Rapid Distance-Based Outlier Detection via Sampling
Distance-based approaches to outlier detection are popular in data mining, as they do not require to model the underlying probability distribution, which is particularly challenging for high-dimensional data. We present an empirical comparison of various approaches to distance-based outlier detection across a large number of datasets. We report the surprising observation that a simple, sampling-based scheme outperforms state-of-the-art techniques in terms of both efficiency and effectiveness. To better understand this phenomenon, we provide a theoretical analysis why the sampling-based approach outperforms alternative methods based on k-nearest neighbor search.

Summary: This paper proposes a modification of
      the method of Wu and Jermanine [21] for distance-based outlier
      detection. The empirical results show that the proposed method
      outperforms [21] and in fact is generally the best (and fastest) out
      of the 7 methods tested. To this reader it is (at least at first)
      surprising that so few samples can be used while retaining good
      performance. Quality: The modification over [21] is to
      only draw one sample from the dataset, rather than repeated samples.
      This would seem to be an effective strategy in terms of variance
      reduction. What is notable from Fig 1 is that so few samples can be
      drawn in order to obtain good performance (indeed it seems preferable
      to use a small number over n). Table 2 shows that this is the
      fastest method, while table 3 shows that method is only beaten on 4/20
      datasets by [21]. In sec 4, please state what parameters (e.g. k)
      are being used here for each method, and also why these are sensible
      choices. Section 6 provides some analysis of why e.g. small sample
      sizes might be desirable. I don't find this very compelling, e.g at
      line 394 they talk about beta being small, but if there are several
      clusters it seems that beta (defined ie eq 2) will be close to 1. To
      really make this convincing I would like to see these analysis
      assumptions tested against values obtained for real data.
      Clarity: I found the writing clear Originality: this could
      be seen as a simple "tweak" on [21], although a tweak that appears to
      have a significant effect. Significance: it appears that the
      proposed method advances the s-o-a in distance-based outlier
      detection. Although this topic is more "data mining" than the usual
      NIPS focus, it could be of practical value. Overall:
      This paper proposes a simple modification of the method of Wu and
      Jermanine [21] for distance-based outlier detection. The empirical
      results presented show that the proposed method outperforms [21] and
      in fact is generally the best (and fastest) out of the 7 methods
      tested. To this reader it is (at least at first) surprising that so
      few sample can be used while retaining good performance. The
      significance to the NIPS community might be limited due to a
      relatively low profile for outlier detection.


Density estimation from unweighted k-nearest neighbor graphs: a roadmap
Consider an unweighted k-nearest neighbor graph on n points that have been sampled i.i.d. from some unknown density p on R d . We prove how one can estimate the density p just from the unweighted adjacency matrix of the graph, without knowing the points themselves or any distance or similarity scores. The key insights are that local differences in link numbers can be used to estimate a local function of the gradient of p, and that integrating this function along shortest paths leads to an estimate of the underlying density.

QUALITY: This work shows an interesting way of
      estimating the density of a random vector from an unweighted k-NN graph.
      It assumes that the density is differentiable and bounded away from zero
      in the epsilon-interior of the support. Some minor points:
      Page 2: in the definition of In(x), "E" has not been defined. Did the
      authors mean "E_n"? Page 2: last paragraph: the unweighted shortest
      path distance needs to be defined. Page 4: Proposition 1: I guess the
      condition n/log(k) goes to infinity must be changed to k/log(n) goes to
      infinity. CLARITY: The paper is nicely written. The main
      results are motivated with examples and illustrations, and the proofs of
      the results are sufficiently sketched. ORIGINALITY: The
      main idea is to use rectifiable paths connecting two vertices to define
      "order" (that is right and left) in a higher dimensional space. This is a
      clever idea. It is known that in Euclidean space, a weighted k-NN graph
      can give a rough (but asymptotically acceptable) estimate of the density.
      In this work, the authors conjecture that even the unweighted k-NN graph
      gives an estimate of the density. The authors show support for their
      conjecture by showing that asymptotically their procedure converges to the
      true density with a little more knowledge of the geometry. But as in the
      case of the weighted graph, for real life applications, this estimate may
      not be too good, unless the size of the sample is large. This is what the
      authors do in their simulation: n=2000 with k=50 in one or two dimensions.
      Higher dimensions will require an enormous quantity if data. The procedure
      uses the knowledge of the vector dimension. In an unweighted graph, the
      actual dimension may be unknown. The suggestion given by the authors to
      estimate it will work again only if n is very large.
      SIGNIFICANCE: I like the extended application suggested at
      the end of the paper for multi-dimensional scaling. This might be a good
      and very practical application of the procedure.


Statistical analysis of coupled time series with Kernel Cross-Spectral Density operators
Many applications require the analysis of complex interactions between time series. These interactions can be non-linear and involve vector valued as well as complex data structures such as graphs or strings. Here we provide a general framework for the statistical analysis of these dependencies when random variables are sampled from stationary time-series of arbitrary objects. To achieve this goal, we study the properties of the Kernel Cross-Spectral Density (KCSD) operator induced by positive definite kernels on arbitrary input domains. This framework enables us to develop an independence test between time series, as well as a similarity measure to compare different types of coupling. The performance of our test is compared to the HSIC test using i.i.d. assumptions, showing improvements in terms of detection errors, as well as the suitability of this approach for testing dependency in complex dynamical systems. This similarity measure enables us to identify different types of interactions in electrophysiological neural time series.

The paper considers kernel cross-spectral density
      (KCSD) as a way to determine interactions among time series in a better
      way than methods developed under the i.i.d assumption, which is typically
      violated for time series data. Such a framework was originally proposed in
      [Besserve et al, ICASSP, 2011]. The main contribution here is to
      characterize cases where KCSD can be used to test independence, and to
      propose and study a way to estimate the properties of cross-spectral
      density operators from finite samples. The method is compared to the
      Hilbert-Schmidt Independence Criterion test under the same kernels on
      simulated and real neural data. Developing independence test for
      time series data that are able to cope with non-linear interactions is an
      important area of research. The present paper provides a sound and
      well-motivated approach. Many applications, however, consider a
      large number of time series data. Even though the proposed approach
      accommodate very general forms of dependencies, it is a *pair-wise*
      independence test, and thus suffers from the limitations inherent to
      pair-wise testing. It would be interesting to discuss whether the proposed
      method could be extended to testing simultaneously multiple time series
      (each being potentially multivariate). The methodology and results
      depend on the choice of kernel, and various kernels might lead to
      contradictory conclusions. This should be discussed. Kernel
      methods seem very promising candidates in capturing dependencies in time
      series, in the present setting and beyond. For instance, it would also be
      relevant to mention the recent work by Sindhwani et al, Scalable
      Matrix-valued Kernel Learning for High-dimensional Nonlinear Multivariate
      Regression and Granger Causality, UAI 2013, which uses kernel methods to
      capture non-linearity in causal inference, via a generalized form of
      sparse vector autoregression.


Active Learning for Probabilistic Hypotheses Using the Maximum Gibbs Error Criterion
We introduce a new objective function for pool-based Bayesian active learning with probabilistic hypotheses. This objective function, called the policy Gibbs error, is the expected error rate of a random classifier drawn from the prior distribution on the examples adaptively selected by the active learning policy. Exact maximization of the policy Gibbs error is hard, so we propose a greedy strategy that maximizes the Gibbs error at each iteration, where the Gibbs error on an instance is the expected error of a random classifier selected from the posterior label distribution on that instance. We apply this maximum Gibbs error criterion to three active learning scenarios: non-adaptive, adaptive, and batch active learning. In each scenario, we prove that the criterion achieves near-maximal policy Gibbs error when constrained to a fixed budget. For practical implementations, we provide approximations to the maximum Gibbs error criterion for Bayesian conditional random fields and transductive Naive Bayes. Our experimental results on a named entity recognition task and a text classification task show that the maximum Gibbs error criterion is an effective active learning criterion for noisy models.

