@article{18371, abstract = {We consider the problem of exact and inexact matching of weighted undirected graphs, in which a bijective correspondence is sought to minimize a quadratic weight disagreement. This computationally challenging problem is often relaxed as a convex quadratic program, in which the space of permutations is replaced by the space of doubly stochastic matrices. However, the applicability of such a relaxation is poorly understood. We define a broad class of friendly graphs characterized by an easily verifiable spectral property. We prove that for friendly graphs, the convex relaxation is guaranteed to find the exact isomorphism or certify its inexistence. This result is further extended to approximately isomorphic graphs, for which we develop an explicit bound on the amount of weight disagreement under which the relaxation is guaranteed to find the globally optimal approximate isomorphism. We also show that in many cases, the graph matching problem can be further harmlessly relaxed to a convex quadratic program with only n separable linear equality constraints, which is substantially more efficient than the standard relaxation involving 2n equality and n2 inequality constraints. Finally, we show that our results are still valid for unfriendly graphs if additional information in the form of seeds or attributes is allowed, with the latter satisfying an easy to verify spectral characteristic.}, author = {Aflalo, Yonathan and Bronstein, Alexander and Kimmel, Ron}, issn = {1091-6490}, journal = {Proceedings of the National Academy of Sciences}, number = {10}, pages = {2942--2947}, publisher = {National Academy of Sciences}, title = {{On convex relaxation of graph isomorphism}}, doi = {10.1073/pnas.1401651112}, volume = {112}, year = {2015}, } @inproceedings{1838, abstract = {Synthesis of program parts is particularly useful for concurrent systems. However, most approaches do not support common design tasks, like modifying a single process without having to re-synthesize or verify the whole system. Assume-guarantee synthesis (AGS) provides robustness against modifications of system parts, but thus far has been limited to the perfect information setting. This means that local variables cannot be hidden from other processes, which renders synthesis results cumbersome or even impossible to realize.We resolve this shortcoming by defining AGS under partial information. We analyze the complexity and decidability in different settings, showing that the problem has a high worstcase complexity and is undecidable in many interesting cases. Based on these observations, we present a pragmatic algorithm based on bounded synthesis, and demonstrate its practical applicability on several examples.}, author = {Bloem, Roderick and Chatterjee, Krishnendu and Jacobs, Swen and Könighofer, Robert}, location = {London, United Kingdom}, pages = {517 -- 532}, publisher = {Springer}, title = {{Assume-guarantee synthesis for concurrent reactive programs with partial information}}, doi = {10.1007/978-3-662-46681-0_50}, volume = {9035}, year = {2015}, } @inproceedings{18380, abstract = {This work presents a novel approach for detecting inliers in a given set of correspondences (matches). It does so without explicitly identifying any consensus set, based on a method for inlier rate estimation (IRE). Given such an estimator for the inlier rate, we also present an algorithm that detects a globally optimal transformation. We provide a theoretical analysis of the IRE method using a stochastic generative model on the continuous spaces of matches and transformations. This model allows rigorous investigation of the limits of our IRE method for the case of 2D-translation, further giving bounds and insights for the more general case. Our theoretical analysis is validated empirically and is shown to hold in practice for the more general case of 2D-affinities. In addition, we show that the combined framework works on challenging cases of 2D-homography estimation, with very few and possibly noisy inliers, where RANSAC generally fails.}, author = {Litman, Roee and Korman, Simon and Bronstein, Alexander and Avidan, Shai}, booktitle = {2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)}, isbn = {9781467369640}, issn = {1063-6919}, location = {Boston, MA, United States}, publisher = {IEEE}, title = {{Inverting RANSAC: Global model detection via inlier rate estimation}}, doi = {10.1109/cvpr.2015.7299161}, year = {2015}, } @inproceedings{18387, abstract = {Sparse models in dictionary learning have been successfully applied in a wide variety of machine learning and computer vision problems, and have also recently been of increasing research interest. Another interesting related problem based on a linear equality constraint, namely the sparse null space problem (SNS), first appeared in 1986, and has since inspired results on sparse basis pursuit. In this paper, we investigate the relation between the SNS problem and the analysis dictionary learning problem, and show that the SNS problem plays a central role, and may be utilized to solve dictionary learning problems. Moreover, we propose an efficient algorithm of sparse null space basis pursuit, and extend it to a solution of analysis dictionary learning. Experimental results on numerical synthetic data and real-world data are further presented to validate the performance of our method.