Reputation-based Worker Filtering in Crowdsourcing
In this paper, we study the problem of aggregating noisy labels from crowd workers to infer the underlying true labels of binary tasks. Unlike most prior work which has examined this problem under the random worker paradigm, we consider a much broader class of adversarial workers with no specific assumptions on their labeling strategy. Our key contribution is the design of a computationally efficient reputation algorithm to identify and filter out these adversarial workers in crowdsourcing systems. Our algorithm uses the concept of optimal semi-matchings in conjunction with worker penalties based on label disagreements, to assign a reputation score for every worker. We provide strong theoretical guarantees for deterministic adversarial strategies as well as the extreme case of sophisticated adversaries where we analyze the worst-case behavior of our algorithm. Finally, we show that our reputation algorithm can significantly improve the accuracy of existing label aggregation algorithms in real-world crowdsourcing datasets.

This work explores the problem of identifying and filtering out *adversarial* workers in crowdsourced classification problems. A worker is adversarial if his/her voting strategy doesn’t follow the standard random process: vote correctly with probability p and incorrectly with probability 1-p, where p is the worker’s reliability.  To solve the problem of adversarial worker filtering, this paper proposes to attach reputation values to workers. The reputation value of a worker is calculated based on if this worker’s votes agree with other workers’ (in particular, this paper proposes to penalize disagreements instead of awarding agreements)  The authors propose two versions of the penalty algorithms and prove their properties with different adversarial worker voting strategies. Experiments on both synthetic and real datasets are conducted.I think this paper addresses a very interesting problem.  Most of other papers on label aggregation assume workers’ votes are i.i.d. samples from some distribution. This paper considers different voting strategies and takes a step towards a more realistic setting. However, the theoretical analysis on hard penalty algorithms are not too satisfactory since 1) it’s hard to interpret the results and 2) the authors make a strong assumption in their analysis (i.e., honest workers are perfect).  I also have some concerns about the experiment results. (Please see comments below.)Some detailed comments:- In the analysis of hard penalty assignment algorithm (and also the simulation), you assume the honest workers are perfect, i.e., give correct votes with probability 1. This seems to be a fairly strong assumption to me. Is this necessary in your analysis? Do you have intuitions on how to relax this assumption?- The results of Theorem 3 and 4 are represented using the workers’ voting graph B_H. It would help the readers to get intuitions by giving examples to illustrate the bounds.- In the experiments results on Table 2, the number of users being filtered out is different in each setting. I think you should show all the results (i.e., set the number of filtered users from 1 to 10) since you won’t know the optimal parameters when running your algorithm in real applications.- In the experiments, your algorithm boosts the performance of ITER (by Karger et. al. 2011) the most. However, ITER assumes all workers complete the same number of tasks. If you want to apply ITER in datasets without this property, you should modify their algorithm by normalizing the messages at every step during the message passing. Otherwise the algorithm performance would just be dominated by the accuracies of workers who complete the most number of tasks.  Without this modification, your algorithm is essentially just filtering out low-accuracy workers completing lots of tasks. It doesn’t provide evidences that your algorithm can filter out adversarial workers.AFTER THE REBUTTAL:Thanks for addressing my concern about the ITER implmentation. I have updated my scores. Please report the updated results if accepted. Overall, I think this is a nice paper addressing a more reasonable setting. I am still a little bit bothered by the perfect-worker assumption, but the empirical evaluations mitigate this shortcoming. I would vote for accept.


Multi-Class Deep Boosting
We present new ensemble learning algorithms for multi-class classification. Our algorithms can use as a base classifier set a family of deep decision trees or other rich or complex families and yet benefit from strong generalization guarantees. We give new data-dependent learning bounds for convex ensembles in the multiclass classification setting expressed in terms of the Rademacher complexities of the sub-families composing the base classifier set, and the mixture weight assigned to each sub-family. These bounds are finer than existing ones both thanks to an improved dependency on the number of classes and, more crucially, by virtue of a more favorable complexity term expressed as an average of the Rademacher complexities based on the ensemble's mixture weights. We introduce and discuss several new multi-class ensemble algorithms benefiting from these guarantees, prove positive results for the H-consistency of several of them, and report the results of experiments showing that their performance compares favorably with that of multi-class versions of AdaBoost and Logistic Regression and their L 1 -regularized counterparts.

Summary of the paper: The paper introduces a new class of multi-class boosting algorithms with base learners that are regularized based on their Rademacher complexities. The experiments show great improvement over other multi-class approaches in the literature and on the non-regularized version of the proposed algorithm.Detailed remarks:For the title: in general, the term "deep" in deep learning is used for saying that the representation is hierarchical in a compositional sense. Trees are obviously not deep in this sense, and so just because you are using large trees in boosting (a quite common setup in practice), it will not make the approach "deep". You still use a single "hidden layer" of trees, combined linearly, this is definitely a shallow architecture. Thus I strongly object to the title, it is misleading.Lines 042-043: In practice, boosted trees almost always outperform boosted stumps \cite{CaNi06, Keg14}, and when the validated tree sizes are obtained by proper hyper-parameter optimization, they can be quite large, the same order as found in your experiments. Moreover, when boosting multi-class Hamming trees in AB.MH, \cite{Keg14} also found that on most of the data sets there is very little overfitting, basically one can boost trees of several tens of inner nodes for ten thousand iterations (see, for example, pendigits or letters, two sets on which most algorithms are tested), without increasing the test error. So, the statement of "boosting has been observed to overfit in practice", derived from 15 year-old papers, should be revised. Sometimes it overfits, sometimes it doesn't, and basically we don't know when it does and why it does when it does.Lines 046-047: To my knowledge, the first paper proposing adaptive regularization of base classifiers is \cite{KeWa04}. The intuitive idea is the same and the final algorithm is not that different either (coefficients have to be shrunk by a quantity related to the empirical complexity of the weak classifier).Although we cannot expect that a conference paper surveys all multiclass boosting algorithms, the paper should at least mention those that seem to be state of the art: AOSO \cite{SuReZh12}, ABC \cite{Li09,Li09a}, Gao-Koller's iterative weak learner in hinge-boost \cite{GaKo11}, and AB.MH with Hamming trees \cite{Keg14} (it seems to me that the trees in this latter are quite similar to those used in this submission).The experimental setup. I was honestly stunned reading this: "We recorded the parameter tuple that had the lowest average error across all 10 runs, and this average error and the standard deviation of the error is reported in Table 1 and Table 2, along with the average number of trees and the average size of the trees in the ensembles." You're validating on the test set, something that we teach to our students never to do. The consequence is twofold. First, I cannot compare the errors to those available in the literature. Some of the errors (e.g. on pendigit) looked suspiciously low, 3-4 times lower than I've ever seen, that's when I started to check your experimental setup. Second, the empirical comparison of the algorithms you tested is tainted. It is obvious that if you take an algorithm and you add hyper-parameters (the AB.MR -> L1 AB.MR -> MDeepBoostSum chain), the minimum test error can only decrease. The ballpark range of the "improvements" is very much in line with this view: you simply harvested the fact that the minimum of a larger sample is smaller than the minimum of a smaller sample, even if they come from the same distribution.Now, I know that this seems like a detail for a theoretician, but for people using these algorithms what you are claiming is important. We have tested a lot of ways of regularizing the weak learners up to about ten years ago (you referred to some of the works), it never worked, more precisely, we didn't seem to need it. There were some indications that it could help on small data sets \cite{KeWa04}, but, exactly because of the small size of the sets, results were inconclusive. If you now claim that it is not the case, the experimental validation has to be rock solid. My suggestion is that you make an attempt to redo the experiments doing proper double cross validation during the rebuttal period, and show us the new results. If they are non-conclusive (that is, the regularized version doesn't beat the standard algorithm), I would say the paper could still be accepted, but the message has to be altered to something like "here is an interesting-looking algorithm with some strong theoretical justifications, but regularization doesn't work".Providing an open source implementation of the algorithm would be a great way to make the experiments reproducible and to let people use the proposed techniques and to build on them.Pseudocode: for those who would like to implement the method starting from the pseudocode, it would be helpful to point towards the definitions of the quantities in the caption: \Lambda and S_t for t = 1 are undefined.@inproceedings{KeWa04,	Address = {Vancouver, Canada},	Author = {K\'{e}gl, B. and Wang, L.},	Booktitle = {Advances in Neural Information Processing Systems},	Pages = {665--672},	Publisher = {The MIT Press},	Title = {Boosting on manifolds: adaptive regularization of base classifiers},	Volume = {17},	Year = {2004}}@inproceedings{CaNi06,	Author = {Caruana, R. and Niculescu-Mizil, A.},	Booktitle = {Proceedings of the 23rd International Conference on Machine Learning},	Pages = {161--168},	Title = {An Empirical Comparison of Supervised Learning Algorithms},	Year = {2006}}@inproceedings{KeBu09,	Address = {Montreal, Canada},	Author = {K\'{e}gl, B. and Busa-Fekete, R.},	Booktitle = {International Conference on Machine Learning},	Pages = {497--504},	Title = {Boosting products of base classifiers},	Volume = {26},	Year = {2009}}@inproceedings{Li09,	Author = {Li, P.},	Booktitle = {International Conference on Machine Learning},	Title = {{ABC}-{B}oost: Adaptive Base Class Boost for Multi-class Classification},	Year = {2009}}@techreport{Li09a,	Author = {Li, P.},	Institution = {Arxiv preprint},	Number = {arXiv:0908.4144},	Title = {{ABC-LogitBoost} for Multi-class Classification},	Year = {2009}}@inproceedings{GaKo11,	Author = {Gao, T. and Koller, D.},	Booktitle = {International Conference on Machine Learning},	Title = {Multiclass boosting with hinge loss based on output coding},	Year = {2011}}@inproceedings{SuReZh12,	Author = {Sun, P. and Reid, M. D. and Zhou, J.},	Booktitle = {International Conference on Machine Learning (ICML)},	Title = {{AOSO-LogitBoost}: Adaptive One-Vs-One {LogitBoost} for Multi-Class Problem},	Year = {2012}}@inproceedings{Keg14,	Abstract = { We train vector-valued decision trees within the framework of AdaBoost.MH. The key element of the method is a vector-valued decision stump, factorized into an input-independent vector of length $K$ and label-independent scalar classifier.},	Author = {K\'{e}gl, B.},	Booktitle = {International Conference on Learning Representations},	Title = {The return of {AdaBoost.MH}: multi-class {H}amming trees},	Url = {http://arxiv.org/abs/1312.6086},	Year = {2014}}----I looked at the new experimental results and indeed they are more reasonable now. As expected, errors increased significantly (eg., on letters and pendigits the errors increased by 6-7 standard deviations). In this light your answer "1) While it is of course possible to overestimate the performance of a learning algorithm by optimizing hyperparameters on the test set, this concern is less valid when the size of the test set is large relative to the "complexity" of hyperparameter space (as any generalization bound will attest). Note that our experiments varied only three hyperparameters over a large data set." looks strange. You just proved that my concern was highly relevant. If I look at your results now, I see no significant improvement by the added regularization which contradicts the main message of the paper (differences are in the 1-2 std range, completely compatible by statistical fluctuation). On the other hand, your results using AB.MR and AB.MR-L1 are really good, you do something in your tree-building procedure which seems to work better than what other people are doing (unfortunately, you don't give details on your procedure). I'm sympathizing with you in the sense that I know that simply describing a state-of-the-art algorithm without any theoretical results will never be accepted at NIPS, but still, at this point your theoretical results are irrelevant for a practitioner (it's not your theory that makes the algorithm good), and your practical results are irrelevant for a theoretician (for the same reason: it's not your practical results that make the theory interesting or relevant). It's two papers in one with a false conclusion. I'd be happy to accept the paper if you were honest about it.