Overview: The authors propose the Gibbs error
      criterion for active learning; seeking the samples that maximize the
      expected Gibbs error under the current posterior. They propose a greedy
      algorithm that maximises this criterion (Max-GEC). The objective reduces
      to maximising a specific instance of the Tsallis entropy of the predictive
      distribution which is very similar to Maximum Entropy Sampling (MES) which
      uses the Shannon entropy of the predictive distribution. They consider the
      non-adaptive, adaptive and batch settings separately, and in each setting
      they prove using submodularity results that the greedy approach achieves
      near-maximal performance compared to optimal policy. They show how to
      implement their fully adaptive policy (approximately) in CRFs with
      application to named entity recognition, and implement the batch algorithm
      with a Naive Bayes classifier, with application to a text classification
      task. Quality: Their algorithm appears to be a sensible
      approach, with the Gibbs error being very closely related to the Bayes
      error. Although it appears very similar to a number of approaches in the
      literature (MES, Query by Committee), it exhibits some useful theoretical
      and practical properties. Primarily, they are able to show near-optimal
      bounds in the adaptive greedy setting with probabilistic predictions;
      previous approaches have been shown only to be optimal in the non-adaptive
      or noiseless case. A second advantage is that their objective permits a
      simpler computation of their objective with CRFs when approximating
      integrals over the posterior with samples; it would be interesting to see
      a discussion of whether this rearrangement is extensible to other models?
      However, I have a concern about the practicality of the algorithm.
      In particular in the non-adaptive/batch case, a sum over the product space
      of all possible labellings of the batch (S) is required (Eqns. 2, 4). When
      applying batch Max-GEC to the NB classifier they approximate the sum using
      Gibbs sampling. Given how large the space of possible labelings of the
      batch could be, this may require a very large number of samples to get a
      reasonable estimate, the requirement to compute/estimate this sum seems to
      restrict the batch algorithm to either small batches or models in which
      computing predictions is cheap. The experiment section is fairly
      convincing; using two tasks and a number of different datasets, they show
      max-GEC usually outperforms a number of baselines, although the
      improvement over LeastConf seems marginal at best. A concern I have is
      that for the CRF model, SegEnt/LeastConf produce almost as good results as
      Max-GEC, which is perhaps unsurprising given the similarity between the
      algorithms, however, for SegEnt/LeastConf the authors use only the MAP
      hypothesis to compute uncertainties, and for Max-GEC they show improvement
      by integrating over parameters (using samples). They should compare also
      to SegEnt and LeastConf with parameter integration, these approaches may
      be more sensitive to accurate estimation of uncertainties and I am
      unconvinced that there would necessarily be a performance difference after
      accounting for parameter uncertainty. Clarity: The paper is
      largely clearly written, however, although they do define the notation, I
      find some of the choices of notation somewhat confusing. In particular use
      of a generic p to denote the posterior as opposed to the prior p_0 is a
      bit unclear (perhaps it could be subscripted by the data used to train the
      model). Also the use of the symbol traditionally used for ‘conditioning’
      (as in y_{A|X}) to denote the labelling of X according to A makes the
      paper harder to read. The use of E(\rho) to denote the set of unlabelled
      examples looks a lot like an expectation, also regarding expectations it
      would be useful to subscript them with the distribution over which the
      expectation is being taken e.g. for an expectation under the prior E_y
      -> E_{p_0(y)}. Significance: Although the optimality proofs
      provide an interesting insight into this particular criterion, and provide
      a decent theoretical contribution, the algorithm itself is sufficiently
      similar to a number of proposed approaches and so this paper does not
      represent a very significant practical contribution to the field of active
      learning.


Sinkhorn Distances: Lightspeed Computation of Optimal Transport
Optimal transport distances are a fundamental family of distances for probability measures and histograms of features. Despite their appealing theoretical properties, excellent performance in retrieval tasks and intuitive formulation, their computation involves the resolution of a linear program whose cost can quickly become prohibitive whenever the size of the support of these measures or the histograms' dimension exceeds a few hundred. We propose in this work a new family of optimal transport distances that look at transport problems from a maximumentropy perspective. We smooth the classic optimal transport problem with an entropic regularization term, and show that the resulting optimum is also a distance which can be computed through Sinkhorn's matrix scaling algorithm at a speed that is several orders of magnitude faster than that of transport solvers. We also show that this regularized distance improves upon classic optimal transport distances on the MNIST classification problem.

The paper studies variants of the Earth Mover's
      distance (EMD) with either a constraint on the entropy or a penalty term
      in the objective linear in the entropy. When there is a bound on the
      entropy, the objective turns out to be a distance metric but the paper
      does not show how to compute it efficiently. The other variant is not a
      distance metric but the paper shows that the optimal transportation is the
      unique stochastic matrix obtained by scaling rows and columns of the
      matrix with entries exp(-lambda*m_{i,j}) where m_{i,j} is the
      distance/transportation cost between i and j and lambda is the coefficient
      of the entropy term in the objective. This stochastic matrix can be
      approximated by Sinkhorn-Knopp's algorithm. The paper makes an interesting
      observation about a variant of EMD that might be efficiently approximated.
      However, the comparison with EMD in the paper is not fair, since the
      authors insist on EMD being computed exactly while the variant being
      studied is only approximated without any statement on the convergence rate
      of the algorithm. It is conceivable that for the random vectors tested in
      the paper, the algorithm converges quickly but it might be slow for
      pathological vectors. It is also not clear if comparing with EMD on just
      the original pixel space is the right comparison when the previous work
      cited by the paper computed EMD in the gradient orientation histograms
      (SIFT features) as well as the pixel space. The authors might also want to
      compare the results with previous work using variants/approximations of
      EMD such as Kristen Grauman, Trevor Darrell. Approximate
      Correspondences in High Dimensions. NIPS 2006. The pyramid match
      approach above is inspired by ideas from work on approximating EMD e.g.
      Indyk, P., and Thaper, N. 2003. Fast Image Retrieval via Embeddings.
      The paper is generally well written but the authors might want to
      include a statement of the Sinkhorn-Knopp's theorem, a description of the
      algorithm using formula rather than Matlab code, and some statement on the
      convergence rate of the algorithm. ============================
      Rebuttal comments: there are many ways to speed up EMD
      computation, one such approach is to use coarser distances as taken by
      Pele and Werman already cited in the paper (round so that distances can
      only be 1,2,3). I am not sure if there are publicly available
      implementations taking advantage of the small weight range even though
      this is an area with a lot of theoretical results such as Gabow,
      Harold N., and Robert E. Tarjan. "Faster scaling algorithms for network
      problems." SIAM Journal on Computing 18.5 (1989): 1013-1036. It
      would be interesting to compare to that approach in terms of speed and
      retrieval accuracy.


Sketching Structured Matrices for Faster Nonlinear Regression
Motivated by the desire to extend fast randomized techniques to nonlinear l p regression, we consider a class of structured regression problems. These problems involve Vandermonde matrices which arise naturally in various statistical modeling settings, including classical polynomial fitting problems, additive models and approximations to recently developed randomized techniques for scalable kernel methods. We show that this structure can be exploited to further accelerate the solution of the regression problem, achieving running times that are faster than "input sparsity". We present empirical results confirming both the practical value of our modeling framework, as well as speedup benefits of randomized regression.

This paper proposes efficient randomization-based
      algorithms for solving two types of regression problems -- corresponding
      to linear least squares and least absolute deviation fitting over convex
      sets -- in settings where the design matrix has a Vandermonde structure.
      To the reviewer's best knowledge, incorporating this type of structure
      into such randomized algorithmic approaches to linear algebra problems is
      novel. Such methods are timely and relevant, given many recent
      applications focused on processing and inference in "big data" regimes.
      The paper is overall well-written and could, in the opinion of the
      reviewer, comprise a solid contribution to the NIPS community, subject to
      some minor revisions, described in some detail here. Primary
      concerns: 1) The authors appear unaware of some connections
      between the subspace embedding they describe (claimed introduced in [6])
      and existing efforts in the sketching literature. Specifically, the matrix
      structure described in section 3.1.2 here was previously proposed as a
      counting sketch in (Charikar, Moses, Kevin Chen, and Martin Farach-Colton.
      "Finding frequent items in data streams." Automata, Languages and
      Programming. Springer Berlin Heidelberg, 2002. 693-703.); see also, e.g.,
      the recent survey article (Gilbert, Anna, and Piotr Indyk. "Sparse
      recovery using sparse matrices." Proceedings of the IEEE 98.6 (2010):
      937-947.). 2) Further, there are implicit connections between the
      embedding results on page 5 and the compressive sensing literature.
      Namely, ensuring that the l_2 norm of vectors Ax remain preserved is
      related under action by a linear operator (here, $\Pi$) is related to the
      well-known restricted isometry property, albeit in this case "restricted"
      to a single subspace of dimension equal to the number of columns in A;
      see, for example, (Candès, Emmanuel J. "The restricted isometry property
      and its implications for compressed sensing." Comptes Rendus Mathematique
      346.9 (2008): 589-592.), as well as (Baraniuk, Richard, et al. "A simple
      proof of the restricted isometry property for random matrices."
      Constructive Approximation 28.3 (2008): 253-263.) Likewise, the l_1
      preservation relation on page 5 here is related to the l_1-RIP condition
      studied in (Berinde, Radu, et al. "Combining geometry and combinatorics: A
      unified approach to sparse signal recovery." Communication, Control, and
      Computing, 2008 46th Annual Allerton Conference on. IEEE, 2008.).
      3) I found the experimental section somewhat unclear.
      Specifically, it was not obvious to me specifically what the
      classification approach was here. It would be helpful if the authors could
      explain this in some more detail. Minor points: 1) In
      several places, including Theorem 6 and Algorithm 2, the authors describe
      a matrix of Gaussians. Is there any reason to prefer, e.g., unit variance
      here? 2) On page 5, the authors state "The best known value of
      $\kappa$, independent of $d$, is $\kappa = O(d^2 \log^2d)." How is this
      independent of d? 3) On page 6, "Let L = (i such that a_i \neq 0
      and ), and ..." typo? 4) Table 1 in the "CENSUS" data set, the
      time is given as 1.4% sec One Final General Suggestion It
      may be helpful for the reader to better appreciate the contributions here,
      if the authors listed in each step of the proposed algorithm the
      corresponding computational complexity. This would be especially helpful
      where, e.g., the procedure requires QR decompositions -- this step gave
      the reviewer pause, at first viewing.


Convex Two-Layer Modeling
Latent variable prediction models, such as multi-layer networks, impose auxiliary latent variables between inputs and outputs to allow automatic inference of implicit features useful for prediction. Unfortunately, such models are difficult to train because inference over latent variables must be performed concurrently with parameter optimization-creating a highly non-convex problem. Instead of proposing another local training method, we develop a convex relaxation of hidden-layer conditional models that admits global training. Our approach extends current convex modeling approaches to handle two nested nonlinearities separated by a non-trivial adaptive latent layer. The resulting methods are able to acquire two-layer models that cannot be represented by any single-layer model over the same features, while improving training quality over local heuristics.

