paper helps address thisproblem.  This is a very nice example of applying a mix of advancedtechniques to show an important application improvement.One question: The authors say that it is difficult (or impossible) toincorporate the steady-flow constraint for weeks 43-45 into a DPmethod. But couldn't that be done within an SMDP framework, where theaction for weeks 43-45 is treated as a single action with a 3-weekduration?  This is more or less what the authors did in theirhand-coded policy for R2. Clarity: The paper is well-written with few exceptions.    Line 142: "or" -> "of"?             insert "the" before "logarithmic case"?   Line 209: You introduce T without defining it. You need to remind   the reader what a "test" is.    Line 236: Should "assuming" be "assume"? You don't discuss Figure 2   very much. Is there more to say?Originality: The work is original within the RL literature. I don't   know about the reservoir management literature. Significance: wrt the research community, the paper is significantbecause it shows (a) the virtues of PSRs for achieving generality, (b)the advantages of policy search for incorporating domain constraintsand achieving smoother policies, and (c) the importance ofinterpretability.  In the reservoir management literature and thelarger sustainability literature, this work is important because itdemonstrates that there is significant advantage in applying thesophisticated techniques coming out of the research community. Thispaper also points the way toward many important areas for futurework. For example, under climate change, the variance in precipitation(and hence, reservoir inputs) can be expected to increase.  Thetechniques in this paper could easily be applied to model the impactof that increased variance on reservoir management and may suggest aneed for additional reservoir capacity and other management changes. This paper is likely to be highly cited in subsequent hydropowermanagement work as well as in the RL community.


Convolutional Neural Network Architectures for Matching Natural Language Sentences
Semantic matching is of central importance to many natural language tasks [2,28]. A successful matching algorithm needs to adequately model the internal structures of language objects and the interaction between them. As a step toward this goal, we propose convolutional neural network models for matching two sentences, by adapting the convolutional strategy in vision and speech. The proposed models not only nicely represent the hierarchical structures of sentences with their layerby-layer composition and pooling, but also capture the rich matching patterns at different levels. Our models are rather generic, requiring no prior knowledge on language, and can hence be applied to matching tasks of different nature and in different languages. The empirical study on a variety of matching tasks demonstrates the efficacy of the proposed model on a variety of matching tasks and its superiority to competitor models.

Summary:The paper presents two novel convolutional neural network architectures for modeling sentences in natural languages. These networks are trained specifically for the problem of matching a pair of sentences.The first architecture is a minor modification to the standard way of using a convolutional network over natural language sentences. After a convolution operation on the word embeddings, instead of doing a pooling operation across time (full sequence of words in a sentence) to select a single feature (or k features), the proposed model applies pooling to features associated with consecutive pairs of words.  This results in a output which is of half the size as the input. One can then apply multiple pairs of similar convolution-pooling layer to this output. In order to match pairs of sentences, this architecture is trained using a ranking loss applied to the final feature vector obtained from this network.The second architecture is far more novel than the first. It also includes convolutions over sentences, however instead of applying convolutions independently to each sentence, the model applies convolutions to all the possible pairs of windows on the pair of sentences to be matched. The idea is to enable the convolution kernels to capture the local interactions among words in the two sentences at low level, as opposed to at the level when the sentence representations have matured (as in the case of the first architecture).Both these models are evaluated on three tasks (two of them are somewhat artificial). They seem to beat the state-of-the-art (under certain conditions: discussed below).Quality:I think the models proposed in the paper are quite novel and certainly interesting (and useful) for others working in the same domain to try them out.However my biggest objection is with the evaluation of the proposed models.  The methodology of pre-training the word embeddings in an unsupervised way (word2vec in their case) and fixing them while training the subsequent convolutional neural network architecture is some what artificial and constrained. There is nothing stopping us from back propagating the gradients back into the word embeddings and tuning them to the task. Usually, when one does that, one observes a significant boost in performance. In particular, systems like senna (which are shown to be much worse than the proposed model in this paper) work extremely well when the embeddings are learnt for the task. My conjecture is that when the embeddings are allowed to learn for the task, architectures where pooling results in selection of a single (or k) features across the whole sentence are sufficient to capture both the internal structures of language objects and interactions among them.In summary, the experimental results as they stand are inconclusive. We do not yet know how superior the proposed model are against the state-of-the-art, and whether we are gaining anything significant.A few other points of note. * While the authors cite reference [9] (which uses k-max pooling in convolutional networks and have been shown to perform quite well), they do not compare it to their model. Any reason why? [9] recently has been shown to work quite well on standard nlp tasks. * The proposed model does not beat the state of the art in task 3 (Paraphrase Identification). It is understandable why is that the case: primarily lack of training data. However, interestingly enough, the authors do not show the numbers in Table 3.  Again, any reason why?Clarity:The paper is reasonably well written and easy to understand. Though it isriddled with typos which need to be fixed. An incomplete list of typos is: * 324: model,and > model, and * 325: the their best > the best * 334: hetergenous > heterogeneous * 373: requires less about > this whole sentence requires a complete re-phraseLastly, the details of their experimental setup were somewhat lacking as well. The values of the various model hyper-parameters used during the experiments are not clearly stated. Its also not clear whether the datasets used in experiments 1 and 2 are available for public use or not.Originality:The ideas proposed in the paper are fairly original and interesting.  Subject to their correct evaluation and validation, I think they can be very useful for others working on similar problem. The prior work is largely complete.Significance:I feel that the proposed models need to be properly evaluated before making any statements about their superiority and usefulness over previous techniques. However, assuming that they are validated correctly and shown to work well, then this work can potentially have a significant impact in NLP community where deep learning is only starting to show its usefulness.