}, author = {Bian, Xiao and Krim, Hamid and Bronstein, Alexander and Dai, Liyi}, booktitle = {2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}, issn = {2379-190X}, location = {South Brisbane, QLD, Australia}, publisher = {IEEE}, title = {{Sparse null space basis pursuit and analysis dictionary learning for high-dimensional data analysis}}, doi = {10.1109/icassp.2015.7178678}, year = {2015}, } @inproceedings{1839, abstract = {We present MultiGain, a tool to synthesize strategies for Markov decision processes (MDPs) with multiple mean-payoff objectives. Our models are described in PRISM, and our tool uses the existing interface and simulator of PRISM. Our tool extends PRISM by adding novel algorithms for multiple mean-payoff objectives, and also provides features such as (i) generating strategies and exploring them for simulation, and checking them with respect to other properties; and (ii) generating an approximate Pareto curve for two mean-payoff objectives. In addition, we present a new practical algorithm for the analysis of MDPs with multiple mean-payoff objectives under memoryless strategies.}, author = {Brázdil, Tomáš and Chatterjee, Krishnendu and Forejt, Vojtěch and Kučera, Antonín}, location = {London, United Kingdom}, pages = {181 -- 187}, publisher = {Springer}, title = {{Multigain: A controller synthesis tool for MDPs with multiple mean-payoff objectives}}, doi = {10.1007/978-3-662-46681-0_12}, volume = {9035}, year = {2015}, } @article{1840, abstract = {In this paper, we present a method for reducing a regular, discrete-time Markov chain (DTMC) to another DTMC with a given, typically much smaller number of states. The cost of reduction is defined as the Kullback-Leibler divergence rate between a projection of the original process through a partition function and a DTMC on the correspondingly partitioned state space. Finding the reduced model with minimal cost is computationally expensive, as it requires an exhaustive search among all state space partitions, and an exact evaluation of the reduction cost for each candidate partition. Our approach deals with the latter problem by minimizing an upper bound on the reduction cost instead of minimizing the exact cost. The proposed upper bound is easy to compute and it is tight if the original chain is lumpable with respect to the partition. Then, we express the problem in the form of information bottleneck optimization, and propose using the agglomerative information bottleneck algorithm for searching a suboptimal partition greedily, rather than exhaustively. The theory is illustrated with examples and one application scenario in the context of modeling bio-molecular interactions.}, author = {Geiger, Bernhard and Petrov, Tatjana and Kubin, Gernot and Koeppl, Heinz}, issn = {0018-9286}, journal = {IEEE Transactions on Automatic Control}, number = {4}, pages = {1010 -- 1022}, publisher = {IEEE}, title = {{Optimal Kullback-Leibler aggregation via information bottleneck}}, doi = {10.1109/TAC.2014.2364971}, volume = {60}, year = {2015}, } @inproceedings{18400, abstract = {We propose a method and a prototype imaging system for real-time reconstruction of volumetric piecewise-smooth scattering media. The volume is illuminated by a sequence of structured binary patterns emitted from a fan beam projector, and the scattered light is collected by a two-dimensional sensor, thus creating an under-complete set of compressed measurements. We show a fixed-complexity and latency reconstruction algorithm capable of estimating the scattering coefficients in real-time. We also show a simple greedy algorithm for learning the optimal illumination patterns. Our results demonstrate faithful reconstruction from highly compressed measurements. Furthermore, a method for compressed registration of the measured volume to a known template is presented, showing excellent alignment with just a single projection. Though our prototype system operates in visible light, the presented methodology is suitable for fast x-ray scattering imaging, in particular in real-time vascular medical imaging.}, author = {Menashe, Ohad and Bronstein, Alexander}, booktitle = {2014 IEEE International Conference on Image Processing (ICIP)}, issn = {2381-8549}, location = {Paris, France}, publisher = {IEEE}, title = {{Real-time compressed imaging of scattering volumes}}, doi = {10.1109/icip.2014.7025264}, year = {2015}, } @inproceedings{18401, abstract = {Intel's newly-announced low-cost RealSense 3D camera claims significantly better precision than other currently available low-cost platforms and is expected to become ubiquitous in laptops and mobile devices starting this year. In this paper, we demonstrate for the first time that the RealSense camera can be easily converted into a real low-cost gaze tracker. Gaze has become increasingly relevant as an input for human-computer interaction due to its association with attention. It is also critical in clinical mental health diagnosis. We present a novel 3D gaze and fixation tracker based on the eye surface geometry captured with the RealSense 3D camera. First, eye surface 3D point clouds are segmented to extract the pupil center and iris using registered infrared images. With non-ellipsoid eye surface and single fixation point assumptions, pupil centers and iris normal vectors are used to first estimate gaze (for each eye), and then a single fixation point for both eyes simultaneously using a RANSAC-based approach. With a simple learned bias field correction model, the fixation tracker demonstrates mean error of approximately 1 cm at 20-30 cm, which is sufficiently adequate for gaze and fixation tracking in human-computer interaction and mental health diagnosis applications.