The paper addresses problem of training two-layer
      network for classification with latent variables. The authors propose a
      convex SDP relaxation of originally non-convex training problem. They also
      provide an approximate optimization algorithm to solve their SDP
      formulation. A proof of concept experiments show promising results,
      namely, that the algorithm outperforms both globally optimized
      single-layer models as well as the same two-layer model optimized with
      local alternating minimization. The proposed reformulation which
      allows SDP relaxation is interesting and novel. Overall the paper is
      sufficiently clear though some parts of the text are dense. The paper
      seems to be technically sound. The main weakness seems to be
      complexity of the resulting SDP problem (21). The authors could
      mention basic properties of the proposed optimization algorithm for
      solving (21), e.g computational time required for the benchmark problems
      and whether the algorithm provides a precise solution (i.e. what was
      the stopping condition used). This is an important information because
      convex problem does not immediately mean easy to solve problem, i.e. a
      convex relaxation can be intractable in practice and it should be
      clear if it is the case or not. However, the proposed relaxation would be
      valuable even in this case. Minor comments: - equ (17):
      variable is missing below the first minimum - equ (18): I think
      N=\Phi'*\Phi should appear in the conditions defining the set. - line
      331: (d) Synhetic results - line 356: It is unclear why the used
      transductive evaluation does not require computing responses of the
      network and thus knowledge of W and V. - I could not find the actual
      size of instances of the problem (21) solved in the experiments.


Stochastic Majorization-Minimization Algorithms for Large-Scale Optimization
Majorization-minimization algorithms consist of iteratively minimizing a majorizing surrogate of an objective function. Because of its simplicity and its wide applicability, this principle has been very popular in statistics and in signal processing. In this paper, we intend to make this principle scalable. We introduce a stochastic majorization-minimization scheme which is able to deal with largescale or possibly infinite data sets. When applied to convex optimization problems under suitable assumptions, we show that it achieves an expected convergence rate of O(1/ √ n) after n iterations, and of O(1/n) for strongly convex functions.
Equally important, our scheme almost surely converges to stationary points for a large class of non-convex problems. We develop several efficient algorithms based on our framework. First, we propose a new stochastic proximal gradient method, which experimentally matches state-of-the-art solvers for large-scale ℓ 1 -logistic regression. Second, we develop an online DC programming algorithm for non-convex sparse estimation. Finally, we demonstrate the effectiveness of our approach for solving large-scale structured matrix factorization problems.

Summary: This paper suggests a stochastic
      algorithm based on majorization-minimization principle, i.e., iteratively
      minimizing a majorizing surrogate of an objective function, for convex,
      strongly convex and also certain non-convex (DC) optimization problems.
      The majorization-minimization principle is known to underlie a number of
      known algorithms such as expectation-maximization (EM). The theoretical
      results are also supported with various numerical experiments.
      Quality: Overall the problem is well-motivated and the
      conditions used in the analyses, theoretical developments and their proofs
      (I did not check the ones used for the math background) seem correct. Yet
      the paper is missing a number of quite related literature on first order
      methods for nonconvex problems such as “Stochastic first-and zeroth-order
      methods for nonconvex stochastic programming“ by Ghadimi and Lan. Also the
      logarithmic loss in Corollary 3.2 due to decreasing step sizes indicates
      this method is not an optimal algorithm. The same is true for strongly
      convex function case given in Proposition 3.2. This should perhaps be
      emphasized a bit clearer. The paper seems to be very closely
      connected with the reference [19]. The authors should state for each
      proposition, lemma, etc., whether they were from [19] or not, or whether
      the corresponding analysis from [19] easily extends to this case or not.
      The numerical results seem promising. Yet there is a caveat
      between the theory presented and numerical results. First of all, almost
      all of the theory is built upon assuming that the domain of the
      optimization problem to be solved is bounded, i.e., for the stepsizes
      theoretically analyzed one needs to know an upper bound on
      \|\theta^*-\theta_0\|_2 where \theta^* is t he optimum solution and
      \theta_0 is the initial point. Also this quantity naturally occurs, as is
      the case with other first order methods, in the convergence rates. Yet in
      the experiments, all of the problems tested have unbounded domains.
      Moreover, the convergence analysis of the algorithms are carried over for
      specific stepsize rules, i.e., {\gamma\over \sqrt{n}} etc. On the other
      hand, the step size rules used in the experiments have quite different
      forms, and changes from problem to problem. I think this is a bit
      disturbing. The authors should either give justification for the step
      sizes used in the experiments theoretically or should use the ones they
      have build the theory for (at least for comparison purposes, they should
      be included in the experiments, anyway). Comparisons against FISTA is nice
      yet there are better (optimal) algorithms for strongly convex functions,
      and comparisons against those should also be presented. Clarity:
      The paper is mostly written in a clear fashion, with a reasonable
      logical structure. On the other hand, reading the supplemental material is
      almost essential in terms of digesting the notation, etc. I guess given
      the page limitation, there is no other way to fix this issue either. There
      are a few minor typos, grammatical errors. Also certain terms and notation
      such as DC or use of options 2 & 3 in Algorithm 1,
      $\overline{f}_n(\cdot)$ should be introduced earlier. Originality
      & Significance: Despite the connections with the existing
      algorithms, to the best of my knowledge the results seem original and
      valuable (especially in the nonconvex case). Minor issues: a.
      On page 4, line 180: “For space limitation details, all proofs…” should be
      “For space limitation all proofs…” b. On page 4, line 198:
      \log(\sqrt(n) should be \log(n) c. On page 5, before Proposition 3.5,
      stating the motivation for the special partially separable structure
      considered in Proposition 3.5 will be nicer. d. On page 6, lines
      284-285, description of the step size rule is confusing. How do you select
      w_n? e. On page 6, how did you decide on the sizes of the training and
      test sets for the datasets? f. On page 7, line 234 define what an
      ``epoch” is g. On page 10, line 491: “notation as us” should be
      “notation to us” h. On page 14, line 715: “function” should be
      “functions” i. On page 14, line 721: ”For … f^*+\mu A_0” should be
      “for … f^*+\mu A_1” j. On page 16, line 821: “this” should be “these”
      k. On page 16, line 823: f(\theta_{k-1}) should be E[f(\theta_{k-1})]
      l. On page 16, line 863: \log(\sqrt{n}) should be \log(n) m. On
      page 17, line 867: \log(\sqrt{n}) should be \log(n) n. On page 17,
      line 901: w_n\leq 1 is also used in this derivation. It should be
      mentioned. o. On page 17, line 908: {… \over \rho\delta} should be {…
      \over \rho^2\delta}


Small-Variance Asymptotics for Hidden Markov Models
Small-variance asymptotics provide an emerging technique for obtaining scalable combinatorial algorithms from rich probabilistic models. We present a smallvariance asymptotic analysis of the Hidden Markov Model and its infinite-state Bayesian nonparametric extension. Starting with the standard HMM, we first derive a "hard" inference algorithm analogous to k-means that arises when particular variances in the model tend to zero. This analysis is then extended to the Bayesian nonparametric case, yielding a simple, scalable, and flexible algorithm for discrete-state sequence data with a non-fixed number of states. We also derive the corresponding combinatorial objective functions arising from our analysis, which involve a k-means-like term along with penalties based on state transitions and the number of states. A key property of such algorithms is thatparticularly in the nonparametric setting-standard probabilistic inference algorithms lack scalability and are heavily dependent on good initialization. A number of results on synthetic and real data sets demonstrate the advantages of the proposed framework.

The paper provides a small-variance asymptotics
      analysis for the standard HMM as well as the infinite HMM, and in
      particular uses the asymptotic analysis to derive "hard clustering"
      optimization programs for learning and inference in both kinds of HMMs.
      The exposition in the paper is excellent, and it deftly explains
      the framework and algorithm derivation (with two approaches, providing
      extra intuition pumps). The paper also explains connections to existing
      algorithms (for standard HMMs, Viterbi re-estimation corresponds to
      setting the algorithm parameter lambda to 1) and previous work in
      small-variance asymptotics. It clearly delineates the challenges in
      adapting the small-variance algorithm approaches to the (infinite) HMM
      (Section 3.2) and explains good methods to overcome those challenges.
      These HMM fitting methods are likely to be very interesting to the
      community, and the development here (and in the supplementary materials)
      is really great. However, the experiments are weak. The data,
      both real and synthetic, are very easy, and it seems unlikely that the
      only comparison to existing techniques (the beam sampler) does justice to
      existing techniques. Despite the fact that synthetic data is
      especially easy, the beam sampler does very poorly, yet I ran the same
      experiment using a library that came up as the first result for 'python
      hmm sampling' (pyhsmm), which primarily uses weak limit samplers (which
      have been used in many application papers and certainly seem to fit these
      experiments well), and got much better results in a fraction of the time.
      Direct comparison to the results in the paper is hard because there is no
      formula or citation provided for the NMI performance metric, and the
      timing plot in Figure 1 has no units (just "log of the time" on the
      vertical axis), but it seems the weak limit sampler is decoding the
      synthetic sequences nearly perfectly in just 0.03 seconds per Gibbs sweep
      on my laptop. Given the papers showing successful applications of weak
      limit samplers (many times without dependence on good initializations or
      slow convergence, as mentioned in this paper's abstract and introduction)
      and the easy availability of code (there are several libraries online), it
      seems misleading not to provide any comparison or comment, yet this paper
      only provides a surprisingly weak showing of the beam sampler.
      There are other weaknesses and points to clarify in the
      experiments section: (1) "For these datasets, we also observe that
      the EM algorithm for the standard HMM (not reported in the figure) can
      easily output a smaller number of states than the ground truth, which
      yields a smaller NMI score." Why not show the results? The synthetic
      dataset should be easy for EM, so the omission is strange and unexplained.
      (2) "Next we demonstrate... along with comparison to the standard
      HMM." I don't see any lines in Figure 2 corresponding to the standard HMM
      methods. Were they left out accidentally? (3) Was the time for the
      grid search over algorithm parameters (mentioned in the third paragraph of
      Section 4) included in the reported run times (which seems appropriate,
      since the iHMM methods are supposedly fitting concentration parameters)?
      What are the units for the vertical axis in the right-hand panel of Figure
      2? Timing experiments can be a rabbit hole and a line must be
      drawn somewhere, but it's not clear what can be learned from the given
      experimental results, and as presented they do not support the paper's
      relative algorithm performance claims. These issues with the experimental
      evaluation provided could be easily remedied by toning down the claims
      about existing methods and focusing instead on the fact that the
      experiments demonstrate the proposed method is competitive with an iHMM
      sampling method (and perhaps also with EM if those results were reported).
      Despite those issues, the paper remains a great treatment of
      an exciting new analytical and algorithmic perspective on the well-loved
      (i)HMM.