Scalable Nonlinear Learning with Adaptive Polynomial Expansions
Can we effectively learn a nonlinear representation in time comparable to linear learning? We describe a new algorithm that explicitly and adaptively expands higher-order interaction features over base linear representations. The algorithm is designed for extreme computational efficiency, and an extensive experimental study shows that its computation/prediction tradeoff ability compares very favorably against strong baselines.

The paper proposes a supervised learning algorithm. It uses stochasticgradient descent and periodically expands the hypothesis space byintroducing new basis functions and adding corresponding components tothe weight vector. As such, as it processes more data, it fits morecomplex models.  The hypothesis space considered here are polynomialsand higher order monomials are gradually introduced to the model.The concept of growing the hypothesis space as more data is introducedis not new (training kernel methods with SGD exhibits this behavior),but in the proposed method, choosing which monomials to add to thehypothesis space is very cheap. The method selects monomials byinspecting the components of the weight vector instead of, say,selecting the monomial that would most reduce the training error (as amatching pursuit variant of the method might).The experiments are thorough and convincing. The method is nearly asfast as fitting a quadratic polynomial, yet just as accurate asfitting a cubic polynomial.The regret bound and its proof are a treat to read. It is pleasantthat the math works out so that more weight is placed on latercomparators.The authors might clarify that the regret bound offers no guidance onhow to choose the monomials to add. Nor does it offer guidance on whento expand the hypothesis space. Rather it states that any nestedhypothesis spaces of this kind (see my note about "this kind" below)do not have high regret.Some suggestions:1) The claim of Theorem 2 can be slightly generalized.  [.]_S(t) picksthe components of . in the support set S(t). But the proof goesthrough if [.]_S(t) is more generally a projection on a linearsubspace S(t). So Theorem 1 holds for any sequence of linear subspacesS(t) whose dimensionality expands with t.2) The two graphs of Figure 2 are informative. But the followingcombination of these two graph would have been more helpful to me: draw one curve peralgorithm as you currently do; let the x-axis be relative time (exactly as youalready compute it in Figure 2(a)), and let the y-axis be the number of datasetson which the algorithm obtains the best score among the other algorithms underthat running time.  [more detail: all of the algorithms being considered refine their solution over time. long below they satisfy their stopping criteria, each produces a useful result. i want to know how many seconds apple requires to beat its competition. i don't need to know its relative error, but rather whether it beats all of its competitors by time T. the graph would tell me how many datasets it dominates at time T.][in the interest of reproducible research, i am also upping my score by +1 because i noticed this technique is publicly available in VW now.]