}, author = {Draelos, Mark and Qiu, Qiang and Bronstein, Alexander and Sapiro, Guillermo}, booktitle = {2015 IEEE International Conference on Image Processing (ICIP)}, location = {Quebec City, QC, Canada}, publisher = {IEEE}, title = {{Intel realsense = Real low cost gaze}}, doi = {10.1109/icip.2015.7351256}, year = {2015}, } @article{1841, abstract = {We propose a new family of message passing techniques for MAP estimation in graphical models which we call Sequential Reweighted Message Passing (SRMP). Special cases include well-known techniques such as Min-Sum Diffusion (MSD) and a faster Sequential Tree-Reweighted Message Passing (TRW-S). Importantly, our derivation is simpler than the original derivation of TRW-S, and does not involve a decomposition into trees. This allows easy generalizations. The new family of algorithms can be viewed as a generalization of TRW-S from pairwise to higher-order graphical models. We test SRMP on several real-world problems with promising results.}, author = {Kolmogorov, Vladimir}, journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence}, number = {5}, pages = {919 -- 930}, publisher = {IEEE}, title = {{A new look at reweighted message passing}}, doi = {10.1109/TPAMI.2014.2363465}, volume = {37}, year = {2015}, } @article{18415, abstract = {Parsimony, including sparsity and low rank, has been shown to successfully model data in numerous machine learning and signal processing tasks. Traditionally, such modeling approaches rely on an iterative algorithm that minimizes an objective function with parsimony-promoting terms. The inherently sequential structure and data-dependent complexity and latency of iterative optimization constitute a major limitation in many applications requiring real-time performance or involving large-scale data. Another limitation encountered by these modeling techniques is the difficulty of their inclusion in discriminative learning scenarios. In this work, we propose to move the emphasis from the model to the pursuit algorithm, and develop a process-centric view of parsimonious modeling, in which a learned deterministic fixed-complexity pursuit process is used in lieu of iterative optimization. We show a principled way to construct learnable pursuit process architectures for structured sparse and robust low rank models, derived from the iteration of proximal descent algorithms. These architectures learn to approximate the exact parsimonious representation at a fraction of the complexity of the standard optimization methods. We also show that appropriate training regimes allow to naturally extend parsimonious models to discriminative settings. State-of-the-art results are demonstrated on several challenging problems in image and audio processing with several orders of magnitude speed-up compared to the exact optimization algorithms.}, author = {Sprechmann, P. and Bronstein, Alexander and Sapiro, G.}, issn = {1939-3539}, journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence}, number = {9}, pages = {1821--1833}, publisher = {IEEE}, title = {{Learning efficient sparse and low rank models}}, doi = {10.1109/tpami.2015.2392779}, volume = {37}, year = {2015}, } @article{18416, abstract = {We construct an extension of spectral and diffusion geometry to multiple modalities through simultaneous diagonalization of Laplacian matrices. This naturally extends classical data analysis tools based on spectral geometry, such as diffusion maps and spectral clustering. We provide several synthetic and real examples of manifold learning, object classification, and clustering, showing that the joint spectral geometry better captures the inherent structure of multi-modal data. We also show the relation of many previous approaches for multimodal manifold analysis to our framework.}, author = {Eynard, Davide and Kovnatsky, Artiom and Bronstein, Michael M. and Glashoff, Klaus and Bronstein, Alexander}, issn = {1939-3539}, journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence}, number = {12}, pages = {2505--2517}, publisher = {IEEE}, title = {{Multimodal manifold snalysis by simultaneous diagonalization of Laplacians}}, doi = {10.1109/tpami.2015.2408348}, volume = {37}, year = {2015}, } @article{18424, abstract = {We present a fast algorithm for global rigid symmetry detection with approximation guarantees. The algorithm is guaranteed to find the best approximate symmetry of a given shape, to within a user-specified threshold, with very high probability. Our method uses a carefully designed sampling of the transformation space, where each transformation is efficiently evaluated using a sublinear algorithm. We prove that the density of the sampling depends on the total variation of the shape, allowing us to derive formal bounds on the algorithm's complexity and approximation quality. We further investigate different volumetric shape representations (in the form of truncated distance transforms), and in such a way control the total variation of the shape and hence the sampling density and the runtime of the algorithm. A comprehensive set of experiments assesses the proposed method, including an evaluation on the eight categories of the COSEG data set. This is the first large-scale evaluation of any symmetry detection technique that we are aware of.