Third-Order Edge Statistics: Contour Continuation, Curvature, and Cortical Connections
Association field models have attempted to explain human contour grouping performance, and to explain the mean frequency of long-range horizontal connections across cortical columns in V1. However, association fields only depend on the pairwise statistics of edges in natural scenes. We develop a spectral test of the sufficiency of pairwise statistics and show there is significant higher order structure. An analysis using a probabilistic spectral embedding reveals curvature-dependent components.

( Required, Visible To Authors During Feedback and
      After Decision Notification ) Synopsis. This paper examines
      third-order co-occurrence statistics of edges in natural images. The main
      finding is that triples of edges co-occur in ways consistent with smooth
      flows, elongated along the tangent direction. Better statistical
      models of the geometry of natural image structure are crucial to
      understanding biological vision as well as making progress in computer
      vision, and the authors are correct in their claim that to date most
      models have focused on 2nd-order relationships, particularly the joint
      distribution of pairs of edges. Thus the investigation of higher-order
      statistics is of great interest. Quality. Overall the methods
      seem sound. Clarity. The paper is understandable in broad
      strokes, but there are many parts that are unclear, and in general the
      paper is a bit sloppy and hurried in presentation. Here are some examples:
      • Line 74. I don’t think this equation is what the authors intend.
      • Line 106. What data were used for this analysis? Later in Section 4,
      the authors indicate that they use the van Hataren dataset, but it’s not
      clear whether this is also used here. • Line 205 What is the K matrix?
      Looks to me like the phis are just the eigenvectors of the P(i,j|0)
      matrix. • Line 232 Do you mean Fig 4 • Line 234 Do you mean Fig 5?
      • Fig 5. This figure is very unclear. What are the dimensions in the
      top panels? The first two eigenvectors? • Lines 264. From the text I
      cannot understand the color coding scheme. “The colors along each column
      correspond, so similar colors map to nearby points along the dimension
      corresponding to the row” – Columns of what? Rows of what? Clearly the
      colors are somehow dependent on phi_2, phi_3 and phi_4 in the left, middle
      and right columns. I assume then, that the color is determined by the
      value of the projection of each point on these eigenvectors? • Line
      249. The authors suggest that the projection on phi_2 reveals colinearity
      and the projection on phi_4 indicates cocircularity. What then does the
      projection on phi_3 represent? • …”each small cluster in diffusion
      space corresponds to half of a cocircular field”. What is a cocircular
      field? Where is the proof of this statement? • Line 274 “Shown
      above..” above where? • Line 280 Why complex cells and not simple
      cells? The assumed circuit model should be specified. • “Such
      curvature-based facilitation can explain the non-monotonic variance in
      excitatory long-range horizontal connections in V1”. This will be
      completely impenetrable except for a very small group of cognoscenti.
      • Line 288. We find that the embedding is only one dimensional, with
      the significant eigenvector a monotonic function…” This is an example of
      methodological sloppiness. What are the criteria for determining
      dimensionality and significance? • Line 298? What does the figure on
      the left represent, and what am I supposed to learn from it? • Line
      312, “the distribution of these directions in 3D shape are an excellent
      proxy for measuring the response of orientation filters to dense textured
      objects”. Why do I want a proxy for measuring orientation filter
      responses? Aren’t these the proximal measurements I can actually measure,
      to make inference about the distal 3D shape variables I cannot directly
      measure? • Line 346. Why are their two clusters (one cylinder, one
      spot)? Originality. There isn’t that much work on higher-order
      geometry statistics, so in this sense the paper is fairly novel.
      Significance. Although the effort here is worthwhile, I do
      think significance is lessened a bit because a) the results are not
      particularly surprising or counter to current thinking, b) there is not a
      clear advance in terms of hypothesis testing, improved quantitative model
      or algorithm and c) the paper is unclear in places. On the other hand,
      perhaps the novel spectral embedding method could in the future be used to
      achieve a more clear contribution. Also, when judging
      significance, it’s important to make clear that most prior work on natural
      edge statistics does not really make the claim that 2nd-order statistics
      are sufficient models for joint edge statistics in natural images.
      For example, Geisler et al and Elder & Goldberg were not
      measuring co-occurrence statistics over images. Geisler was measuring
      co-occurrence statistics over object boundaries, and Elder & Goldberg
      were measuring sequential statistics along object boundaries. Thus the
      Elder & Goldberg data, for example, provide the statistics required
      for a first-order Markov model of contours, not a Markov model of the 2D
      edge (association) field. Thus in Fig 2, the conditional distribution for
      contours is being misapplied to the problem of modeling the edge field.
      To make this clearer, note that generally the E&G model would
      predict the existence of higher-order co-occurrence statistics over the
      edge field. For example, suppose this model is used to generate a number
      of contours sparsely distributed over the image. The edge elements
      belonging to the same contour would generate strong third-order
      co-occurrences explainable by second-order statistics along the contour
      but NOT explainable by second order statistics in the 2D association
      field. This does not mean that the present effort to understand
      these third-order co-occurrences in the edge field is not worthwhile, but
      it’s important to put it in the right context. In particular, given this
      presentation it is still not clear whether a model like the E&G model
      might be sufficient to explain the 2D edge field. (Although we know this
      is unlikely: Ren & Malik (2002) have in fact shown that contours are
      not 1st-order Markov – no surprise.) X. F. Ren and J. Malik. A
      probabilistic multi-scale model for contour completion based on image
      statistics. In Lecture Notes in Computer Science, Proc. ECCV, volume 2350,
      pages 312–327, Berlin, 2002. Springer-Verlag.


Non-Linear Domain Adaptation with Boosting
A common assumption in machine vision is that the training and test samples are drawn from the same distribution. However, there are many problems when this assumption is grossly violated, as in bio-medical applications where different acquisitions can generate drastic variations in the appearance of the data due to changing experimental conditions. This problem is accentuated with 3D data, for which annotation is very time-consuming, limiting the amount of data that can be labeled in new acquisitions for training. In this paper we present a multitask learning algorithm for domain adaptation based on boosting. Unlike previous approaches that learn task-specific decision boundaries, our method learns a single decision boundary in a shared feature space, common to all tasks. We use the boosting-trick to learn a non-linear mapping of the observations in each task, with no need for specific a-priori knowledge of its global analytical form. This yields a more parameter-free domain adaptation approach that successfully leverages learning on new tasks where labeled data is scarce. We evaluate our approach on two challenging bio-medical datasets and achieve a significant improvement over the state of the art.

This paper addresses the problem of domain adaptation
      in bio-medical data based on boosting. The basic idea of the algorithm is
      to learn a non-linear transformation of different domains to a shared
      feature space where a single boundary shared across all tasks can be used
      for classification. The algorithm exploits the boosting trick to handle
      the non-linearities. The algorithm is applied on two challenging
      bio-medical datasets, achieving significant performance improvements in
      both. Overall, I thought that the paper was well written, and the
      algorithm was novel enough to encourage further research in this
      direction. While the experiments show good results, I think the
      experimental evaluation was limited in the set of datasets used, and could
      be further improved by applying to a larger variety of datasets. Also,
      some potentially missing baselines and comparisons as mentioned below.
      Specifically: - It would be good to test the same algorithm on
      visual datasets such as the one by Saenko et al. Do the same findings hold
      in that case? - Why isn't the method by Gopalan et al on unsupervised
      domain adaptation included as another baseline? - What is the running
      time of your algorithm, for both training and testing? - It would be
      good to compare your work against the following set of papers (mentioned
      with Z to be different from paper citations): [Z1] Regularized
      Multi-Task Learning, KDD 2004 [Z2] Unbiased Look at Dataset Bias, CVPR
      2011 [Z3] Undoing the Damage of Dataset Bias, ECCV 2012 Z1 is
      another popular work on multi-task learning that has a common and shared
      part in a max-margin framework. In addition, the problem seems to be
      closely related to Z2 and Z3. Specifically, in Z3, the authors also modify
      multi-task learning formulation for dataset bias (similar to domain
      adaptation) to learn a single classifier for all
      datasets.