Reducing the Rank of Relational Factorization Models by Including Observable Patterns
Tensor factorization has become a popular method for learning from multirelational data. In this context, the rank of the factorization is an important parameter that determines runtime as well as generalization ability. To identify conditions under which factorization is an efficient approach for learning from relational data, we derive upper and lower bounds on the rank required to recover adjacency tensors. Based on our findings, we propose a novel additive tensor factorization model to learn from latent and observable patterns on multi-relational data and present a scalable algorithm for computing the factorization. We show experimentally both that the proposed additive model does improve the predictive performance over pure latent variable methods and that it also reduces the required rank -and therefore runtime and memory complexity -significantly.

The factorization rank which is also the number of latent variables is an important parameter in using matrix factorization methods. It affects both model predictive performance and runtime. Most importantly the scalability of most implemented methods for matrix factorization is limited by this parameter.This paper derives upper bound (number of strongly connected components) and lower bound (diclique partition number) on the required rank to recover adjacency tensors and determine the conditions under which factorization is an efficient approach for learning from relational data. The paper provides analysis on tensor rank and multi-linear rank. They provide three interesting insights from their analysis about efficiency of factorization methods with respect to the number of non-trivial connected components in relations, independence of rank and regularities between relations, and relation of dicliques with efficiency of factorization methods in comparison with common similarity metrics.Based on these findings an additive factorization model called additive relational effects model (ARE) is proposed. ARE augments RESCAL model with an additive term that holds the predictions of observable pattern methods.While the paper provides interesting insights and theoretical analysis seems valid, the use of oracle tensor in the evaluation is not very clear; When the ARE is defined the oracle tensor is formed by putting in predictions from heuristic similarity measures such as Jaccard or common neighbors. In the empirical evaluation however it is mentioned that a copy of observed tensor is used as M.  Yet, it is not clear if any of the similarity heuristics were used in construction of the oracle tensor in the evaluation section. If they were used, does the other compared methods perform factorization on the oracle tensor or the original observed one? In the former case, the performance boost of ARE could be due to benefiting mostly from the information of similarity heuristics, which is not a fair comparison. If they are not used, some performance analysis of including these measures in the oracle tensor could be discussed. The paper provides related arguments of this matter in section 3, and it would be beneficial to clearly discuss the effect of including them in the evaluation section.


Exclusive Feature Learning on Arbitrary Structures via 1,2 -norm
Group LASSO is widely used to enforce the structural sparsity, which achieves the sparsity at the inter-group level. In this paper, we propose a new formulation called "exclusive group LASSO", which brings out sparsity at intra-group level in the context of feature selection. The proposed exclusive group LASSO is applicable on any feature structures, regardless of their overlapping or non-overlapping structures. We provide analysis on the properties of exclusive group LASSO, and propose an effective iteratively re-weighted algorithm to solve the corresponding optimization problem with rigorous convergence analysis. We show applications of exclusive group LASSO for uncorrelated feature selection. Extensive experiments on both synthetic and real-world datasets validate the proposed method.