}, author = {Korman, Simon and Litman, Roee and Avidan, Shai and Bronstein, Alexander}, issn = {1467-8659}, journal = {Computer Graphics Forum}, number = {1}, pages = {2--13}, publisher = {Wiley}, title = {{Probably approximately symmetric: Fast rigid symmetry detection with global guarantees}}, doi = {10.1111/cgf.12454}, volume = {34}, year = {2015}, } @article{18425, abstract = {The recent introduction of 3D shape analysis frameworks able to quantify the deformation of a shape into another in terms of the variation of real functions yields a new interpretation of the 3D shape similarity assessment and opens new perspectives. Indeed, while the classical approaches to similarity mainly quantify it as a numerical score, map-based methods also define (dense) shape correspondences. After presenting in detail the theoretical foundations underlying these approaches, we classify them by looking at their most salient features, including the kind of structure and invariance properties they capture, as well as the distances and the output modalities according to which the similarity between shapes is assessed and returned. We also review the usage of these methods in a number of 3D shape application domains, ranging from matching and retrieval to annotation and segmentation. Finally, the most promising directions for future research developments are discussed.}, author = {Biasotti, S. and Cerri, A. and Bronstein, Alexander and Bronstein, M.}, issn = {1467-8659}, journal = {Computer Graphics Forum}, number = {6}, pages = {87--119}, publisher = {Wiley}, title = {{Recent trends, applications, and perspectives in 3D shape similarity assessment}}, doi = {10.1111/cgf.12734}, volume = {35}, year = {2015}, } @article{18436, author = {Haim, Harel and Bronstein, Alexander and Marom, Emanuel}, issn = {1094-4087}, journal = {Optics Express}, number = {19}, pages = {24547 -- 24556}, publisher = {Optica Publishing Group}, title = {{Computational multi-focus imaging combining sparse model with color dependent phase mask}}, doi = {10.1364/oe.23.024547}, volume = {23}, year = {2015}, } @inproceedings{18439, abstract = {Intel’s newly-announced low-cost and high precision RealSense 3D (RGBD) camera is becoming ubiquitous in laptops and mobile devices starting this year, opening the door for new applications in the mobile health arena. In this paper, we demonstrate how the Intel RealSense 3D camera can be used for low-cost gaze tracking and passive pulse rate estimation. We develop a novel 3D gaze and fixation tracker based on the eye surface geometry as well as an illumination invariant pulse rate estimation method using near-infrared images captured with RealSense. We achieve a mean error of 1cm at 20 − 30cm for the gaze tracker and 2.26bpm (beats per minute) for pulse estimation, which is adequate in many medical applications, demonstrating the great potential of novel consumer-grade RGBD technology in mobile health.}, author = {Qiu, Qiang and Chang, Zhuoqing and Draelos, Mark and Chen, Jie and Bronstein, Alexander and Sapiro, Guillermo}, booktitle = {Proceedings of the 5th EAI International Conference on Wireless Mobile Communication and Healthcare}, isbn = {9781631900884}, location = {London, United Kingdom}, publisher = {ICST}, title = {{Low-cost gaze and pulse analysis using realsense}}, doi = {10.4108/eai.14-10-2015.2261657}, year = {2015}, } @article{1508, abstract = {We consider generalized Wigner ensembles and general β-ensembles with analytic potentials for any β ≥ 1. The recent universality results in particular assert that the local averages of consecutive eigenvalue gaps in the bulk of the spectrum are universal in the sense that they coincide with those of the corresponding Gaussian β-ensembles. In this article, we show that local averaging is not necessary for this result, i.e. we prove that the single gap distributions in the bulk are universal. In fact, with an additional step, our result can be extended to any C4(ℝ) potential.