Greedy Subspace Clustering
We consider the problem of subspace clustering: given points that lie on or near the union of many low-dimensional linear subspaces, recover the subspaces. To this end, one first identifies sets of points close to the same subspace and uses the sets to estimate the subspaces. As the geometric structure of the clusters (linear subspaces) forbids proper performance of general distance based approaches such as K-means, many model-specific methods have been proposed. In this paper, we provide new simple and efficient algorithms for this problem. Our statistical analysis shows that the algorithms are guaranteed exact (perfect) clustering performance under certain conditions on the number of points and the affinity between subspaces. These conditions are weaker than those considered in the standard statistical literature. Experimental results on synthetic data generated from the standard unions of subspaces model demonstrate our theory. We also show that our algorithm performs competitively against state-of-the-art algorithms on realworld applications such as motion segmentation and face clustering, with much simpler implementation and lower computational cost.

The paper considers the problem of subspace clustering where the goal is to jointly find the spaces and the subset of points belonging to each. As pointed out in the related work, this area has seen very interesting progress recently starting with the SSC algorithm Elhamifar and Vidal using l1 minimization.Most of these methods are done in two steps, first one finds a neighborhood matrix indicating which points belong in the same subspace, and then performing some sort of clustering to find the subspaces.Here the authors propose a greedy approach for both steps. To find the neighborhood of a point i, the point j closest to i is added first, followed by the point closest to the span of i and j etc. Once the neighborhood matrix is constructed, one can either perform spectral clustering or use another greedy procedure the authors describe to find the subspaces.Interestingly this procedure has very nice theoretical properties (analogous in some sense to how orthogonal matching pursuit often performs just as well as lasso under certain conditions). Compared to most methods which just prove the correctness of the first step (picking neighborhoods) here the authors prove the correctness of both steps (i.e. exact clustering). They allow the subspaces to intersect (controlled by some max affinity). Interestingly, they show that as the number of points grows a higher max affinity is allowed for their approach (as one would like). This is different from another greedy approach TSC.The experiments compare the authors approach to SSC (l1 minimization) and two greedy approaches GFS and TSC. The new approach performs better than the other greedy approaches while being comparable to SSC. (Of course being greedy it is much faster than SSC).Quality: Paper is thorough, authors provide a novel algorithm, theory and experiments.Clarity: I found the work to be very well written and easy to understand.Originality: Good, not incremental but also not revolutionarySignificance: Moderate, again not incremental, but also not revolutionary.


Learning the Learning Rate for Prediction with Expert Advice
Most standard algorithms for prediction with expert advice depend on a parameter called the learning rate. This learning rate needs to be large enough to fit the data well, but small enough to prevent overfitting. For the exponential weights algorithm, a sequence of prior work has established theoretical guarantees for higher and higher data-dependent tunings of the learning rate, which allow for increasingly aggressive learning. But in practice such theoretical tunings often still perform worse (as measured by their regret) than ad hoc tuning with an even higher learning rate. To close the gap between theory and practice we introduce an approach to learn the learning rate. Up to a factor that is at most (poly)logarithmic in the number of experts and the inverse of the learning rate, our method performs as well as if we would know the empirically best learning rate from a large range that includes both conservative small values and values that are much higher than those for which formal guarantees were previously available. Our method employs a grid of learning rates, yet runs in linear time regardless of the size of the grid.

The paper proposes a Learning the Learning Rate (LLR) algorithm for learning from expert advice which while retaining several worst case bounds for the problem enjoyed by previous algorithms like exponential weights algorithm, in addition also enjoys a guarantee on regret that is at most a poly logarithmic factor in number of experts and inversely in learning rate to the regret of exponential weights algorithm with that prescribed learning rate (for learning rates in a prescribed interval).  Further the proposed algorithm employs a grid over learning rates in the interval and yet runs in linear time regardless of the granularity of the grid. The problem of adaptively learning from expert advice in a way which while retains worst case guarantees also enjoys better practical performance against benign adversaries has been a problem of great interest. The algorithm proposed first of all neatly combines three adaptive bounds from previous works, the variance type bound, the L* type bound for small losses and a more recent bound of the order of follow-the-leader algorithm which has been shown to work well in practice (eg. for iid data). Overall the paper is well written and the problem considered is of practical interest.  Some remarks : 1. I do have some concerns over the lower limit of learning rate used though. Yes, it is true that sqrt{log K / T} is as small a learning rate one needs to consider to be able to guarantee the absolute worst case performance for prediction with experts advice. However in the regret bound you provide, the bound is with respect to eta chosen in hindsight. So it would make sense to provide bounds for even smaller learning rates. I wonder if one could get a guarantee over entire range of step sizes while worsening the regret bound by an additive factor beyond only the multiplicative factor over regret bound of best eta. 2. The paper only considers hind sign bounds w.r.t. to experts algorithms with optimal fixed step sizes. However in practice often step size schemes that vary with time are considered. For instance one might consider step sizes of form eta_t =  eta / t^a  where eta and a are tuned. The result in this paper only refers to a = 0. At least glancing from the results it is not clear to me that the results can be adapted to the non-zero a case.


On the Information Theoretic Limits of Learning Ising Models
We provide a general framework for computing lower-bounds on the sample complexity of recovering the underlying graphs of Ising models, given i.i.d. samples. While there have been recent results for specific graph classes, these involve fairly extensive technical arguments that are specialized to each specific graph class. In contrast, we isolate two key graph-structural ingredients that can then be used to specify sample complexity lower-bounds. Presence of these structural properties makes the graph class hard to learn. We derive corollaries of our main result that not only recover existing recent results, but also provide lower bounds for novel graph classes not considered previously. We also extend our framework to the random graph setting and derive corollaries for Erdős-Rényi graphs in a certain dense setting.

This theoretical paper derives low bounds on the number of samples needed to learn graphs (and not factors) from data. The paper uses various versions of the Fano lemma, e.g.  conditional to particular graph classes. Derivations and arguments are purely information-theoretic.  The results are probably correct (I did not check the algebra), however I am not sure about the value of what is reported.  Here is the list of deficiencies/questions troubling me in this paper:1)	Assumption on the ferromagnetic and zero-field nature of the Ising model is highly unrealistic for majority of interesting cases.  2)	Assumption on the constancy of the factors (leaving only an “effective temperature” in otherwise uniform ferromagnetic Ising model) within the graph makes it even more restrictive. I am not aware of any learning or inference application where such an assumption may be of a practical inference. 3)	Once the (conditional) Fano lemma is formulated (and this part is rather straightforward and formal) the authors turn to finding subsets of sub-graphs which are large in size and yet have small KL-diameter. Question of the KL divergence is then linked to analysis of the difference in correlations between two representative graphs within the class. Next , the authors suggest that the difference between correlations will be small if one of the correlations is very large, that is when ``spins” at a pair of measurement points are completely aligned (very small temperature), or (another scenario) when  compared graphs are simply close to each other.  These two principles are then used in the ``application” part to modify a preselected candidate sub-graph (as a good candidate) in the way that the new sub-graph would remain close (in terms of the KL divergence). These arguments are correct but trivial – using very little information about the potentially rich correlations GM of the Ising type can provide. This observation emphasizes the very loose nature of the bounds derived.4)	In the application sections (#5,6) the authors apply the scheme to estimate the lower bounds for graphs of special types --- limited by path-length or girth and finally random Erdos-Renyi graphs.  And here again, straightforward estimations (algebra used) seem correct, however I don’t really see a value in any of these results. 5)	The story sold is not constructive. I did not find anywhere in the paper discussion of possible consequences of the information-theoretic consideration for actual learning algorithms.