The paper proposes a new penalty term that can be used in learning a regression model;it's based on the idea that features are grouped into (possibly overlapping) groupsand the penalty term discourages the use of nonzero weights for several featuresfrom the same group.  The paper describes how to solve the resulting optimization problemand presents an evaluation on several synthetic and realistic datasets, demonstratingthat the proposed approach works better than several alternatives.The paper is clearly written and well organized, and seems to present an interestingincremental improvement on various earlier LASSO methods (which are mentionedin the related work section).Comments for the authors:"exclusive group LASSO" [caption of Fig. 1] -- should be "Exclusive" "Eq.(2)" [caption of Fig. 1] -- space missing; there are several similar occurrences elsewhere"G_g \in P({1, 2, ..., p}) denotes a set of group g" [page 2] -- I found thissentence unclear.  What exactly is the relationship between g and G_g?  Earlieryou say that a group g is a subset of {1, 2, ..., p}, and later you give anexample where G_g = {1, 2, 4}, so it would appear that G_g is also a subset of{1, 2, ..., p}; what then is the difference between g and G_g at all?"feature index u \in supp(g) will be non-zero" [page 3] -- I found this sentencea bit unclear as well.  What exactly is this feature index u, how is it chosenand what is its purpose?On page 3, there are several instances where groups are described using squarebrackets: G_u = [1, 2], G_v = [2, 3] and so on.  Why do you use brackets herewhereas on page 2 you used curly braces (e.g. "G_g = {1, 2, 4}")?  This makes itseem as if the groups were now real-number intervals, but probably that's notintended here."is a diagonal matrices" [page 4] -- should be "matrix"I was slightly surprised when I saw that your experiments on realistic dataall focus on using your improved LASSO (and other methods) for feature selection(and then applying SVM to train a classifier); when I read about the definitionof LASSO in [21], I was under the impression that its original purpose was toimprove the training of regression models, and your eq. (2) seemed to be alongthe same lines as well, so I thought that you would use some regression tasksto evaluate the method in your experiments.  It might be useful to add some discussionon why you use the method only for feature selection (in the context of a classificationtask), and not for any regression tasks.  Additionally, it might be good to addsome of the more traditional feature-selection methods for comparison (e.g. informationgain etc.).Above the first table on p. 7, you say "we list the mean and variance of classificationaccuracy", but it wasn't quite clear to me what the mean and variance are taken over.  Did you perform some sort of cross-validation or something like that?


Time-Data Tradeoffs by Aggressive Smoothing
This paper proposes a tradeoff between sample complexity and computation time that applies to statistical estimators based on convex optimization. As the amount of data increases, we can smooth optimization problems more and more aggressively to achieve accurate estimates more quickly. This work provides theoretical and experimental evidence of this tradeoff for a class of regularized linear inverse problems.

In regularized linear inverse problems, the sample complexity for recovering the true signal has recently been well understood. This paper agues that excess observations than needed in the sample complexity bound can be used to reduce the computational cost. This is achieved through carefully smoothing the original nonsmooth regularizer (such as the ell_1 norm) hence reducing computational iterations,  and without violating the sample complexity bound for recovery. The paper is clearly written and the idea seems interesting, however, there are several practical issues that perhaps should have been addressed.The reviewer found the idea to squeeze more smoothing from excess observations quite interesting, however, this is at the expense of potentially compromising the recovery probability (eta in Fact 2.3, in particular the success recovery bound). A bit disappointingly, in the experiments the authors did not simulate the probability of "exact" recovery at all; instead, only some predefined "closedness" to the true signal is used to declare victory of the algorithm. The authors did decrease the smoothing parameter by a factor of 4 to hedge against failure, but this is adhoc and insufficient. It would be very interesting (in some sense also necessary) to see whether or not, or to what extent, does the aggressive smoothing affect the (exact) recovery probability. Judging from the bound (Fact 2.3), there should be another tradeoff. The experiments can be improved. The reviewer expected to see the following comparison: When we compare against some constant smoothing parameter, say mu = 0.1, we can compute the number of samples needed for high probability recovery, call it m_mu, which is smaller than the number of available samples m. Then we just randomly throw away m - m_mu samples. This way one also reduces the computational cost by reducing the size of the problem. In the reviewer's opinion, this should be the "conventional" constant smoothing algorithm to compare to. Right now, the authors seem to let the competitor run on all available samples, putting it in a disadvantageous position. The two strategies (throwing away redundant data or aggressively smoothing) are really two blades of the same sword: both aim at maintaining the recovery bound in the minimal sense. But the first approach is even more appealing: it certainly requires less memory. The reviewer strongly recommends the authors to perform a serious comparison and report the relative strengths and weaknesses.Another issue the reviewer would like to see addressed is practicality: so far the analysis and experiments are done with prior knowledge of the true signal. In practice this is not available. How could one still be able to apply the aggressive smoothing without being too aggressive? On the other hand, it all appears to "tune" the smoothing parameter, which is what is done in practice anyways. From a fully practical aspect, what is new and different here then? If the new message (as argued in line 325) is that the smoothing parameter needs to depend on the sample size, then how can this be implemented without too much prior knowledge of the true signal?