}, author = {Erdös, László and Yau, Horng}, journal = {Journal of the European Mathematical Society}, number = {8}, pages = {1927 -- 2036}, publisher = {EMS Press}, title = {{Gap universality of generalized Wigner and β ensembles}}, doi = {10.4171/JEMS/548}, volume = {17}, year = {2015}, } @article{1832, abstract = {Linearizability of concurrent data structures is usually proved by monolithic simulation arguments relying on the identification of the so-called linearization points. Regrettably, such proofs, whether manual or automatic, are often complicated and scale poorly to advanced non-blocking concurrency patterns, such as helping and optimistic updates. In response, we propose a more modular way of checking linearizability of concurrent queue algorithms that does not involve identifying linearization points. We reduce the task of proving linearizability with respect to the queue specification to establishing four basic properties, each of which can be proved independently by simpler arguments. As a demonstration of our approach, we verify the Herlihy and Wing queue, an algorithm that is challenging to verify by a simulation proof. }, author = {Chakraborty, Soham and Henzinger, Thomas A and Sezgin, Ali and Vafeiadis, Viktor}, journal = {Logical Methods in Computer Science}, number = {1}, publisher = {International Federation for Computational Logic}, title = {{Aspect-oriented linearizability proofs}}, doi = {10.2168/LMCS-11(1:20)2015}, volume = {11}, year = {2015}, } @inproceedings{1610, abstract = {The edit distance between two words w1, w2 is the minimal number of word operations (letter insertions, deletions, and substitutions) necessary to transform w1 to w2. The edit distance generalizes to languages L1,L2, where the edit distance is the minimal number k such that for every word from L1 there exists a word in L2 with edit distance at most k. We study the edit distance computation problem between pushdown automata and their subclasses. The problem of computing edit distance to pushdown automata is undecidable, and in practice, the interesting question is to compute the edit distance from a pushdown automaton (the implementation, a standard model for programs with recursion) to a regular language (the specification). In this work, we present a complete picture of decidability and complexity for deciding whether, for a given threshold k, the edit distance from a pushdown automaton to a finite automaton is at most k.}, author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Ibsen-Jensen, Rasmus and Otop, Jan}, booktitle = {42nd International Colloquium on Automata, Languages, and Programming}, isbn = {978-3-662-47665-9}, location = {Kyoto, Japan}, number = {Part II}, pages = {121 -- 133}, publisher = {Springer Nature}, title = {{Edit distance for pushdown automata}}, doi = {10.1007/978-3-662-47666-6_10}, volume = {9135}, year = {2015}, } @inproceedings{1657, abstract = {We consider Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) objectives. There exist two different views: (i) ~the expectation semantics, where the goal is to optimize the expected mean-payoff objective, and (ii) ~the satisfaction semantics, where the goal is to maximize the probability of runs such that the mean-payoff value stays above a given vector. We consider optimization with respect to both objectives at once, thus unifying the existing semantics. Precisely, the goal is to optimize the expectation while ensuring the satisfaction constraint. Our problem captures the notion of optimization with respect to strategies that are risk-averse (i.e., Ensure certain probabilistic guarantee). Our main results are as follows: First, we present algorithms for the decision problems, which are always polynomial in the size of the MDP. We also show that an approximation of the Pareto curve can be computed in time polynomial in the size of the MDP, and the approximation factor, but exponential in the number of dimensions. Second, we present a complete characterization of the strategy complexity (in terms of memory bounds and randomization) required to solve our problem. }, author = {Chatterjee, Krishnendu and Komárková, Zuzana and Kretinsky, Jan}, location = {Kyoto, Japan}, pages = {244 -- 256}, publisher = {IEEE}, title = {{Unifying two views on multiple mean-payoff objectives in Markov decision processes}}, doi = {10.1109/LICS.2015.32}, year = {2015}, } @misc{5435, abstract = {We consider Markov decision processes (MDPs) with multiple limit-average (or mean-payoff) objectives. There have been two different views: (i) the expectation semantics, where the goal is to optimize the expected mean-payoff objective, and (ii) the satisfaction semantics, where the goal is to maximize the probability of runs such that the mean-payoff value stays above a given vector. We consider the problem where the goal is to optimize the expectation under the constraint that the satisfaction semantics is ensured, and thus consider a generalization that unifies the existing semantics. Our problem captures the notion of optimization with respect to strategies that are risk-averse (i.e., ensures certain probabilistic guarantee). Our main results are algorithms for the decision problem which are always polynomial in the size of the MDP. We also show that an approximation of the Pareto-curve can be computed in time polynomial in the size of the MDP, and the approximation factor, but exponential in the number of dimensions. Finally, we present a complete characterization of the strategy complexity (in terms of memory bounds and randomization) required to solve our problem.}, author = {Chatterjee, Krishnendu and Komarkova, Zuzana and Kretinsky, Jan}, issn = {2664-1690}, pages = {51}, publisher = {IST Austria}, title = {{Unifying two views on multiple mean-payoff objectives in Markov decision processes}}, doi = {10.15479/AT:IST-2015-318-v2-1}, year = {2015}, }