Dynamic Rank Factor Model for Text Streams
We propose a semi-parametric and dynamic rank factor model for topic modeling, capable of (i) discovering topic prevalence over time, and (ii) learning contemporary multi-scale dependence structures, providing topic and word correlations as a byproduct. The high-dimensional and time-evolving ordinal/rank observations (such as word counts), after an arbitrary monotone transformation, are well accommodated through an underlying dynamic sparse factor model. The framework naturally admits heavy-tailed innovations, capable of inferring abrupt temporal jumps in the importance of topics. Posterior inference is performed through straightforward Gibbs sampling, based on the forward-filtering backwardsampling algorithm. Moreover, an efficient data subsampling scheme is leveraged to speed up inference on massive datasets. The modeling framework is illustrated on two real datasets: the US State of the Union Address and the JSTOR collection from Science.

This paper proposes the dynamic rank factor models, which can extract topics changes along time, and also discover the topic and word correlations. The two case studies using the proposed model show interesting topic changing patterns, which are aligned well with true events; and the structures between topics and words are also visualized and discussed. In general, this is a good paper. However, I have two main concerns. First, while the introduction is well motivated and the experiment section is clearly written, Section 2 is not well structured and under selling.- The authors start from dynamic factor models (section 2.1), and then talk about general topic models (without time involvement) and then come back to dynamic models again in section 2.3. This structure can be improved to avoid jump back and forth.- Section 2.2 is not related with dynamic changing, but the authors use the subscript "t" to denote the t^th document, while using "t" to denote the time t in Section 2.1 and Section 2.3, and "n_t" to denote the document at time t. This is very confusing. - Probably because the math part is dense, the proposed model in general is mixed with existing work and is not well emphasized. Even the dynamic part (Section 2.3), an important proposed work, only gives the latent factor model, but does not say anything about dynamic changing but refer back to Section 2.1- It would be stronger if the nice properties of the proposed model are discussed more, instead of just listing.Second, while the authors indicates that the proposed model is an alternative to dynamic topic models and correlated topic models, there is no comparison at all against these models in the experiment section. - The experiment shows the changing of topics posterior mean along time and the detected topics, however, there is no evaluation of topic quality, like topic coherence, etc.- This paper would be stronger with comparison against dynamic topic models and correlated topic models. - For some interesting topics, it would be nice to see the actual topic changes (the top words) along time.Some minor comments:- \alpha and \beta are used as the parameters for gamma distribution and also the parameters for Dirichlet distributions.- Figure 1, the displayed topics are the final topics after observing all documents? This should be clear.- Figure 2, it would be nice to display a topic name rather than topic index, it would be easier to interprete the meanings of the topics.- Figure 2, it's hard to read the word dendrogram, too small. It would be great if there is more discussion about the results.


Learning to Discover Efficient Mathematical Identities
In this paper we explore how machine learning techniques can be applied to the discovery of efficient mathematical identities. We introduce an attribute grammar framework for representing symbolic expressions. Given a grammar of math operators, we build trees that combine them in different ways, looking for compositions that are analytically equivalent to a target expression but of lower computational complexity. However, as the space of trees grows exponentially with the complexity of the target expression, brute force search is impractical for all but the simplest of expressions. Consequently, we introduce two novel learning approaches that are able to learn from simpler expressions to guide the tree search. The first of these is a simple n-gram model, the other being a recursive neuralnetwork. We show how these approaches enable us to derive complex identities, beyond reach of brute-force search, or human derivation.

The paper introduces a novel use case for neural nets, which is learning a representation for symbolic expressions and finding their mathematical identities.Even though the expressions studied are very limited and there is no proof that they can be extended to more complicated expressions, I find the paper interesting. And I believe it could have good impact for symbolic software libraries. -The problem statement states that we're looking for expressions with lower computational complexity. But nowhere in the algorithm such a constraint is enforced. I understand that this is not trivial, but have authors taught about possible solutions to limit the search space to such solutions?-About the restrictions mentioned in section 2, is the scheduler the only limiting factor for more complicated mathematical expression? I would have liked to see more formal or mention of empirical experiments for setting these restrictions.-Also the structure of the paper is a not easy to follow. It would be better if stages were explained more clearly. -Is there a constraint for size of the vector/matrix? e.g. for k=1,n=1 the expression for RBM-1 in the supplementary material doesn't seems to be valid.Some typos:332: show for148: has contains289: is is338: by be


Attentional Neural Network: Feature Selection Using Cognitive Feedback
Attentional Neural Network is a new framework that integrates top-down cognitive bias and bottom-up feature extraction in one coherent architecture. The top-down influence is especially effective when dealing with high noise or difficult segmentation problems. Our system is modular and extensible. It is also easy to train and cheap to run, and yet can accommodate complex behaviors. We obtain classification accuracy better than or competitive with state of art results on the MNIST variation dataset, and successfully disentangle overlaid digits with high success rates. We view such a general purpose framework as an essential foundation for a larger system emulating the cognitive abilities of the whole brain.

The authors introduce the Attentional Neural Network which integrates top-downbias and bottom-up feature extraction in a single architecture.I like very much the idea of integrating top-down connections, but I have someconcerns on how these have been implemented in the proposed approach and onthe evaluation protocol.Generally the paper reads well. I strongly recommend to run a spell-check (Ifound many typos) and to rewrite few convoluted sentences. Please always favorlinear and short sentences.The denoising idea to segment out some patterns of interest to be fed to aclassifier is interesting.It needs to be said that having this gated interaction is not completely noveland there are already studies on gated RBM and gated Autoencoder. However, the cognitive bias is a binary N (number of classes) dimensionalvector, and this requires to perform exhaustive search.Why isn't the bias function of some intermediate representation? Also, having a separate training for each of the modules makes tricky to assessthe best strategy to "confirm the initial b guess", as also stated in theparagraph beginning at line 113. This is in my opinion a weak point of thework which makes it unfeasible for many problems.I always prefer end-to-end systems, at least here the classifier could havebeen trained jointly with the M module, even following the proposed alternatingminimization scheme.The classification experiment is fine, but it is not clear to me why theauthors did not train the classifier C on the same data. Abaseline is paramount to evaluate the relative improvement of the proposedapproach; how does aNN perform when compared with the simple classifier Cused after M?The MNIST-2 problem is interesting. The proposed way to disentangle thevarious digits is a bit tricky though because of the "validate the guess"criterion, which is not easy to be selected.If we are interested in classification, again, what is the performance of Cwhen taking the first two best guesses (naive) or when C is trained withcross-entropy to predict the presence of given objects?Even following the proposed scheme, what if the number of objects is notknown? How to set the criterion? Let's say we were to apply it to a generalobject detection benchmark.Overall I like the approach but there are important experiments which need tobe performed to correctly evaluate the relative improvement of aNN.Thanks for the work.


Bayesian Sampling Using Stochastic Gradient Thermostats
Dynamics-based sampling methods, such as Hybrid Monte Carlo (HMC) and Langevin dynamics (LD), are commonly used to sample target distributions. Recently, such approaches have been combined with stochastic gradient techniques to increase sampling efficiency when dealing with large datasets. An outstanding problem with this approach is that the stochastic gradient introduces an unknown amount of noise which can prevent proper sampling after discretization. To remedy this problem, we show that one can leverage a small number of additional variables to stabilize momentum fluctuations induced by the unknown noise. Our method is inspired by the idea of a thermostat in statistical physics and is justified by a general theory.

The Firefly paper is interesting, but to me it looked like a bunch ofwork for a tiny speed-up: I wouldn't recommend practitioners bother. Itisn't clear that developments in that direction will be useful either,so it's not time to shut down brainstorming of other ideas.Welling and Teh's work has had impact. I don't think it's particularlyjustified except in the limit of small step sizes either? Thejustification of past work has largely been empirical. I think thispaper's three varied and moderate-sized applications is good enough.The benefits aren't huge, but they are there.Negatives:While I can infer what is meant in some of the places thatAssigned_Reviewer_31 queries, I agree that the paper is hard to follow.The core idea is barely explained at all. The background section and thematerial around equation (4) would benefit from revision.Given the exposition in the paper, it's perhaps surprising that the 1Dexample (n=1) works out so well, given that above (4) it says that n islarge. However, in this example, things are favourable because having ascalar \xi is ok. I'm more worried about the high-dimensional case, whensampling noise can upset the momentum in different directionsdifferently. Then fixing up the scalar p'*p/n isn't enough to samplefrom the correct distribution. (Acknowledged around the end of Section4.2, but could be made clearer / more prominent in discussion.)Final opinion:It's an interesting approach, with someweaknesses in the paper. The sampler won't be correct, but theexperimental evaluation shows incremental improvement over past work.The dynamics: The presentation of SDE's is hard going, and could beimproved with a discussion of the stability of the discrete-timealgorithm. I don't think their potentially-unstable choice of discretedynamics is necessarily fatal if it works (although a discussion wouldbe nice). I'm personally more concerned theoretically with the posteriorbeing wrong due to non-isotropic noise.