Learning Multiple Models via Regularized Weighting
We consider the general problem of Multiple Model Learning (MML) from data, from the statistical and algorithmic perspectives; this problem includes clustering, multiple regression and subspace clustering as special cases. A common approach to solving new MML problems is to generalize Lloyd's algorithm for clustering (or Expectation-Maximization for soft clustering). However this approach is unfortunately sensitive to outliers and large noise: a single exceptional point may take over one of the models. We propose a different general formulation that seeks for each model a distribution over data points; the weights are regularized to be sufficiently spread out. This enhances robustness by making assumptions on class balance. We further provide generalization bounds and explain how the new iterations may be computed efficiently. We demonstrate the robustness benefits of our approach with some experimental results and prove for the important case of clustering that our approach has a non-trivial breakdown point, i.e., is guaranteed to be robust to a fixed percentage of adversarial unbounded outliers.

The authors propose in this paper a regularized
      weighting technique for multi-model learning. Multi-model learning
      consists in fitting a "mixture" of simple models to a data set in a quite
      generic sense where each model is associated to a convex loss and the
      mixture is optimized with respect to both the model parameters and their
      weights (each model is associated to a set of weights that describe how
      much the model claims to explain each data point). This model generalizes
      several classical approaches such as k-means and classical probabilistic
      mixture modeling. The authors propose to penalize the weights of each
      model so as to favor uniform weight distributions as a way to bring
      robustness of the mixture with respect to outliers. The paper contains
      several theoretical results and some limited experimental validation.
      The paper is interesting and well written. In particular, the
      generality of the approach is very well presented. The authors also
      managed to pack a nice collection of results in a limited space. They
      pushed all the proofs in supplementary material, but nevertheless, the
      paper feels quite self contained. Limitations of the technique are also
      clearly presented (see Figure 2.2 for instance). My overall
      impression is therefore very positive. That said, the paper is not without
      flaws. A very minor one concerns notations: - \Delta^n is introduced a
      bit too late (in footnote 1 which falls on page 3 while the notation is
      used on page 2). - P_C (the orthogonal projection operator) is defined
      only in the supplementary material while it is used in Lemma 2 (in the
      s.m. the definition is also a bit too delayed). - while the gamma
      parameter used in the discussion below definition 2 is indirectly defined,
      I think the discussion would be clearer by being more explicit (for
      instance by saying that the proportion of zero weights (i.e., ignored data
      points) should be between this and that). While the overall paper
      is very clear, Section 3.1 is a bit too cryptic and lacks too much
      details: how was the noise generated? what is the value of alpha? what is
      the effect of said value on the performances? does MAD in the legend
      stands for MD in the text? if the base learning is PCA, is there any
      dimensionality reduction done? if yes how? All in one, this unique
      experimental evaluation raises more questions that it brings answers or
      insights on the proposed method. Coming back to the choice of
      alpha, it is obvious, as discussed in Section 2 and 3.2, that its actual
      value will have at least some impact on the performances of the final
      model. And of course, any practitioner would want to optimize said alpha.
      Yet the experimental section does not show the effects of alpha (whose
      value is not specified) and the authors offer almost no clue on how to
      tune it. This is quite a shortcoming in the paper, in my opinion. As alpha
      appears explicitly in Theorem 3, it is quite clear that even on a
      theoretical point of view the parameter has some complex effect on the
      results. Another point is the upper bound assumption (B
      everywhere). I'm familiar with clipping techniques used in rather old
      papers (for instance the Zeger and Lugosi's 1995 paper, see
      http://www.code.ucsd.edu/~zeger/publications/journals/LuZe95-IT-Nonparametric/LuZe95-IT-Nonparametric.pdf)
      but I'm not sure how to understand the assumption in the present context.
      In particular, it seems too me that the very idea of fighting arbitrary
      outliers might prevent this assumption to be true in practice. In other
      words, moving from Theorem 3 to a more general one which applies when the
      bound assumption is not valid (as in done in the paper referenced above)
      does not seem completely obvious to me. I might be missing something that
      should then be emphasized more in the paper. A final point is that
      despite the (short) Section 1.1, the discussion on related works seem
      quite limited. In particular, mixture models can accommodate many types of
      reasonable outliers by modeling them explicitly, for instance via some
      Student component instead of Gaussian ones, or via some explicit noisy
      components added to the mixture. Bayesian priors can be included into the
      mix to avoid some strong effects of very badly behaving outliers. I'm not
      saying that such an approach might lead to non zero breakdown point, but
      in practice, such variants do work very well.


Stochastic Gradient Riemannian Langevin Dynamics on the Probability Simplex
In this paper we investigate the use of Langevin Monte Carlo methods on the probability simplex and propose a new method, Stochastic gradient Riemannian Langevin dynamics, which is simple to implement and can be applied to large scale data. We apply this method to latent Dirichlet allocation in an online minibatch setting, and demonstrate that it achieves substantial performance improvements over the state of the art online variational Bayesian methods.

This paper combines the recently proposed stochastic
      gradient Langevin dynamics with Riemannian Langevin dynamics. The new
      sampling algorithm is able to use a locally adaptive preconditioning
      matrix for a faster convergence rate. It is applied to draw samples in the
      posterior distribution of the LDA model under the online learning setting,
      and achieves a better predictive performance than online variational
      Bayesian methods. The combination of SGLD with RLD provides a
      promising direction to improve the application of MCMC methods on large
      scale data set. It is usually difficult to choose a suitable and
      easy-to-compute Riemannian metric. But the Dirichlet model is one of the
      exceptions where the expected Fisher information can be computed exactly
      and efficiently. How likely is it that SGRLD would be applied to a more
      general area or probably with some extra approximation? In order
      to converge to the exact posterior distribution, SGLD has to anneal the
      step size towards 0, which will slow down the mixing of the Markov chain
      even with the help of RLD. Is it possible to run SGRLD with a fixed step
      size for a faster mixing at the price of introducing bias in the
      stationary distribution? Also, is there any strategy/heuristic to choose
      appropriate step size parameters instead of doing a grid search?
      Among the four parameterization, RLD + expanded-mean is shown to
      obtain the best performance. However, with the mirroring trick, the
      log-likelihood of the model is not differentiable at 0. Would that result
      in extra error of Langevin dynamics? In Table 1, what does “n.”
      mean? Also, it seems there are some errors in G(\theta). E.g. in
      reduced-mean, there is a factor of n, but in expanded-mean, G(\theta) does
      not depend on n. So is reduced-nature vs. expanded-natural. Besides,
      \theta in reduced-nature should be replaced with exp(\theta). The
      text and markers in all the figures are too small to read. It would be
      better to put the description of the parameter values in the caption.
      Other typos: Line 42, are based a batch → missing “on”
      Line 79, a SGLD → an SGLD Figure 1(b), Phi → \pi Line 399, The
      algorithms’ performances … was assessed Line 402, in vocabulary size →
      missing “a”


Simultaneous Rectification and Alignment via Robust Recovery of Low-rank Tensors
In this work, we propose a general method for recovering low-rank three-order tensors, in which the data can be deformed by some unknown transformation and corrupted by arbitrary sparse errors. Since the unfolding matrices of a tensor are interdependent, we introduce auxiliary variables and relax the hard equality constraints by the augmented Lagrange multiplier method. To improve the computational efficiency, we introduce a proximal gradient step to the alternating direction minimization method. We have provided proof for the convergence of the linearized version of the problem which is the inner loop of the overall algorithm. Both simulations and experiments show that our methods are more efficient and effective than previous work. The proposed method can be easily applied to simultaneously rectify and align multiple images or videos frames. In this context, the state-of-the-art algorithms "RASL" and "TILT" can be viewed as two special cases of our work, and yet each only performs part of the function of our method.