Clustering from Labels and Time-Varying Graphs
We present a general framework for graph clustering where a label is observed to each pair of nodes. This allows a very rich encoding of various types of pairwise interactions between nodes. We propose a new tractable approach to this problem based on maximum likelihood estimator and convex optimization. We analyze our algorithm under a general generative model, and provide both necessary and sufficient conditions for successful recovery of the underlying clusters. Our theoretical results cover and subsume a wide range of existing graph clustering results including planted partition, weighted clustering and partially observed graphs. Furthermore, the result is applicable to novel settings including time-varying graphs such that new insights can be gained on solving these problems. Our theoretical findings are further supported by empirical results on both synthetic and real data.

Clustering from Labels and Time-Varying GraphsThe authors consider graph clustering i.e. nodes are assigned to groups based on dense interconnectivity, with no/sparse connectivity to other nodes not in the same group. As pointed out by the authors, their model is in the vein of the stochastic labelled block model. However, they can cover additional scenarios such as time-varying graphs. The basic scenario is presented in eqn (1). This is restated as a relaxed convex optimisation problem in (2) (incidentally a bug ‘and thus and has nuclear …’). The only concern with (2) is that, though convex, and a linear objective, it may be computational intensive for large graphs. The experiment with n=400 in the Supplementary suggests otherwise but it would have been interesting to know algorithmic time complexity dependence on n.The main theorems in the text give bounds on the estimate of the true cluster matrix Y for the convex program (2). Specifically, Theorem 1 gives sufficient conditions for this convex program to find the true cluster matrix, dependent on label distribution, minimum size of the true clusters (note: I don’t think you would know this in reality?) and the weight function. I wasn’t sure of the significance of c (a universal constant) here. Thus the later Corollary 3 gives a condition on recovering Y which has some support in the experimental Section 5 (below Fig. 1-3), for a particular special case. I was only able to check two lemmas in the Supplementary – though argument looked sound. In section 4 the author(s) move from the general argument of Section 3 to two special cases (e.g. non-uniform edge densities, Corollary 3). This includes Markov sequence and time-varying e.g. Corollary 5 presents sufficient conditions on finding the true cluster matrix based on the same dependency on c, \mu, \nu, K and n for the case of Markov snapshots. Section 5 presents some brief experimental results (there is no Conclusion), though the Supplementary (Section A) gives more detail about the experiments.In short, the authors present a convex program for graph clustering which has broader implantation to time-varying graphs. They present criteria for establishing if the true cluster matrix has been found – which appears sound and has experimental support (see e.g. Figure 4 in the Supplementary). The criterion (Theorem 1, for the general case) appears useable (possibly as a stopping criterion – or if stopped early, whether a sound solution has been achieved). I think the topic of graph clustering is important in terms of real-word applications in bioinformatics, social networks, etc, and this paper looks like a valid and useful contribution. Thus I recommend acceptance of the paper.