Compressive Sensing of Signals from a GMM with Sparse Precision Matrices
This paper is concerned with compressive sensing of signals drawn from a Gaussian mixture model (GMM) with sparse precision matrices. Previous work has shown: (i) a signal drawn from a given GMM can be perfectly reconstructed from r noise-free measurements if the (dominant) rank of each covariance matrix is less than r; (ii) a sparse Gaussian graphical model can be efficiently estimated from fully-observed training signals using graphical lasso. This paper addresses a problem more challenging than both (i) and (ii), by assuming that the GMM is unknown and each signal is only observed through incomplete linear measurements. Under these challenging assumptions, we develop a hierarchical Bayesian method to simultaneously estimate the GMM and recover the signals using solely the incomplete measurements and a Bayesian shrinkage prior that promotes sparsity of the Gaussian precision matrices. In addition, we provide theoretical performance bounds to relate the reconstruction error to the number of signals for which measurements are available, the sparsity level of precision matrices, and the "incompleteness" of measurements. The proposed method is demonstrated extensively on compressive sensing of imagery and video, and the results with simulated and hardware-acquired real measurements show significant performance improvement over state-of-the-art methods.

This paper proposes a method to recover signals from compressive measurements. The method consists of jointly estimating the signal and a Gaussian Mixture Model (GMM) capable of representing it succinctly. The main contribution of the paper is the idea of imposing a sparse structure on the GMM adapted to the case when the signal of interest corresponds to image patches. This is further exploited by a more structured prior that promotes an appropriate group-sparsity pattern (essentially interactions between adjoining pixels are not penalized by the sparsity-inducing penalty). Some theoretical results are provided for the case in which there is just one Gaussian in the mixture, but their implication or the conditions under which they hold are not explained clearly. Numerical simulations show that the method yields good results for very small images and for individual image patches. However the question of how to apply the method to normal-sized images is not addressed. This paper presents an interesting and potentially useful method for the compressed sensing of image patches and provides some hopeful numerical results. Its main weaknesses are:-The theoretical results are very confusing.  It is very difficult to derive any conclusions from the statement of the theorems or the additional explanations, which are very vague. The conditions for the theorems, which seem quite strong and ad hoc, are not explained. For example, a bound delta_max on the error seems to be assumed in Theorem 3. Also, the results in Theorem 2 are asymptotic and in high probability but this is not mentioned anywhere (except in the proof within the supplementary material). Finally, no attempt is made to clarify for what kind of sensing matrices the results would hold. -The extension of the theory to the case of several Gaussians, which does not seem trivial and is the method that is actually applied in practice, is not discussed. -Not a lot of visual results are shown either in the paper or in the supplementary material (this would be a good sanity check and I encourage the authors to include them).-It is not discussed how to combine the patches obtained from the method to produce whole images. Reference [3] states that this is not trivial, so the authors should at least discuss it.Quality:The paper introduces a novel approach to signal estimation using GMMs by promoting sparsity and group sparsity in the covariance matrices. The authors provide some numerical evidence for very small images and image patches, although they do not tackle the reconstruction of whole images. The theoretical results are not very conclusive.Clarity:The paper is relatively clearly written, except for the more technical parts which are confusing and difficult to follow. This is apparent in Section 3, where the authors barely discuss the conditions and the results of the theorems. Theorem 3 for example can only hold with high probability and asymptotically as it is “a combination of Theorems 1 and 2”, but this is not even mentioned!Some of the other mathematical statements are not very rigorous. For example, in equation (15) it seems that the authors consider x hat and x tilde random variables but they do not clarify in what sense the equality holds. The equality “follows from [21]” if delta_i is independent of x_i, but it is not clear to me that this is true. If it is, the authors should explain in what sense (in expectation, with high probability, etc.). Also, the authors refer to other works: “Following [21]” (line 280), “Similar to [21]” (line 284) … in a very vague way without specifying what part of the cited works they mean, which makes it difficult for the reader to follow. Originality:The idea of promoting a sparse or group-sparse structure of the covariance matrices in a GMM while performing signal estimation is novel to the best of my knowledge.Significance:I don’t think that the contribution of the paper is very significant because of the limited scope of the theory and because the numerical results do not include reconstructions of whole images.After reading the authors' rebuttal, my views on the paper are basically unchanged, although I'm increasing the score to 6. In particular, even though it might be straightforward to combine the patches, this does not mean that they should produce an accurate estimate of features in the image that span several patches. However, it is perhaps understandable that the authors do not address this given the space constraints.


Multi-Scale Spectral Decomposition of Massive Graphs
Computing the k dominant eigenvalues and eigenvectors of massive graphs is a key operation in numerous machine learning applications; however, popular solvers suffer from slow convergence, especially when k is reasonably large. In this paper, we propose and analyze a novel multi-scale spectral decomposition method (MSEIGS), which first clusters the graph into smaller clusters whose spectral decomposition can be computed efficiently and independently. We show theoretically as well as empirically that the union of all cluster's subspaces has significant overlap with the dominant subspace of the original graph, provided that the graph is clustered appropriately. Thus, eigenvectors of the clusters serve as good initializations to a block Lanczos algorithm that is used to compute spectral decomposition of the original graph. We further use hierarchical clustering to speed up the computation and adopt a fast early termination strategy to compute quality approximations. Our method outperforms widely used solvers in terms of convergence speed and approximation quality. Furthermore, our method is naturally parallelizable and exhibits significant speedups in shared-memory parallel settings. For example, on a graph with more than 82 million nodes and 3.6 billion edges, MSEIGS takes less than 3 hours on a single-core machine while Randomized SVD takes more than 6 hours, to obtain a similar approximation of the top-50 eigenvectors. Using 16 cores, we can reduce this time to less than 40 minutes.

The paper addresses the problem of estimation of eigenvalues and eigenvectors of large sparse graph matrices. It uses a nice divide-and-conquer approach to obtain better estimates of top-k eigenspace. Such an estimate can be used in several classic tasks, such as link prediction and recommender systems.The paper is build upon a divide-and-conquer method, taking advantage of the particular characteristics of some graphs (e.g. social networks): sparsity and cluster structure.The theoretical part is strong, with theoretical bounds provided. The divide part uses a decomposition of the adjacency matrix as a sum of a block-diagonal matrix and an almost zero non-diagonal matrix. A spectral decomposition of block matrices is done, and the k first eigen values are chosen among the resulting union of eigenvalues.In the conquer step, the corresponding eigenvectors are used as initialization step in a block-Lanczos (or random SVD) method on the whole matrix.Theoretical bounds are provided, with respect to the norm of the remaining matrix (the non-block one).Experiments show that the method is quite accurate for the eigenspace identification, compared to classic spectral methods (randomized SVD or Lanczos).In tasks such as label propagation and matrix completion, the methods performs as well as other classical methods.The paper is well written. It uses quite sophisticated methods and the theoretical part is solid. The main weakness of the paper is that the tasks that are presented as highly dependent on the accuracy of eigenspace estimation (link prediction, etc.) reveals to be not so dependent: the experiments show that the method presented in the paper is much more accurate than previous state-of-the-art in eigenspace estimation, but this does not implies significantly better results in the label propagation or matrix completion tasks.In other words, The goal of the method (a good estimate of the eigenspace) is reached, but it appears that it has no effect on the tasks that it was supposed to solve (except for the computing time).Also, the method (and the bound) should highly depend on the quality of the first step (the graph clustering step), and it would have been nice to have an idea of the accuracy of the method with respect to this first step.However, the method is original and could be used in other spectral decomposition problems (provided that they are sparse and likely to be clustered). Pros:- nice divide-and-conquer algorithm- solid theoretical part- theoretical bounds- experiments show that the method reaches good accuracyCons:- for real-world tasks, the algorithm does not perform significantly better that previous methods- dependency between first clustering step and quality of the solution is not studied.


Median Selection Subset Aggregation for Parallel Inference
For massive data sets, efficient computation commonly relies on distributed algorithms that store and process subsets of the data on different machines, minimizing communication costs. Our focus is on regression and classification problems involving many features. A variety of distributed algorithms have been proposed in this context, but challenges arise in defining an algorithm with low communication, theoretical guarantees and excellent practical performance in general settings. We propose a MEdian Selection Subset AGgregation Estimator (message) algorithm, which attempts to solve these problems. The algorithm applies feature selection in parallel for each subset using Lasso or another method, calculates the 'median' feature inclusion index, estimates coefficients for the selected features in parallel for each subset, and then averages these estimates. The algorithm is simple, involves very minimal communication, scales efficiently in both sample and feature size, and has theoretical guarantees. In particular, we show model selection consistency and coefficient estimation efficiency. Extensive experiments show excellent performance in variable selection, estimation, prediction, and computation time relative to usual competitors.