This paper considers the (unrectified and misaligned)
      tensor recovery problem, which is an interesting problem.
      Originality: This work extends the matrix case in [1] to the
      tensor case. Specifically, it replaces the matrix nuclear norm in Eq. (3)
      of [1] by the tensor nuclear norm. I am afraid that this type of extension
      may not be treated as a substantial contribution any more since similar
      extensions have appeared in many early papers like [10-14, etc]. The new
      staff beyond this extension seems to consider the misalignment issue in
      tensors. The technique used to deal with unrectification and misalignment
      actually follows [1] as well. This paper just simply splits the tensor
      data into matrices and uses the technique proposed in [1] to deal with
      uncertification and misalignment in matrices. Although this paper claims
      that the proposed method align across images unlike [1], that is just due
      to the tensor nuclear norm rather than any new alignment technique.
      A variant of the ADMM method is used to solve a key step of the
      proposed formulation. This paper claims ADMM is not efficient to solve
      (12-1) --- the first subproblem in (12) because (12-1) does not give a
      closed form. To my experiences, if properly introduce new variables into
      (11), it can be formulated into a structure good for ADMM (that is, all
      subproblems have closed form solutions): you can try duplicate \L and \E
      in (11). The proof for Theorem 1 seems unnecessary. The
      convergence for many variants for ADMM, including using the proximal
      gradient descent (used in this paper) to replace the exactly solving, has
      been shown in many optimization papers already, for example, [A], [B].
      Overall, this paper is not of sufficient contribution in term of
      originality. My novelty judgement is only based on the aspects of modeling
      and algorithm. Contributions in numerical results may be ignored.
      Clarity: Some equations are not clear enough, and some
      notations are abused apparently in section 3.1. Readers like me have to
      read [1] to understand those undefined and unclear notations and
      equations. Authors should seriously treat the following issues. - (5)
      reuses "\circ" which has been used in (2). Two ``\circ'' actually mean
      totally different things. Readers that unfamiliar with [1] may be misled
      in (5). Moreover, the followed explanation for "A\circ \Tau" is also
      unclear. ``Applying the transformation \tau_i to each matrix A(:,:,i)''
      sounds like the matrix multiplication \tau_i A(:,:,i). It actually means
      A(\tau_x, \tau_y, i) from [1]. - What is the value of ``p'' in two
      lines before (5)? - (8) is suddenly relaxed into (9) by using a
      ``popular'' way. What is the ``popular'' way? No explanation, no
      citations. Readers have to figure out it from other papers like [1]. -
      The last line of Section 3.1: what is the value of "n". This notation "n"
      appears for multiple times before this line. Apparently, they denote
      different things. [A] On the Linear Convergence of the Alternating
      Direction Method of Multipliers, Mingyi Hong, Zhi-Quan Luo, 2012. [B]
      Linearized Alternating Direction Method of Multipliers for Constrained
      Linear Least-Squares Problem, Raymond H. Chan1, Min Tao, Xiaoming Yuan,
      2012.


Sequential Transfer in Multi-armed Bandit with Finite Set of Models INRIA Lille -Nord Europe Team SequeL
Learning from prior tasks and transferring that experience to improve future performance is critical for building lifelong learning agents. Although results in supervised and reinforcement learning show that transfer may significantly improve the learning performance, most of the literature on transfer is focused on batch learning tasks. In this paper we study the problem of sequential transfer in online learning, notably in the multi-armed bandit framework, where the objective is to minimize the total regret over a sequence of tasks by transferring knowledge from prior tasks. We introduce a novel bandit algorithm based on a method-of-moments approach for estimating the possible tasks and derive regret bounds for it.

Summary: This paper studies online transfer learning
      in multi-armed bandits (MAB), where each instance of MAB encountered
      belongs to a finite model class. Instead of running single-task MAB
      algorithm, the paper shows how one can do better through sequential
      transfer across tasks. The paper first studies a variant of UCB1 (called
      mUCB): it assumes a set of MAB models is given as input, and improves on
      UCB1 by restricting the upper confidence bound calculation to the given
      models. Then, this algorithm is extended to the sequential transfer case
      (called tUCB), where the set of models is unknown, but has to be
      discovered by the algorithm. Here, the authors build on recent advances in
      tensor-based techniques to estimate the set of models. Under certain
      assumptions, tUCB enjoys lower per-task regret bounds than standard UCB1.
      Numerical experiments in synthetic problems verify the theoretical
      findings. * Quality: The problem studied by the paper (online
      transfer learning in MAB) is new, and the proposed methods are very
      reasonable. While mUCB is a relatively straightforward variant, its
      extension to tUCB, where the set of models is unknown, is definitely
      nontrivial. The theory appears correct. * Clarify: Overall the
      paper is written clearly, but the notation is very heavy and I wonder if
      it can be simplified. Also, there are a few places where the presentation
      can be improved (such as undefined quantities). Please see the detailed
      comments below. * Originality: The problem formulation is new, to
      the best of my knowledge. The first new algorithm, mUCB, is a simple
      variant of UCB1, as mentioned before. But tUCB is sufficiently novel from
      previous bandit algorithms. While the analysis techniques are mostly based
      on existing literature (including MAB and the recent tensor-related work),
      its use of method-of-moment methods in the context of MAB is interesting
      and first of its kind. * Significant: While the problem is
      interesting and important, the algorithm/analysis appear somewhat
      preliminary, for two reasons. One is the pretty strong dependence on the
      condition number of the second moment matrix M_2. The other is the
      assumption that the vectors {\mu(\theta)}_\theta are linearly independent.
      Please see the detailed comments below. Detailed comments:
      * The finite-sample convergence rate in Thm. 2 may be too loose in
      practice --- the strong dependence on #arms, #models, and the reciprocal
      of the smallest eigenvalue can make the bound too loose to be useful. One
      may wonder if these dependences are necessary, or are due to the non-tight
      analysis in this work. * A more critical problem that limits the
      significance of the results is assumption 1, which requires linear
      independence of {\mu(\theta)}_\theta. Note that this is a set of m vectors
      of dimension K. To satisfy this assumption, it must be the case that m
      (number of all possible models) is no larger than K (number of arms). This
      restriction is both too strong and (I think) unnecessary. * The
      current algorithms (mUCB and tUCB) are both variants of UCB1, with changes
      in the calculation of the confidence intervals. As acknowledged in the
      paper, a much better approach might be to consider the amount of
      information obtained by pulling an arm --- a suboptimal arm may result in
      larger regret in the short term but may help identify the current model
      more quickly. It is possible that, by considering such arms the
      restrictive assumption 1 is not needed. * Title and in the paper:
      'multi-arm bandit' should be 'multi-armed bandit' * The sentence
      in line 62 (starting with 'This') does not seem to parse. * Line
      76: should X be realization of *arms*, or *reward* of the arms? *
      Section 2: it seems more nature to swap paragraphs 2 and 3. * Line
      96: apparently, K is also part of the input to the learner. * Line
      117: the notation \Theta_+ should probably be \Theta_+(\bar{\theta}) to
      emphasize its dependence on \bar{\theta}. * Line 189: 3 samples
      are not enough to *accurately* estimate the moments, but are enough to
      make the estimates *well-defined*. * Line 211: 'finite sample
      complexity bounds' -> 'sample complexity bounds'? Sample complexity
      bounds are by definition about finite samples. * Line 222:
      \sigma_max = max ..., instead of min...? * Line 222:
      \lambda(\theta) seems undefined? * Line 224 (assumption 1): why
      does one need \rho(\theta)>0? If \rho(\theta)=0 for some \theta, then
      the model is not going to affect the algorithm anyway. * Line 269:
      what is alpha_0? * Line 279: since \Gamma is defined as the
      absolute difference, its estimate should probably be: \hat{\Gamma} =
      max(0, current_definition_in_the_paper). * Line 342: again, should
      'arms' be 'rewards', in the last sentence of Thm. 4? * Line 419:
      'rises' -> 'raises'.


Deep Neural Networks for Object Detection
Deep Neural Networks (DNNs) have recently shown outstanding performance on image classification tasks [14]. In this paper we go one step further and address the problem of object detection using DNNs, that is not only classifying but also precisely localizing objects of various classes. We present a simple and yet powerful formulation of object detection as a regression problem to object bounding box masks. We define a multi-scale inference procedure which is able to produce high-resolution object detections at a low cost by a few network applications. State-of-the-art performance of the approach is shown on Pascal VOC.

This paper addresses the object detection problem
      using deep neural networks (DNNs). Recently DNNs have been successfully
      applied in image recognition and draw much attention from the vision
      community. This paper, however, moves a step forward to an arguably more
      challenging task: object detection. This work formulates detection as a
      regression problem, and uses DNNs to predict binary object masks directly
      from image pixels. A post-processing step of multi-scale refinement is
      used to further improve the detection accuracy. The paper reports
      comparable results to the state-of-the-art deformable part models (DPMs)
      on the VOC 2007 benchmark. To my knowledge, this is the first paper that
      report the detection performance of DNNs on VOC dataset. Pros:
      1. A novel application of DNNs, and the paper gives an initial answer
      to an often discussed question: how DNNs work on object detection? 2.
      Comparable results to the existing state-of-the-arts. Cons:
      1.Some ad-hoc choices without clear justifications/evaluations, such
      as - the choices of splitting the boxes into 4 halves. How did that
      affect the performance compared with using the full box only? Why is this
      splitting better than other arbitrary splittings (e.g. 3x3 grids), any
      insights? - the second step refinement. Fig4 shows that the refinement
      dramatically improves the performance, but refinement step doesn't seem to
      be fundamental different to the first step of detection. I'm not clear
      where the boost is from. I don't see any new information is used. One
      explanation in the paper is that the refinement step provides higher
      resolution masks thus can detect smaller objects. Can't you just train a
      single step DNNs with proper parameters so that the resolution is high
      enough? - The way of producing bounding boxes from the predicted
      binary mask sounds like a hack. 2. This work uses DNNs to make
      separate predictions on if each small cell is in an object or on the
      background. This is similar in spirit to the work of running classifiers
      on image pixels/superpixels to decide segmentations. (e.g. section 5 of
      "Semantic Texton Forests for Image Categorization and Segmentation"
      CVPR08). what do you think will happen if we replace the DNNs with other
      classifiers (e.g. random forest) on small image patches to generate the
      binary masks? It would be nice to have comparison with such a baseline.
      A few questions/suggestions (These are not criticisms): - I'd
      been curious to see more diagnosis on the error cases. Are they the same
      mistakes that DPMs make? (which I guess no). - L343 says that you
      first trained the net for classification to start with good weights and
      later tuned the higher level layers. In the pre-training step, did you
      only use VOC2007 data, or extra data were used? - The poor results of
      sliding window detector (second row in table 1) suggest that DNNs suffer
      from false positives. Any thoughts on improving its ability to prune the
      background patches? - For reported results in Table 1, were there any
      filter/parameter sharing between classes? Typos: L21: extra
      "few" L205: missing the closing parenthesis. L429:
      "course-to-file" -> "coarse-to-fine"


Sensor Selection in High-Dimensional Gaussian Trees with Nuisances
We consider the sensor selection problem on multivariate Gaussian distributions where only a subset of latent variables is of inferential interest. For pairs of vertices connected by a unique path in the graph, we show that there exist decompositions of nonlocal mutual information into local information measures that can be computed efficiently from the output of message passing algorithms. We integrate these decompositions into a computationally efficient greedy selector where the computational expense of quantification can be distributed across nodes in the network. Experimental results demonstrate the comparative efficiency of our algorithms for sensor selection in high-dimensional distributions. We additionally derive an online-computable performance bound based on augmentations of the relevant latent variable set that, when such a valid augmentation exists, is applicable for any distribution with nuisances.