Scaling-up Importance Sampling for Markov Logic Networks
Markov Logic Networks (MLNs) are weighted first-order logic templates for generating large (ground) Markov networks. Lifted inference algorithms for them bring the power of logical inference to probabilistic inference. These algorithms operate as much as possible at the compact first-order level, grounding or propositionalizing the MLN only as necessary. As a result, lifted inference algorithms can be much more scalable than propositional algorithms that operate directly on the much larger ground network. Unfortunately, existing lifted inference algorithms suffer from two interrelated problems, which severely affects their scalability in practice. First, for most real-world MLNs having complex structure, they are unable to exploit symmetries and end up grounding most atoms (the grounding problem). Second, they suffer from the evidence problem, which arises because evidence breaks symmetries, severely diminishing the power of lifted inference. In this paper, we address both problems by presenting a scalable, lifted importance sampling-based approach that never grounds the full MLN. Specifically, we show how to scale up the two main steps in importance sampling: sampling from the proposal distribution and weight computation. Scalable sampling is achieved by using an informed, easy-to-sample proposal distribution derived from a compressed MLN-representation. Fast weight computation is achieved by only visiting a small subset of the sampled groundings of each formula instead of all of its possible groundings. We show that our new algorithm yields an asymptotically unbiased estimate. Our experiments on several MLNs clearly demonstrate the promise of our approach.

This paper combines evidence-based clustering with an importance sampling approach. It further optimizes the weight function calculation of importance sampling, by using a second sampler to estimate the number of true groundings.     I recommend to accept this paper because of the importance of the evidence problem, and the fact that the proposed solution is very general and scalable.     The paper is well-written and clear, except for Figure 1 (b) and Equations 5,6, and 7, which are poorly explained.     A disadvantage of the paper is that its clustering algorithm is reused from a recent publication:    "Evidence-based Clustering for Scalable Inference in Markov Logic" at ECML 2014.    Thus, the clustering algorithm is not a contribution of this paper.    Another disadvantage is the complexity of the setup.     The introduction says that the combination of the base importance sampler, and the sampler for the number of groundings yield unbiased estimates. This claim is not supported by the main text. The first sampler is obviously unbiased when using the exact number of groundings. Proposition 2 says that the second sampler is unbiased. I don't think this implies that the combination of the two is unbiased. Even if the second sampler is unbiased, it has a variance because it uses a finite fixed sample size. This variance can induce a bias in the first sampler?     The experimental setup is impressive, because of the scale of the MLN models considered. The results are slightly disappointing though: the errors do not go down significantly. Is this to be expected?     Beta is used in line 300 and 400/Fig3 for different variables? Is the second beta explained?


Deep Learning for Real-Time Atari Game Play Using Offline Monte-Carlo Tree Search Planning
The combination of modern Reinforcement Learning and Deep Learning approaches holds the promise of making significant progress on challenging applications requiring both rich perception and policy-selection. The Arcade Learning Environment (ALE) provides a set of Atari games that represent a useful benchmark set of such applications. A recent breakthrough in combining model-free reinforcement learning with deep learning, called DQN, achieves the best realtime agents thus far. Planning-based approaches achieve far higher scores than the best model-free approaches, but they exploit information that is not available to human players, and they are orders of magnitude slower than needed for real-time play. Our main goal in this work is to build a better real-time Atari game playing agent than DQN. The central idea is to use the slow planning-based agents to provide training data for a deep-learning architecture capable of real-time play. We proposed new agents based on this idea and show that they outperform DQN.

Summary.This paper studies a number of variations on the topic of training a deep network using data generated by a Monte-Carlo Tree Search (MCTS) agent. The paper focuses on the Atari 2600 platform and is motivated by the observation that, while MCTS performs extremely well on Atari 2600 games, it is also too computationally expensive to be used in a realistic setting. The authors provide empirical results on a number of Atari 2600 games.Overall.To me, the main contribution of this paper is to propose to ``compile'' the UCT value function (or policy, according to the algorithm used) into a deep network. The paper is clear, and the results of good quality, but the work lacks in significance. While there are some nice results -- and performance improvements on all but one game -- I feel the topic is simply not sufficiently explored. There is little insight gained into how these results might carry over to other domains, or significant algorithmic improvements that could result from this work.A few major hurdles:    . The UCC-I algorithm, described here, is very reminiscent of the DAgger algorithm of Ross et al. (2011). It would probably be good to discuss the relationship. Do we expect better sampling guarantees than their approach?    . Are UCR/UCC really valid competitors to previous learning approaches? They still require full access to the simulator.    . The fact that the empirical results rely on game-specific tunings somewhat devalues said results. Are the results so different when a uniform environment parametrization is used?There are a number of research directions which I believe could improve the paper:    . Further studying how well a policy/value function can be summarized into a deep network. Which is easier? Your results hint that it is better to summarize the policy. Does this tell us something about the nature of Atari 2600 environments?    . What about performing regression on the empirical return, rather than the UCT value? Is there a sense in which one is better than the other?    . The UCT agent doesn't use "features", but these might emerge from the "policy compilation". A related idea was studied by Cobo et al. (2013) in learning features from expert data. Can something like this be investigated here as well?     . How is partial observability handled? The optimal stimuli plots hint at some of this, but it still seems an understudied question.Minor points:    . line 120: "two broad classes of approaches": this seems to suggest no other way would be valid. Can this be rephrased?     . line 136-143: it would be nice if the related work section discussed how the non-deep network features differ from the new stuff. For example: is the main distinction that the visual features are learned, or that we are using a deep architecture?    . line 136: I believe cite [4] is incorrect in the bibliography. Other cites also seemed incorrectly numbered.