This paper presents a new method to scale up training of large-scale linear models, where the tacit assumption is that the parameter set fits in a single machine but not all training instances do. The idea starts by splitting the training set into m disjoint subsets and allocating each to a different machine. Then sparsity-inducing regularised risk minimisation (such as lasso or GIC) is run independently in each machine, thus recovering a support set of features in each machine (say s_im=1 if feature i in machine m survived the selection and 0 otherwise). Then a critical step: find a consensus support by picking for each feature the median of its survival indicator value over all machines (ie compute median_m s_im for all features i). Then run OLS with those features independently in each machine and average the resulting models.This simple, elegant and intuitive approach seems to yield impressive results. The accuracy of both support recovery and prediction are on par with bootstrap lasso, while being much more scalable (constant rather than linear since embarrassingly paralellizable). I'm also impressed by the quality and clarity of presentation. The theoretical results presented are precisely those that matter: accuracy of support recovery and accuracy of the estimator.Empirical results are presented both for suitably designed synthetic experiments and interesting real-world datasets.Some minor points:1 - I dind't find a definition of \lambda_{min}. I suppose it's the minimum eigenvalue (?) this should be made clear since notation overloads with \lambda for regularization parameter.2 - In the algorithm description, I presume you use OLS in line 11 (which is hinted at in the end of page 2). Please make this explicit in the algorithm description (you use "loss" to denote different losses in lines 5 and 11, and this causes confusion)3 - I think you never give details about *how* the dataset should be split. I feel it needs to be randomly (is that correct?). Could you please make this clear.4 - Second sentence of introduction starts with lower-case.Overall a really good paper.


Recurrent Models of Visual Attention
Applying convolutional neural networks to large images is computationally expensive because the amount of computation scales linearly with the number of image pixels. We present a novel recurrent neural network model that is capable of extracting information from an image or video by adaptively selecting a sequence of regions or locations and only processing the selected regions at high resolution. Like convolutional neural networks, the proposed model has a degree of translation invariance built-in, but the amount of computation it performs can be controlled independently of the input image size. While the model is non-differentiable, it can be trained using reinforcement learning methods to learn task-specific policies. We evaluate our model on several image classification tasks, where it significantly outperforms a convolutional neural network baseline on cluttered images, and on a dynamic visual control problem, where it learns to track a simple object without an explicit training signal for doing so.

The paper describes a method for sequentially learning sequences of action for classification and regression tasks in the context of visual scenes. The motivation comes from attentional models in vision where decisions are made by considering sequentially selected information.  The model is formulated as a POMDP and the algorithm is implemented using a recurrent neural network. The hidden layer of this network serves as the state of the POMDP and the approximated policy is learned via the neural network. Experiments are performed on image classification tasks (noisy digits) and on toy control problem.The paper is well motivated and clear. Some precisions could be added especially for the dynamic environment setting (both for the model, e.g. LSTM units and for the experiments). The paper originality, in the context of this application, is in the use of a recurrent net for dynamically updating the state of the model in its hidden layer and in the regression model for the prediction of the next place to look for.The test beds on the other hand concern only very simple problems (both classification and dynamic prediction), so that the state space is probably not that big for all these problems. Experiments on stronger benchmarks are needed in order to effectively assess the capacity of this method to handle more realistic problems. Also, the proposed system could be compared with other sequential approaches. You could at least compare with a random policy + see the references below. The complexity of the method should be discussed, there is no mention of this aspect, and it should be compared to the complexity of other methods, both sequential and non-sequential.  There is neither discussion nor analysis on the usefulness of the hidden layer recurrence. Did you made experiments with different memory sizes or decay rate (weights of the recurrent connections) or did you attempt to learn the weight values?Detailed comments: It seems that for the classification, the number of steps is fixed in advance and is the same for all the images. This is probably a useless assumption (by the way, how do you set up the value of this variable?).Below are some references which could be interesting for this work.Karayev, Sergey, Baumgartner, Tobias, Fritz, Mario, and Darrell, Trevor. Timely object recognition. In NIPS, pp. 1–9, 2Cuccu, Giuseppe, Luciw, Matthew, Schmidhuber, Jurgen, and Gomez, Faustino. Intrinsically motivated neuroevolution for vision-based reinforcement learning. In Development and Learning (ICDL), 2011 IEEE International Conference on, volume 2, pp. 17. IEEE, 2011.012.Contardo, Gabriella , Denoyer, Ludovic , Artieres, Thierry,  Gallinari, Patrick, Learning State Representations in POMDP, ICLR 2014Dulac-Arnold, Gabriel , Denoyer, Ludovic, Thome, Nicolas, Cord, Matthieu, Gallinari, Patrick, Sequentially Generated Instance-Dependent Image Representations for Classification, ICLR 2014


An Accelerated Proximal Coordinate Gradient Method
We develop an accelerated randomized proximal coordinate gradient (APCG) method, for solving a broad class of composite convex optimization problems. In particular, our method achieves faster linear convergence rates for minimizing strongly convex functions than existing randomized proximal coordinate gradient methods. We show how to apply the APCG method to solve the dual of the regularized empirical risk minimization (ERM) problem, and devise efficient implementations that avoid full-dimensional vector operations. For ill-conditioned ERM problems, our method obtains improved convergence rates than the state-ofthe-art stochastic dual coordinate ascent (SDCA) method.

The authors propose an accelerated proximal block coordinate descent      algorithm, describe its application to standard regularized loss      minimization problems, and conclude with experiments on a smoothed SVM.      On the question of clarity: I found the paper on the whole difficult to      follow, with the authors showing a marked preference for writing      equations in lieu of explanations. There are also numerous small      grammatical errors.      I'm not aware of other algorithms that are designed to work on      block-coordinate problems (although single-coordinate algorithms are      common enough), and have to question the advantage of this formulation,      aside from being slightly more general. Given that the application      considered in section 4 is single-coordinate (am I correct about this?),      it might simplify the presentation to work from a single-coordinate      formulation, and merely mention that block-coordinate updates are also      possible.      On originality: I'm not familiar enough with the literature to judge. The      stated improvement over the best-known convergence rates is small (not      including the arxiv paper cited as [18]), and I think the authors      shouldn't minimize the difference between converging quickly in the      primal (as the other algorithms mentioned on the bottom of page 6 do) and      in the dual (as APCG, at least for the regularized ERM application). At      least for SVMs, with which I am most familiar, the two objectives are      very different, and fast convergence in the dual does not necessarily      imply fast convergence in the primal.      The experiments appear to show a clear win for APCG over SDCA, and I      agree with the authors that SDCA is a natural baseline. However, I do      have a question about a potential issue: in some of the plots,      particularly on the news20 dataset with small lambda, it appears that      SDCA "levels out" at a higher suboptimality than that found by APCG. This      indicates to me that perhaps at that point SDCA has converged, and has      done so to a slightly higher objective function value due to numerical      issues or implementation differences (the log scale exaggerating such      small discrepancies). Do you have any evidence that this is not the case?      For example, if you can show that your algorithm converges faster than      SDCA in terms of testing classification accuracy, it would simultaneously      assuage fears about a potential numerical issue, and demonstrate that the      use of APCG has practical benefits.      Also did you forget a square root in the equation on lines 190-191?


Spectral k-Support Norm Regularization
The k-support norm has successfully been applied to sparse vector prediction problems. We observe that it belongs to a wider class of norms, which we call the box-norms. Within this framework we derive an efficient algorithm to compute the proximity operator of the squared norm, improving upon the original method for the k-support norm. We extend the norms from the vector to the matrix setting and we introduce the spectral k-support norm. We study its properties and show that it is closely related to the multitask learning cluster norm. We apply the norms to real and synthetic matrix completion datasets. Our findings indicate that spectral k-support norm regularization gives state of the art performance, consistently improving over trace norm regularization and the matrix elastic net.

In this paper, the authors derive new properties of the k-support norm [1], devise a new efficient algorithm for computing its proximal operator and generalize it to matrices.First, they show that the k-support norm can be written as a box norm. Box norms are defined using a variational formulation (infimum of quadratics: |w| = \inf_{t \in T} \sum w_i^2 / t_i) and are a special case of the norms described in [2]. Conversely, squared box norm can be written as the sum of squared l2 norm and k-support norm.Since the box norms are symmetric gauge function, they propose to extend them (and the k-support norm as a special case) to matrices. They also show that the cluster norm is equivalent to spectral box norm. They devise efficient algorithms to compute both the norm and their associated proximal operator, with a complexity of O(d log(d)), where d is the dimension. Finally, they report experimental results for matrix completion problems on synthetic and real datasets, showing that the spectral k-support norm perform slightly better than the trace norm.This is a solid and well written article about the relations between the k-support norm and the box norms. The extension of those norms to matrices is pretty straightforward. The algorithm proposed in the paper for computing the proximal operator of the k-support norm should be useful to the NIPS community, as it is more efficient than previously known methods: the authors demonstrate that their approach is several order of magnitude faster than the algorithm in [1]. My only small concern is the lack of really convincing experiments about the usefulness of the spectral k-support norm, compared to the trace norm or the matrix elastic net.[1] A. Argyriou, R. Foygel, N. Srebro. Sparse Prediction with the k-Support Norm. 2012[2] C. Micchelli, J. Morales, M. Pontil. Regularizers for Structured Sparsity. 2010.


Message Passing Inference for Large Scale Graphical Models with High Order Potentials
To keep up with the Big Data challenge, parallelized algorithms based on dual decomposition have been proposed to perform inference in Markov random fields. Despite this parallelization, current algorithms struggle when the energy has high order terms and the graph is densely connected. In this paper we propose a partitioning strategy followed by a message passing algorithm which is able to exploit pre-computations. It only updates the high-order factors when passing messages across machines. We demonstrate the effectiveness of our approach on the task of joint layout and semantic segmentation estimation from single images, and show that our approach is orders of magnitude faster than current methods.