The paper introduces a method to select incrementally
      a subset of features that are informative about a specific relevant
      set of variables. The issue at hand is about being able to be better
      than a generic detector with respect to target variables when these
      are specified, and nuisance nodes exist. A core assumption is
      Gaussianity which allows much of the procedure to work. Finally, an
      enhanced relevance set is introduced to "lift" the original,
      non-submodular process towards a sub-modular one which exhibits
      performance guarantees for greedy sensor selection. Though a
      quite technical paper, I enjoyed reading it. There are lots of
      interesting and - to me - novel ideas combined in the work, the
      construction of the composable warped MI measure, the relation to
      distributed computing, and making the model sub-modular were all
      attractive properties of the work. It is a contentful paper, which I
      found worth the time reading. One potential aspect that the
      reviewer is not sure about is whether the Gaussian scenario is really
      relevant in practice for the type of networks considered here. In
      particular in large networks with, possibly, very simple sensors where
      this approach would be most interesting, Gaussianity is not really a
      default, and the question is how much one would lose when that
      happens. The authors indicate that treatment of non-Gaussianity is
      future work, but a short discussion on the relevance of the results in
      case of non-Gaussian variables (perhaps, as an extreme guiding
      example, one could consider binary variables as thought model) may be
      in place here; it's clear that a full computation is out of the place
      here, but some comments as to what can be expected to change.
      Generally clear, notwithstanding its technicality, there are a
      number of issues that might be improved in the presentation, I will
      list them below: - line 62: Gaussian belief propagation is
      introduced as (BP), but later referred to as GaBP. Please make it
      consistent. - line 181: the use of the indicator function seems to
      miss an argument - the right side of the inequality is a scalar, the
      left side is a function. - lines 262-264: I read and reread
      the argument, but it was to compact. Please rephrase the argument of
      Remark 6 (first three lines of the remark). - line 269: what
      is a pair of *unique* vertices? - line 272: the explanation for
      \zeta is unclear here. How do you compute it? Where does this term
      arise from? - line 289: I did not follow the reasoning why in the
      term W(i;j|A) + \zeta(r,j; G), the \zeta contains the r,j pair? In
      (9), \zeta is computed for the boundary nodes u and v, but here, j
      replaces the boundary node on the opposite side of the path
      emanating from r. What if there is a node, say q, further down the
      path? Surely \zeta will not be unchanged if we replace j by q? So,
      why then, are we allowed to use j? Perhaps it's a simple argument, but
      I didn't see it. - line 322: I did not immediately see the
      operation suggested in footnote 2 - I do not see how the setting to
      -\inf works; what causes the blocking in the chain following
      procedure? - line 399: "running on a fictitious problem" - this
      formulation is unfortunate. Do you mean that you generate a surrogate
      problem ^R (i.e. \hat R) by making S conditionally independent and
      then run your algorithm? This is what I understood. But it may mean
      something different. Please clarify. ** Supplementary Material
      Comments - line 22: "joint potential over the chain" - please define
      the term "joint potential". You do not use jargon in the paper (which
      is good), please keep that style in the Supplementary Material.
      - line 66: "subchain" -> "subchains" - line 67: font of
      I(x_1;x_k) - lines 69-77: The argument is a bit tight and
      difficult to follow. Please reformulate. You have space here.


Solving the multi-way matching problem by permutation synchronization
The problem of matching not just two, but m different sets of objects to each other arises in many contexts, including finding the correspondence between feature points across multiple images in computer vision. At present it is usually solved by matching the sets pairwise, in series. In contrast, we propose a new method, Permutation Synchronization, which finds all the matchings jointly, in one shot, via a relaxation to eigenvector decomposition. The resulting algorithm is both computationally efficient, and, as we demonstrate with theoretical arguments as well as experimental results, much more stable to noise than previous methods.

* Summary This manuscript studies a
      combinatorial optimization problem that is motivated by a number of
      applications within the scope of NIPS. It is defined w.r.t. a finite
      number of finite sets, all of the same cardinality. A feasible solution
      consists in as many bijections as there are pairs of distinct sets. These
      bijections are constrained to be consistent in the following sense: For
      any three sets, A, B, C, if "a" in A is mapped to b in B and b in B is
      mapped to c in C, then "a" needs to be mapped to c. The objective function
      is defined w.r.t. so-called "tentative (noisy)" matchings. Instead of
      solving this combinatorial problem, a relaxation is proposed that can be
      solved efficiently, by computing leading eigenvectors of a matrix. The
      solution of the relaxed problem is shown to be robust to noise and also
      accurate compared to ground truth in a number of practical applications.
      * Strengths - The manuscript addresses a relevant
      combinatorial optimization problem that has several applications within
      the scope of NIPS. - The proposed relaxation of this problem is
      interesting and original. - The experimental results suggest that the
      relaxation may be tight in practice. * Weaknesses - A
      relaxation of an integer program is proposed but not put into perspective.
      Is it tighter than simpler relaxations? How does it compare to the optimal
      solution of small problems that can be solved exactly? Is there a
      guaranteed bound? - The writing can be improved. In its present
      form, the objective function is not easy to understand because the
      notation is convoluted. In order to understand (3), one needs to expand
      the definitions of d, p, tau, and the inner product. As an alternative, I
      suggest that the problem should be written as an integer program that is
      easy to grasp, perhaps in addition to the present formulation. The
      readability of Section 2 can be improved. I suggest that the permutations
      sigma should be defined before the matchings tau and before stating that
      any set of sigmas induces a set of consistent taus. The structure
      of Section 3 can be improved. Statements should be made first informally,
      then formally, e.g. as lemmata, and then proved. * Technical
      questions - I do not understand the introduction of "tentative
      (noisy)" matchings in the objective function. After reading the
      introduction, I would have expected a formulation in terms of weights,
      positive or negative, one for any possible match (between any two elements
      of any two distinct sets). Is the objective function (3) a special case of
      such a general formulation? I think the manuscript can be improved by
      starting with the general formulation and then specializing this
      formulation to the problem under consideration. - Can the
      combinatorial problem not be solved to optimality by means of a
      state-of-the-art branch-and-cut solver, at least in applications where the
      number of elements to be matched is small? If it can be solved to
      optimality, a comparison of run-times as well as an assessment of the
      relaxation gap would be interesting. * Minor remarks - All
      equations should be numbered.


Memory Limited, Streaming PCA
We consider streaming, one-pass principal component analysis (PCA), in the highdimensional regime, with limited memory. Here, p-dimensional samples are presented sequentially, and the goal is to produce the k-dimensional subspace that best approximates these points. Standard algorithms require O(p 2 ) memory; meanwhile no algorithm can do better than O(kp) memory, since this is what the output itself requires. Memory (or storage) complexity is most meaningful when understood in the context of computational and sample complexity. Sample complexity for high-dimensional PCA is typically studied in the setting of the spiked covariance model, where p-dimensional points are generated from a population covariance equal to the identity (white noise) plus a low-dimensional perturbation (the spike) which is the signal to be recovered. It is now well-understood that the spike can be recovered when the number of samples, n, scales proportionally with the dimension, p. Yet, all algorithms that provably achieve this, have memory complexity O(p 2 ). Meanwhile, algorithms with memory-complexity O(kp) do not have provable bounds on sample complexity comparable to p. We present an algorithm that achieves both: it uses O(kp) memory (meaning storage of any kind) and is able to compute the k-dimensional spike with O(p log p) samplecomplexity -the first algorithm of its kind. While our theoretical analysis focuses on the spiked covariance model, our simulations show that our algorithm is successful on much more general models for the data.