Efficient Minimax Strategies for Square Loss Games
We consider online prediction problems where the loss between the prediction and the outcome is measured by the squared Euclidean distance and its generalization, the squared Mahalanobis distance. We derive the minimax solutions for the case where the prediction and action spaces are the simplex (this setup is sometimes called the Brier game) and the 2 ball (this setup is related to Gaussian density estimation). We show that in both cases the value of each sub-game is a quadratic function of a simple statistic of the state, with coefficients that can be efficiently computed using an explicit recurrence relation. The resulting deterministic minimax strategy and randomized maximin strategy are linear functions of the statistic.

Summary:This paper derived the minimax solutions for online prediction problems where the loss between the prediction and the outcome is measured by the squared Euclidean distance and the squared Mahalanobis distance. Two cases of prediction and action space are included: probability simplex and L_2 ball. For each problem, it provides detailed analysis for the optimal strategy and regret bound. This is a purely theoretical work without experiments. Quality:This paper is of poor quality. Although lots of detailed analysis are given, there seems an important mistake in its mathematic calculation, making the correctness of one of the two contributions of this paper, the minimax strategy for probability simplex, being in doubt. Clarity:This presentation is clear in most cases, although there are a few typos. Another problem appears at the end of the first page. To make the presentation clear, it should provide a detailed mathematic definition for the probability simplex. Originality:This seems an original work. Although minimax analysis has been proposed in existing works, the specific problem, Mahalanobis distance loss in simplex or L2 ball, has not been studied.Significance:This is obviously a theoretical work. There is no experiment in the paper. Also there is no discussion for its application to real world problems. It is unknown for the significance of the theory. Comments on the main problem, the simplex problem:One of the two main contributions of this work is the minimax solutions for predictions and actions on probability simplex. And all this section is based on Lemma 4.1. This lemma is about the solution of an optimization problem on “probability simplex”. Since there is no clear definition of “probability simplex” in this paper, we have to use the usual definition: sum_i(p_i)=1 and p_i > 0. But in this lemma, “positive” is not mentioned as a constraint and not involved in Lagrange multiplier. Thus, the optimizer p* and optimized value are obtained without positive constraint. In addition, it is easy to show that the p* derived in this lemma is not always positive: for example, take c=[2,1;1,2] which is symmetric and positive definite, d=[2;5], p*=c*(d-(sum(c*d)-1)/sum(sum(c)))=[-1;2], not positive.Theorem 4.2 is based on Lemma 4.1, where p is assumed as the distribution of k and thus should be positive. This obviously contradicts with the assumption (p does not need to be positive) of lemma 4.1.  Therefore, it is not proper for Theorem 4.2 to apply the conclusion of Lemma 4.1.  We can conclude that Theorem 4.2 is wrong.Theorem 4.3 and Lemma 4.4 are based on 4.2 and thus should be incorrect. Thus, for the simplex problem, both the strategy and the regret bound are problematic.