The paper improves on previous work on parallelizing MRF inference. The main insight is that when passing messages, summations over large state spaces can be delayed until the appropraite messages across computers are received. This is performed elegantly by adding new regions (typically correspodning to variable cliques)containing unions of high order parent regions' children, thus separating the higher order region for computation until the message from another computer arrives. Results are impressive, far better than the baselines compared with. The paper was carefully written (perhaps overoptimized in some ways).The two pieces of criticisms are:1. The basic idea is relatively straightforward (but, has not been done before, apparently).2. The writing is so dense and technical that it takes a while to get through the math and understand the relatively simple idea. Perhaps the authors should have a less abstract example (e.g., define an image task and a small number of regions, and then explain what the various messages mean). The details of the experiments (the expplanation/description of the task and the dataset) are also very compressed. Generally, the paper is succinct to the point that it has to be reread several times to be understood (but all details are there - that's why I say it was overoptimized).THe above pieces of criticism are there just to help the authors in writing. I do, however, support acceptance (even in current form).


Robust Classification Under Sample Selection Bias
In many important machine learning applications, the source distribution used to estimate a probabilistic classifier differs from the target distribution on which the classifier will be used to make predictions. Due to its asymptotic properties, sample reweighted empirical loss minimization is a commonly employed technique to deal with this difference. However, given finite amounts of labeled source data, this technique suffers from significant estimation errors in settings with large sample selection bias. We develop a framework for learning a robust bias-aware (RBA) probabilistic classifier that adapts to different sample selection biases using a minimax estimation formulation. Our approach requires only accurate estimates of statistics under the source distribution and is otherwise as robust as possible to unknown properties of the conditional label distribution, except when explicit generalization assumptions are incorporated. We demonstrate the behavior and effectiveness of our approach on binary classification tasks.

Paper ID: 39Title: Robust Classification Under Sample Selection BiasNOTE: Due to the short reviewing time and out of fairness to the other papers I was reviewing, I DID NOT do more than glance over the supplementary material.  In most cases, I therefore did not verify that results claimed by the authors are correct, but instead checked that they are plausible.Summary: This paper is about how to adjust a classifier when the training set is not representative of the test set; a canonical example is active learning, but the problem can also appear in recalibration.  The goal is to find an effective method in the finite-sample regime, since most results are asymptotics.  The author(s) take a minimax approach.Quality, clarity, originality and significance:  This work takes a novel approach to address an important problem in the practical application of classifiers.  The manuscript is generally well-written and clear, but I have some comments about works that seem related to this problem.  Some imprecision in the mathematical description was confusing.Recommendation:  Overall, I believe this is a nice contribution which will be appreciated by the NIPS community, assuming that the manuscript can be clarified appropriately.Comments:  (comments are numbered to allow for easy reference in the rebuttal)1) There are some works on recalibrating classifiers to adjust for different populations (a Google search turned up some papers from IJCAI, CVPR, KDD, and other venues).  Is there a connection between this problem and that literature that may be relevant?2)  The formulation in (1) assumes the alphabets for X and Y are both discrete, but this is not what happens in the experiments.  It may be better to express (1) as an expectation rather than writing it out explicitly.  Otherwise the generality is lost, since one has to replace sums by integrals.3) After Definition 1 it may be appropriate to comment on why matching the constraints *exactly* is even relevant in this setting (this is relaxed later but at the moment Definition 1 seems already like a bad idea).4)  In 2.2, I was not sure what the authors meant by "assuming that source distribution statistics generalize more broadly than the source distribution itself may be justifiable and useful."  What does expert knowledge have to do with this?  I was rather confused by this motivation.5)  By introducing some slack in the constraints the estimator seems somewhat "similar" to things one sees in robust statistics.  Is there a connection here?6)  Somehow the form of the estimator in Theorem 2 comes out of the blue.  Is there a way to explain some of the intuition behind it before introducing it?7)  What does \approx mean in (8)?  That seems very imprecise.8)  In 2.5, this goes back to 2) -- densities have thus far not appeared in the story and suddenly it seems all variables are continuous...9)  In Algorithm 1, how does gamma relate to epsilon in the error bounds in 2.4?10)  In 3.1, are the other methods from other papers on this problem?  If so, please provide citations.11)  In general, in the experiments section, using some notation that had been previously established to connect the plots back to the preceding theory would be extremely helpful.12) Just as a thought, how would increasing the training set size help in Figures 2-3?Small things:- Perhaps before Definition 2 the c' variables could be actually defined, e.g. using \stackrel{\Delta}{=} or some other macro.- check the referenes -- there are some typos (c.f. Bickel's first name inPlease summarize your review in 1-2 sentences:  The authors propose a new method for handling mismatch between the training and test distributions when training a classifier.  Experiments illustrate the benefit of the method over competing approachesQuality Score (1-10):  7Impact Score (1-2):  2Confidence (1-5):  3COMMENTS AFTER AUTHOR FEEDBACK:  The authors have proposed a rather extensive set of revisions to address the feedback from the reviewers. With those changes I think the paper may indeed be in the top 50% of NIPS papers.  I am therefore revising my score upward to an 8.Quality Score (1-10):  8


Testing Unfaithful Gaussian Graphical Models
The global Markov property for Gaussian graphical models ensures graph separation implies conditional independence. Specifically if a node set S graph separates nodes u and v then X u is conditionally independent of X v given X S . The opposite direction need not be true, that is, X u ⊥ X v | X S need not imply S is a node separator of u and v. When it does, the relation X u ⊥ X v | X S is called faithful. In this paper we provide a characterization of faithful relations and then provide an algorithm to test faithfulness based only on knowledge of other conditional relations of the form X i ⊥ X j | X S .

Identifying conditional independence of variables in graphical models is a key to finding tractable solutions, and faithfulness is a key condition of these relationships. The authors provide necessary and sufficient conditions for determining faithfulness in Gaussian graphical models (based on partitioning variables outside the conditioning set into two disjoint subsets), and show how this theoretical result can be translated into an algorithm for determining if a distribution is faithful.PROS:- Clear, well-written paper with illustrative examples- Addresses a relevant problem and provides a meaningful theoretical result - Provides a practical test for faithfulness in Gaussian graphical modelCONS:- Theoretical result is restricted to Gaussian graphical modelsQuality: This paper provides addresses a theoretical problem  (faithfulness in Gaussian graphical models). The claims are well-reasoned and the proofs support the claims. The resulting algorithm provides a useful test of faithfulness. Although the claims are extremely specific, the results are well-reasoned.Clarity: This paper is very well written (although minor grammatical issues), logically organized,  and effectively introduces major concepts, illustrates ideas with examples. The proofs are clear and easy to follow.Originality: I am unfamiliar of any work that addresses this particular problem, but I do not believe the analysis is particularly innovative either.Significance: The specificity of this theoretical result (Gaussian graphical models) limits the significance of the paper, but this paper will be very useful to the particular community it targets.


Repeated Contextual Auctions with Strategic Buyers
Motivated by real-time advertising exchanges, we analyze the problem of pricing inventory in a repeated posted-price auction. We consider both the cases of a truthful and surplus-maximizing buyer, where the former makes decisions myopically on every round, and the latter may strategically react to our algorithm, forgoing short-term surplus in order to trick the algorithm into setting better prices in the future. We further assume a buyer's valuation of a good is a function of a context vector that describes the good being sold. We give the first algorithm attaining sublinear (Õ(T 2/3 )) regret in the contextual setting against a surplus-maximizing buyer. We also extend this result to repeated second-price auctions with multiple buyers.

This paper introduces the problem of repeated auctions with contextual information. Specifically, the auctioneer interacts with a single agent (at least in their initial model) who has a context vector x, corresponding to observable attributes, and a privately held weight vector w, such that the agent’s value for the good is x*w. The goal of the auctioneer is to maximize the revenue from the posted price auction by learning w over time. However, the agent understand that the auctioneer may be adjusting prices based off of the his purchasing behavior, so he may lie (that is, not purchase the product even though it would give him positive surplus) in order to lower the price in future rounds. The authors present an algorithm based on stochastic gradient descent. The authors prove that the number of “lies” by an agent is mitigated b the agent’s discount factor for future utility and use existing results to show that these bounded number of lies do not affect the learning algorithm too much, thereby bounding the “strategic regret” in this model. I like this paper and I view its main contribution as introducing the use of contextual information to repeated auctions. The authors make a good point that the reason that so many auctions on the web have only a single participant is because of targeting, so it seems natural that the mechanism itself should be able to use targeted information (i.e. context) to set prices.I think this model (or at least this family of models) is very compelling and raises a lot of interesting questions. This paper does a good job at beginning to address this model and will inspire more work to be done on this area.The technical strength of this paper is solid, primarily consisting of extending existing techniques to the details of this model (although this is not a trivial task) and the exposition is relatively clear. The technical strength could have been improved via discussion of regret lower bounds in this model. It would have been nice to have a deeper understanding of regret lower bounds in this model versus similar models without context (e.g. Amin et al 2013). However this seems like significant extra work and is reasonably outside the scope of this paper. I found the section on multiple buyers a little unconvincing, which is not to imply that I believe it is wrong, but rather that the extension from posted-pricing to a reserve price auction is not straightforward and warrants more exposition/exploration. Its not obvious how the LEAP algorithm extends in the case of multiple buyers during the exploit phase. Presumably, the algorithm realizes the context vectors for all agents and then posts a reserve price of max_{i in N} x_i * w_t but this is not actually stated. As the authors note, the “market value” assumption seems a little odd; its not clear that one can simply convert between the two settings (that is, taking the maximum of a number of agents versus just acting as if there were one agent that always had the maximum value). Personally, I’m more interested in expanding this case than I am in the extension of non-linear valuation functions and I wish the paper had expanded more on these details rather than showing kernelized extension. Beyond these small confusions, it seems that the multiple bidder setting has more complexity and nuance than presented in this paper. For example, it seems that more buyers should decrease regret in a number of ways. First, more buyers should increase the effect of the discount factor because, all else being equal, a buyer will expect to wait a longer time to purchase in the future (because now he needs to take into consideration the probability that he has the highest valuation amongst the group of agents that show up in any given round). Under the assumption of IID valuations, this should increase his expected wait time by a factor K (the number of players), hence decreasing his future utility exponentially (due to discounting). So it seems that lying should become less of an issue. In terms of related work, the authors could connect better to the study of contextual multi-armed bandits as the settings are similar. In summary, I think this work is a valuable contribution because this is a good model, in the sense that is practically relevant and is an interesting example of the intersection of machine learning and algorithmic game theory. The case of multiple bidders case is more complex than the current work considers and deserves future work but the work is technically strong enough with the single agent model.