Summary: proposes an approach to one-pass SVD
      based on a blocked variant of the power method, which variance is reduced
      within each block of streaming data, and compares to exact batch SVD.
      Figure 1d is offered as an example where the proposed Algo 1 can scale
      to data for which the authors claim to be so large that "traditional batch
      methods" could not be run and reported. Yet there are many existing
      well-known SVD methods which are routinely used for even larger data sets
      than the largest here (sparse 8.2M vectors for 120k dimensions). These
      include the EMPCA (Roweiss 1998) and fast randomized SVD (Haiko et at
      2011), both of which the author's cite. Why were these methods (both very
      simple to implement efficiently even in Matlab, etc.) not reported for
      this data? Especially necessary to compare against is the randomized SVD,
      since it too can be done in one-pass (see Haiko et al); although that
      cited paper discusses the tradeoffs in doing multiple passes -- something
      this paper does not even discuss. The authors say it took "a few hours"
      for Algo 1 to extract the top 7 components. Methods like the randomized
      SVD family of Haiko et al scale linearly in those parameters (n=8.2M and
      d=120k and k=7 and the number of non-zeros of the sparse data) and
      typically run in less than 1 hour for even larger data sets. So,
      demonstrating both the speed and accuracy of the proposed Algo 1 compared
      to the randomized algorithms seems necessary at this point, to establish
      the practical significance of this proposed approach. Even though
      the paper argues that previous approaches do not have "finite sample
      guarantees", this does not excuse them from having to demonstrate that
      their approach is actually better in practice than existing methods. As
      written, this paper basically presents yet another way to do SVD, for
      which there are already many existing methods, including streaming
      one-pass methods (such as the above mentioned randomized SVD).
      Also, the focus on spiked covariance models in the theory parts of
      this paper is confusing. What is the point of proving finite sample
      complexity results for that case, but then failing to compare to existing
      state of the art methods (like EMPCA and randomized SVD) for data (like
      PubMed) which does not fall into the spiked covariance type of data?


Mixed Optimization for Smooth Functions
It is well known that the optimal convergence rate for stochastic optimization of smooth functions is O(1/ √ T ), which is same as stochastic optimization of Lipschitz continuous convex functions. This is in contrast to optimizing smooth functions using full gradients, which yields a convergence rate of O(1/T 2 ). In this work, we consider a new setup for optimizing smooth functions, termed as Mixed Optimization, which allows to access both a stochastic oracle and a full gradient oracle. Our goal is to significantly improve the convergence rate of stochastic optimization of smooth functions by having an additional small number of accesses to the full gradient oracle. We show that, with an O(ln T ) calls to the full gradient oracle and an O(T ) calls to the stochastic oracle, the proposed mixed optimization algorithm is able to achieve an optimization error of O(1/T ).

The paper considers optimization with a "mixed"
      oracle, which provides the algorithm access to the standard stochastic
      oracle as well as a small number of accesses to an exact oracle. In this
      setting, the authors give an algorithm that achieves a convergence rate of
      O(1/T) after O(T) calls to the stochastic oracle and O(log T) class to the
      exact oracle, improving on the known rates of O(1/sqrt(T)) after O(T)
      calls to the stochastic oracle and O(1/T) after O(T) calls to the exact
      oracle. Comments: The paper asks an interesting question,
      and provides an interesting answer to it. The paper has the potential to
      change the way many optimization problems are solved, and is certainly of
      interest to the NIPS community. The first sentence of the
      abstract: "It is well known that the optimal convergence rate for
      stochastic optimization of smooth functions is O(1/sqrt(T))". (This is
      also repeated elsewhere, with a reference to Nemirovski and Yudin's book.)
      As far as I am aware, this bound has never been shown. The lower
      bound has been shown for Lipschitz-continuous functions, but I'm not aware
      of such a lower bound on smooth functions so please provide a citation.
      Indeed, the recent work of Bach and Moulines ["Non-strongly-convex smooth
      stochastic approximation with convergence rate O(1/n)"] gives an algorithm
      for special cases that achieves an O(1/T) rate, indicating that this lower
      bound may not be true. Note that an O(1/T) rate can also be
      achieved in some special cases, such as the one given above or cases where
      the noise goes to zero as the minimizer is approached (as with methods
      that use a growing sample-size). "A small L2 regularizer does NOT
      improve the convergence rate of stochastic optimization." Since
      this paper focuses on the case of smooth optimization, wouldn't adding a
      small L2 regularizer allow one to use the methods of [18,20] to achieve a
      faster (linear) convergence rate? The first bullet point in in the
      introduction should indicate that the gradient is available too.
      Please add to the paper that Definition 1 is equivalent to f'
      being beta-Lipschitz continuous. It is worth adding a sentence to
      the paper pointing out that reducing the amount of regularization over
      time is closely-related to the classic proximal-point algorithm.
      In the conclusion, please comment on whether O(1/T^2) rates could
      be achieved by an accelerated method in the mixed optimization scenario,
      and whether linear convergence rates could be achieved in the
      strongly-convex case. It is worthwhile to add a sentence to the
      paper contrasting the mixed optimization approach with the very
      closely-related approaches that use growing sample-sizes of Friedlander
      and Schmidt ["Hybrid Deterministic-Stochastic Methods for Data Fitting"]
      and Byrd et al. ["Sample size selection in optimization methods for
      machine learning"].


Translating Embeddings for Modeling Multi-relational Data
We consider the problem of embedding entities and relationships of multirelational data in low-dimensional vector spaces. Our objective is to propose a canonical model which is easy to train, contains a reduced number of parameters and can scale up to very large databases. Hence, we propose TransE, a method which models relationships by interpreting them as translations operating on the low-dimensional embeddings of the entities. Despite its simplicity, this assumption proves to be powerful since extensive experiments show that TransE significantly outperforms state-of-the-art methods in link prediction on two knowledge bases. Besides, it can be successfully trained on a large scale data set with 1M entities, 25k relationships and more than 17M training samples.

This paper presents a model of multi-relational data,
      such as the set of facts of the form (subject, predicate, object) that
      comprise the Freebase database. Perhaps the most common use case of such a
      model is the following: given a triple with either the subject or object
      missing, rank all possible completions of that triple. The proposed model
      is energy-based, and thus assigns a score to each possible completion. The
      lower the score, the more likely that triple represents a true fact that
      is typically not already present in the database. In addition to a
      description of the model, the paper presents a training algorithm and
      reports large-scale experimental results on Freebase and other datasets on
      the aforementioned completion task. The essense of the model is to
      embed each entity and relation into a continuous vector space. The
      dimensions of this space have no direct interpretable meaning except that
      entities which are semantically similar (in the sense of participating in
      the same set of facts) will be nearby in the latent space (according to L1
      or L2), as is standard in matrix factorization. The latent representation
      of the tail of a triple is modeled as a translation of the latent
      representation of the head of the triple, with a different learned
      translation vector for each relation. The quality of a proposed latent
      embedding is given by an objective function which is essentially the total
      score of all observed true facts minus the total score of all triples not
      known to be true, plus a margin term. The parameters of the model (a
      latent vector for each entity and relation) are learned via a
      straightforward stochastic gradient descent algorithm from a training set
      of known facts. Many similar latent-embedding models of
      multi-relational data exist in the literature. The main novelty in this
      paper is the restriction that the embedding of tail of a triple be a
      relationship-dependent translation of the embedding of the subject, rather
      than an arbitrary linear transformation. I believe this boils down to the
      assumption that the contribution of each of the features represented by
      each dimension of the latent space to the energy function are independent
      of each other, for a given relationship. As the authors points out, this
      is strictly a special case of of the 'Structured Embeddings' model. SE
      embeds each relationship into a matrix rather than a vector, allowing for
      the possiblity that the transformation represented by the relationship
      between head and tail embeddings is an arbitrary linear transformation.
      The experimental results use the established metrics for this kind
      of model and show impressive state-of-the-art performance on standard
      benchmarks. It seems that the expressivity reduction of this model allows
      for more efficient training and more resilience to overfitting. As these
      benchmarks are standard, I have no serious complaint with the methodology
      here. Some minor comments: It would have been interesting to also see
      results for a task where a missing relationship has to be predicted given
      a head and tail. The 'filtered' dataset concept, while a good innovation
      over the 'raw' dataset, seems superflous to this paper given how close the
      results are between them and since it was not even used for the FB1M
      dataset, which is the largest and perhaps most important dataset the
      authors tested on. The authors claim all experimental results are
      significant (line 302), but do not name the statistical test being used or
      justify the assumptions behind the test. They also do not say how the
      latent dimensionality constant was chosen (268). My main concern
      with this paper is that is fairly light on novelty and is rather more
      incremental than a top-tier conference demands. The model is a simple
      restriction of Structued Embedding, an existing, well-known model:
      relationship embeddings are replaced with vectors instead of matrices, and
      so encode translations in latent space rather than arbitrary linear
      transformations. The learning algorithm is entirely standard stochastic
      gradient descent. The empirical results are standard benchmarks on
      standard datasets. While the restriction is shown to be benefial on these
      tasks, there is somewhat of a lack of in-depth analysis of why. Vague
      claims in lines 71-93 and on 304 ('appropriate design of the model
      according to the data') are made that this model is well-suited to the
      data, but the experiments do not make it clear what is actually helping
      over SE: Is it that the model is more efficiently trainable? Is it the
      margin term in the optimization function? Is it that it inherently
      generalizes better? What exactly is it about these datasets that make
      translation a good model of relations? The authors present each of these
      as hypotheses but do not elaborate. As it stands, I feel this paper is
      presenting a useful idea which could become the core of a good paper, but
      it needs a deeper analysis of why and when this restriction works.
      Some minor comments: * The handling of negative data and the role
      the closed-world assumption is making to the training procedure was
      somewhat unclear to me in 134-148. What exactly is being assumed about the
      truth of facts missing from the database? * On 195, the authors state that
      experiments with the Neural Tensor Model could not be run, but do not give
      a reason. * On 236, they state that a corrupted triple 'would' be ranked
      about the test triplet if the corrupted triple is in fact true, but I
      would think it may or may not be. * The paper only has a single figure,
      which comes at the end and displays results. I think a figure earlier in
      the paper presenting a graphical depiction of the model and its output
      would be useful.