Latent Support Measure Machines for Bag-of-Words Data Classification
In many classification problems, the input is represented as a set of features, e.g., the bag-of-words (BoW) representation of documents. Support vector machines (SVMs) are widely used tools for such classification problems. The performance of the SVMs is generally determined by whether kernel values between data points can be defined properly. However, SVMs for BoW representations have a major weakness in that the co-occurrence of different but semantically similar words cannot be reflected in the kernel calculation. To overcome the weakness, we propose a kernel-based discriminative classifier for BoW data, which we call the latent support measure machine (latent SMM). With the latent SMM, a latent vector is associated with each vocabulary term, and each document is represented as a distribution of the latent vectors for words appearing in the document. To represent the distributions efficiently, we use the kernel embeddings of distributions that hold high order moment information about distributions. Then the latent SMM finds a separating hyperplane that maximizes the margins between distributions of different classes while estimating latent vectors for words to improve the classification performance. In the experiments, we show that the latent SMM achieves state-of-the-art accuracy for BoW text classification, is robust with respect to its own hyper-parameters, and is useful to visualize words.

Latent Support Measure Machines for Bag-of-Words Data ClassiﬁcationThis paper presents a kernel-based latent support measure machine for bag-of-word data to jointly learn word embedding and a document classifier. It assumes each word can be represented as a latent vector and each document is represented as a distribution of the latent vectors associated with the words in the document. Then latent support measure machine learns a model to classify documents based on the latent distribution. The proposed method is a nice extension of support measure machines. Experiments show that the proposed method outperforms other methods using word embedding or word cluster.   The paper is nice written and easy to follow. Comments:	- My main concern is the scalability of the proposed method. All the experiments are conducted using less than 1,000 examples. However, it is easy to encounter a bag-of-word data in the scale of hundred thousand in text classification problems. It is unclear if the proposed method can scale up to deal with such datasets.	- The paper demonstrates promising results using a small dataset. However, it is hard to judge if Latent SMM can improve the accuracy of text classification when the training samples are sufficient. For example, new20 achieves 0.82 accuracy using SVM with linear kernel when training on the whole dataset (http://web.ist.utl.pt/acardoso/datasets/). The accuracy of the best method trained on 1,000 samples reported in Figure 1 (c) is around 0.6. It would be more promising to report the results on the whole dataset as well.	- I wonder if the proposed method can be extended for other applications.	- In figures 4, it seems that the method performs better when using a large C to fit training data. Is there an explanation for that?Minor comments/typos:	- Lines 361, 364: should be Figure 3, Figure 4, respectively.I like the experimental analysis about the word occurrence threshold (line 356~363). However, it is hard to see the performance difference with different thresholds in Figure 3.


Provable Submodular Minimization using Wolfe's Algorithm
Owing to several applications in large scale learning and vision problems, fast submodular function minimization (SFM) has become a critical problem. Theoretically, unconstrained SFM can be performed in polynomial time [10,11]. However, these algorithms are typically not practical. In 1976, Wolfe [21]  proposed an algorithm to find the minimum Euclidean norm point in a polytope, and in 1980, Fujishige [3]  showed how Wolfe's algorithm can be used for SFM. For general submodular functions, this Fujishige-Wolfe minimum norm algorithm seems to have the best empirical performance.
Despite its good practical performance, very little is known about Wolfe's minimum norm algorithm theoretically. To our knowledge, the only result is an exponential time analysis due to Wolfe [21]  himself. In this paper we give a maiden convergence analysis of Wolfe's algorithm. We prove that in t iterations, Wolfe's algorithm returns an O(1/t)-approximate solution to the min-norm point on any polytope. We also prove a robust version of Fujishige's theorem which shows that an O(1/n 2 )-approximate solution to the min-norm point on the base polytope implies exact submodular minimization. As a corollary, we get the first pseudo-polynomial time guarantee for the Fujishige-Wolfe minimum norm algorithm for unconstrained submodular function minimization.

The present paper gives a version of the Fujishige-Wolfealgorithm for submodular function minimization and shows itspseudo-polynomial time complexity.The Fujishige-Wolfe algorithm has been widely used and runsefficiently in practice, but the problem of determining itsalgorithmic complexity has been open until now.The pseudo-polynomiality result of the present paper is thefirst big step toward determining its exact complexity.Comments (mostly minor ones) are listed below.Major ones are Comments 11 and 13. Comments 1 and 8 are medium.(Three-digit numbers denote the corresponding lines in thetext.)----------------------------------------------1. 055-056: Iwata and Orlin's algorithm [11] is not thefastest. Orlin's algorithm published in MathematicalProgramming, Ser.A, Vol.118 (2009), pp.237-251 is currently thefastest and runs in O(n^5EO + n^6) time where EO denotes thetime for the function evaluation oracle.2. 066: Here should be mentioned the relation between $n$ and$X$, which will appear on Line 105.3. 093: $F$ should be defined here.4. 095: `the Wolfe's' should be read `the Wolfe' or  `Wolfe's.'5. 107: `for any two' should be read `for all two' (within the``if'' clause).6. 109: `to find the set' should be read `to find a set.'7. 138: `for a subset' should be read `for an affinelyindependent subset.'8. 176: The inequality at the end of this line can be  $N_{\rm min} \le N_{\rm maj}$ without factor $n$,   since $N_{\rm maj}-N_{\rm min} \ge {\rm the dimension of the final $S$}.9. 178: The factor $n$ can be removed (due to the previouscomment).10. 213-214: The comment starting with ``Observe that …'' is not precise (or invalid), which should be removed. It is actuallyirrelevant to the present proof.11. 263: I cannot see $t=32Q^2/\epsilon^2$, but can only see$t=32Q^4/\epsilon^4$, which is much larger than the former.(Please check it carefully. I could be wrong. Any short proofof it would be useful for readers.) This would affect thecomplexity estimation all through the rest.Also the present $t$ and the one appearing before havedifferent meanings; the two should be distinguished.12. 316: `(abusing notation) is' should be read `(abusingnotation) that is.'13. 359 (Theorem 7): When $2n\epsilon < 1$, we can finda set $S$ in Theorem 7 without any oracle call by setting$S=\{ i \mid x_i < -1/(2n) \}$.(Compare the rounding technique proposed in Fujishige andIsotani's paper [7]. (See the remark below Theorem 3.3 andequations (3.11) and (3.12) on Page 7 in [7]. Note that we alsohave $||x - x_*|| \le \epsilon$.)Theorem 7 itself is still correct.14. 375: `at least $\epsilon^2$' should be read `at least$-\epsilon^2$.'15. 409: Check the complexity. See Comment 11.----------------------------------------------------------------


Unsupervised learning of an efficient short-term memory network
Learning in recurrent neural networks has been a topic fraught with difficulties and problems. We here report substantial progress in the unsupervised learning of recurrent networks that can keep track of an input signal. Specifically, we show how these networks can learn to efficiently represent their present and past inputs, based on local learning rules only. Our results are based on several key insights. First, we develop a local learning rule for the recurrent weights whose main aim is to drive the network into a regime where, on average, feedforward signal inputs are canceled by recurrent inputs. We show that this learning rule minimizes a cost function. Second, we develop a local learning rule for the feedforward weights that, based on networks in which recurrent inputs already predict feedforward inputs, further minimizes the cost. Third, we show how the learning rules can be modified such that the network can directly encode non-whitened inputs. Fourth, we show that these learning rules can also be applied to a network that feeds a time-delayed version of the network output back into itself. As a consequence, the network starts to efficiently represent both its signal inputs and their history. We develop our main theory for linear networks, but then sketch how the learning rules could be transferred to balanced, spiking networks.

This submission describes a novel autoencoder method, that uses unsupervised learning to configure a recurrent network to encode both the current and past states of an input.  I am not a mathematician nor machine learning expert, and thus am not qualified to review the work for technical merit.  However, I have extensive experience in neural network modeling, and thus appreciate both the objective and purported accomplishments:  the ability to train a recurrent network to store input sequences in an efficient manner using non-supervised learning.  The authors describe a mechanism that addresses the problem by breaking it into two stages — autoencoding, and then optimization — that are carried out over different times scales.  The assumptions are reasonable and, of the derivations I could follow, they seemed reasonable.  This approach is clever and, to the best of my knowledge, is novel.  However, I would like to have seen more extensive evaluation of the network performance, including a benchmark comparison with other standard approaches to the problem using supervised learning (e.g., simple recurrent networks; back propagation through time).  While I think such results would strengthen the submission, and its appeal to the audience at NIPS, the results strike me as being of sufficient interest and potential importance to be accepted for presentation.


LSDA: Large Scale Detection through Adaptation
A major challenge in scaling object detection is the difficulty of obtaining labeled images for large numbers of categories. Recently, deep convolutional neural networks (CNNs) have emerged as clear winners on object classification benchmarks, in part due to training with 1.2M+ labeled classification images. Unfortunately, only a small fraction of those labels are available for the detection task. It is much cheaper and easier to collect large quantities of image-level labels from search engines than it is to collect detection data and label it with precise bounding boxes. In this paper, we propose Large Scale Detection through Adaptation (LSDA), an algorithm which learns the difference between the two tasks and transfers this knowledge to classifiers for categories without bounding box annotated data, turning them into detectors. Our method has the potential to enable detection for the tens of thousands of categories that lack bounding box annotations, yet have plenty of classification data. Evaluation on the ImageNet LSVRC-2013 detection challenge demonstrates the efficacy of our approach. This algorithm enables us to produce a >7.6K detector by using available classification data from leaf nodes in the ImageNet tree. We additionally demonstrate how to modify our architecture to produce a fast detector (running at 2fps for the 7.6K detector). Models and software are available at lsda.berkeleyvision.org.

This paper addresses the issue of object detection, in particular the challenge of obtaining bounding boxes on a scale similar to which category labels exist for object categorization. The authors side-step this challenge by proposing to adapt object classifiers for the detection task. Their algorithm is fairly simple and straightforward, which is not a bad thing in itself. Their experimental protocol uses 100 categories for training (with both category labels and bounding boxes), and tests on 100 left-out categories. These left-out categories had only category labels. The results obtained were reasonably good, filling about 35% of the gap between an oracle and a baseline on the 100 left-out categories.Quality and clarity: This is a good quality, clearly-written paper.Originality: This paper combines two existing ideas related to adaptation: adapting object classifiers for detection, and adapting from one set of categories to another. To the best of this reviewer's knowledge, this is a novel and interesting idea -- but not ground-breaking.Significance: The main contribution of this paper is the novel (but not ground-breaking) approach. Because results-wise, it is hard to judge the long-term significance, although they will likely be surpassed later by more sophisticated method. (This is to be expected). The main issue with the results is that they inevitably sacrifice performance (mAP) by using fewer bounding boxes, and there is no objective way to judge if this trade-off is worth it.(As a side note, it is not clear if the issue being tackled is really an important long-term challenge. Yes, bounding boxes are more "expensive" to obtain than category labels. But who is to say that throwing resources at the problem won't fix it? Not too many years ago, having millions of images labeled with 20,000 object categories seemed almost impossible...)Detailed issues that should be addressed:- In Figure 3a, which methods do (or do not) use category labels to help with detection, other than their method and R-CNN? The authors should state this clearly, to be clear about an apples-to-apples comparison.- My judgment of how good the proposed approach is, is based on the the blue bars in Figure 3b. DNN is about 1/3 between baseline and oracle. Do the authors agree that this is one of the main results? If yes, please highlight it, not the 78% (line 341) -- which is not quite the right number for 2 reasons: 1) should judge based only left-out categories, and 2) should not simply be a percentage of oracle performance (should take baseline into account). Analogous problem for the claim of 50% improvement (line 425).- Authors should devote a table or a sub-section to clearly stating the differences from R-CNN, which seems to be the closest competing alternative. Currently, these statements seem to be scattered or not as prominent as they could be. I would suggest "sacrificing" Figure 6, which are simply anecdotal examples.Minor issues (no need to respond)- Is the proposed method called "DNN" or "DDA"???- Typo on line 431 ("classi?ers")


An Integer Polynomial Programming Based Framework for Lifted MAP Inference
In this paper, we present a new approach for lifted MAP inference in Markov logic networks (MLNs). The key idea in our approach is to compactly encode the MAP inference problem as an Integer Polynomial Program (IPP) by schematically applying three lifted inference steps to the MLN: lifted decomposition, lifted conditioning, and partial grounding. Our IPP encoding is lifted in the sense that an integer assignment to a variable in the IPP may represent a truth-assignment to multiple indistinguishable ground atoms in the MLN. We show how to solve the IPP by first converting it to an Integer Linear Program (ILP) and then solving the latter using state-of-the-art ILP techniques. Experiments on several benchmark MLNs show that our new algorithm is substantially superior to ground inference and existing methods in terms of computational efficiency and solution quality.

Paper Summary: The paper presents an approach to encode the MAP inference problem in Markov logic networks as an integer polynomial program (IPP) using three steps: lifted decomposition, lifted conditioning, and partial grounding. In order to solve the IPP, it converts it into an integer linear program using [25], and then resorts to using the standard Gurobi solver.Originality: The techniques of lifted decomposition, lifted condition and partial grounding have previously been used for lifted MAP inference for MLNs previously [6,18]. So the main contribution of the paper is to realise that the MAP inference problem can be formulated as an IPP. Solving the problem in this way does seem to result in faster inference, but the practical usefulness of such an approach is unclear (see below).Clarity: The paper is a difficult read. The main problem is that the paper is not self-contained, and relies on the reader's familiarity with [6]. It also uses several terms without definition, for example,- Line 162: What are the 'arguments' i_R and j_S?- Line 172: What are the 'atoms of a predicate'? This is confusing since the previous section describes atoms as predicates (line 94).- Line 179: What is the function D?While these terms become clearer from context, especially through the examples provided, they still hurt the paper's clarity. The general NIPS audience will not be familiar with MLNs, which have been proposed relatively recently. While I understand that it is difficult to define everything concretely within the page limit, it would help to publish an accompanying self-contained technical report.Significance: The experiments compare to the state of the art [11,14,18], and demonstrate significant speed-up for three MLNs. However, some details are missing. How were the weights for the MLN estimated? Is there a separate training set? While the performance of the methods has been reported only in terms of the cost, can it also be reported in terms of the accuracy of the output? Although the main aim of the paper is better optimisation, it's case would be made much stronger if better optimisation leads to better accuracy. Also, is there any theoretical bound on the size of the IPP obtained using the proposed method? If not, at least the empirical size of the IPP and the ILP should be reported.Post-rebuttal comments: My main concern with the paper is that the experiments are conducted on artificial MLNs (with hand-tuned weights), and the performance is reported purely in terms of the cost and not the accuracy. Nonetheless, since the main objective of the paper is improved inference and the experiments are able to demonstrate the benefit of the proposed method in this regard, I vote for accepting the paper. If accepted, please include the explanations provided in the rebuttal, as well as the size of the IPP and ILP. It would also be beneficial to release a longer, self-contained tech report instead of relying on the readers familiarity with the state of the art.


Partition-wise Linear Models
Region-specific linear models are widely used in practical applications because of their non-linear but highly interpretable model representations. One of the key challenges in their use is non-convexity in simultaneous optimization of regions and region-specific models. This paper proposes novel convex region-specific linear models, which we refer to as partition-wise linear models. Our key ideas are 1) assigning linear models not to regions but to partitions (region-specifiers) and representing region-specific linear models by linear combinations of partitionspecific models, and 2) optimizing regions via partition selection from a large number of given partition candidates by means of convex structured regularizations. In addition to providing initialization-free globally-optimal solutions, our convex formulation makes it possible to derive a generalization bound and to use such advanced optimization techniques as proximal methods and decomposition of the proximal maps for sparsity-inducing regularizations. Experimental results demonstrate that our partition-wise linear models perform better than or are at least competitive with state-of-the-art region-specific or locally linear models.

The paper introduces a novel convex region-specific linear models called partition-wise linear model. It assigns linear models to partitions of the input space and linear combination of these partition-specific models define the region-specific linear models. This allows them to construct convex objective functions.  They optimize both the regions and predictors by using sparsity inducing structured penalties.  As a specific example of the partition-wise linear model, they propose a global and local residual model which uses one global linear weight vector and a set of partition-wise linear weights. They provide generalization bounds from which they conclude that they can use a large number of partition candidates with little risk of over fitting.  The algorithm for solving the optimization problem is based on the decomposition of proximal maps.  They efficiently compare their method to others emphasizing that their method is the only one that achieves: joint optimization of regions and region specific predictors, initialization-independent optimizers, and meaningful generalization bounds. Experiments demonstrate the their models perform better or as well as region-specific or locally linear models. Quality: Their claims are well supported both by theoretical analysis and experimental results. They carefully describe their new key ideas and derive generalization bounds.  Thorough experiments show that their methods perform well in comparison with other methods. Clarity: The paper is well-organized, but at times, it is not as clear as it could be. This is primarily due to awkward sentence structure and missing articles. Originality: The approach is a novel way to overcome the challenge of non-convex simultaneous optimization of region and region specific models. The related work is well referenced and effectively compared to their model.