Abstract The task of object viewpoint estimation has been a challenge since the early days of computer vision. To estimate the viewpoint (or pose) of an object, people have mostly looked at object intrinsic features, such as shape or appearance. Surprisingly, informative features provided by other, extrinsic elements in the scene, have so far mostly been ignored. At the same time, contextual cues have been proven to be of great benefit for related tasks such as object detection or action recognition. In this paper, we explore how information from other objects in the scene can be exploited for viewpoint estimation. In particular, we look at object configurations by following a relational neighbor-based approach for reasoning about object relations. We show that, starting from noisy object detections and viewpoint estimates, exploiting the estimated viewpoint and location of other objects in the scene can lead to improved object viewpoint predictions. Experiments on the KITTI dataset demonstrate that object configurations can indeed be used as a complementary cue to appearance-based viewpoint estimation. Our analysis reveals that the proposed context-based method can improve object viewpoint estimation by reducing specific types of viewpoint estimation errors commonly made by methods that only consider local information. Moreover, considering contextual information produces superior performance in scenes where a high number of object instances occur. Finally, our results suggest that, following a cautious relational neighbor formulation brings improvements over its aggressive counterpart for the task of object viewpoint estimation.
To some extent, the proposed method bears some resemblance to the message-passing algorithms @cite_64 commonly used for inference in graphical models. In the same fashion as the message-passing algorithms, we start from input elements for which information is available, in this case the objects that define the nodes in the graph. Then, we iteratively select a target node, in our case each of the object hypotheses to be re-estimated, and each of the neighboring nodes (objects) casts a vote (or sends a message) indicating the level of agreement they have with the target node taking a specific state. Furthermore, similar to message-passing algorithms, for the case of loopy graphs the proposed method aims at providing an approximate solution to the problem at a relative low computation time. Different from message-passing algorithms, which operate over a graph defined over two types of nodes (variable nodes and check nodes), our method only considers variable nodes.
@cite_64
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We consider a message passing model with n nodes, each connected to all other nodes by a link that can deliver a message of B bits in a time unit (typically, B = O(log n)). We assume that each node has an input of size L bits (typically, L = O(n log n)) and the nodes cooperate in order to compute some function (i.e., perform a distributed task). We are interested in the number of rounds required to compute the function. We give two results regarding this model. First, we show that most boolean functions require ‸ L B ‹ − 1 rounds to compute deterministically, and that even if we consider randomized protocols that are allowed to err, the expected running time remains Ω(L B) for most boolean function. Second, trying to find explicit functions that require superconstant time, we consider the pointer chasing problem. In this problem, each node i is given an array Ai of length n whose entries are in [n], and the task is to find, for any j ∈ [n], the value of An-1[An-2[. . .A0[j] . . .]]. We give a deterministi... Gaussian and quadratic approximations of message passing algorithms on graphs have attracted considerable recent attention due to their computational simplicity, analytic tractability, and wide applicability in optimization and statistical inference problems. This paper presents a systematic framework for incorporating such approximate message passing (AMP) methods in general graphical models. The key concept is a partition of dependencies of a general graphical model into strong and weak edges, with the weak edges representing small, linearizable couplings of variables. AMP approximations based on the central limit theorem can be readily applied to aggregates of many weak edges and integrated with standard message passing updates on the strong edges. The resulting algorithm, which we call hybrid generalized approximate message passing (HyGAMP), can yield significantly simpler implementations of sum-product and max-sum loopy belief propagation. By varying the partition of strong and weak edges, a performance-complexity tradeoff can be achieved. Group sparsity and multinomial logistic regression problems are studied as examples of the proposed methodology. We consider the estimation of an i.i.d. random vector observed through a linear transform followed by a componentwise, probabilistic (possibly nonlinear) measurement channel. A novel algorithm, called generalized approximate message passing (GAMP), is presented that provides computationally efficient approximate implementations of max-sum and sum-problem loopy belief propagation for such problems. The algorithm extends earlier approximate message passing methods to incorporate arbitrary distributions on both the input and output of the transform and can be applied to a wide range of problems in nonlinear compressed sensing and learning. Extending an analysis by Bayati and Montanari, we argue that the asymptotic componentwise behavior of the GAMP method under large, i.i.d. Gaussian transforms is described by a simple set of state evolution (SE) equations. From the SE equations, one can predict the asymptotic value of virtually any componentwise performance metric including mean-squared error or detection accuracy. Moreover, the analysis is valid for arbitrary input and output distributions, even when the corresponding optimization problems are non-convex. The results match predictions by Guo and Wang for relaxed belief propagation on large sparse matrices and, in certain instances, also agree with the optimal performance predicted by the replica method. The GAMP methodology thus provides a computationally efficient methodology, applicable to a large class of non-Gaussian estimation problems with precise asymptotic performance guarantees. In this paper we present a Bayesian framework for parsing images into their constituent visual patterns. The parsing algorithm optimizes the posterior probability and outputs a scene representation as a "parsing graph", in a spirit similar to parsing sentences in speech and natural language. The algorithm constructs the parsing graph and re-configures it dynamically using a set of moves, which are mostly reversible Markov chain jumps. This computational framework integrates two popular inference approaches--generative (top-down) methods and discriminative (bottom-up) methods. The former formulates the posterior probability in terms of generative models for images defined by likelihood functions and priors. The latter computes discriminative probabilities based on a sequence (cascade) of bottom-up tests filters. In our Markov chain algorithm design, the posterior probability, defined by the generative models, is the invariant (target) probability for the Markov chain, and the discriminative probabilities are used to construct proposal probabilities to drive the Markov chain. Intuitively, the bottom-up discriminative probabilities activate top-down generative models. In this paper, we focus on two types of visual patterns--generic visual patterns, such as texture and shading, and object patterns including human faces and text. These types of patterns compete and cooperate to explain the image and so image parsing unifies image segmentation, object detection, and recognition (if we use generic visual patterns only then image parsing will correspond to image segmentation (Tu and Zhu, 2002. IEEE Trans. PAMI, 24(5):657--673). We illustrate our algorithm on natural images of complex city scenes and show examples where image segmentation can be improved by allowing object specific knowledge to disambiguate low-level segmentation cues, and conversely where object detection can be improved by using generic visual patterns to explain away shadows and occlusions. We propose a graphical model for representing networks of stochastic processes, the minimal generative model graph. It is based on reduced factorizations of the joint distribution over time. We show that under appropriate conditions, it is unique and consistent with another type of graphical model, the directed information graph, which is based on a generalization of Granger causality. We demonstrate how directed information quantifies Granger causality in a particular sequential prediction setting. We also develop efficient methods to estimate the topological structure from data that obviate estimating the joint statistics. One algorithm assumes upper bounds on the degrees and uses the minimal dimension statistics necessary. In the event that the upper bounds are not valid, the resulting graph is nonetheless an optimal approximation in terms of Kullback-Leibler (KL) divergence. Another algorithm uses near-minimal dimension statistics when no bounds are known, but the distribution satisfies a certain criterion. Analogous to how structure learning algorithms for undirected graphical models use mutual information estimates, these algorithms use directed information estimates. We characterize the sample-complexity of two plug-in directed information estimators and obtain confidence intervals. For the setting when point estimates are unreliable, we propose an algorithm that uses confidence intervals to identify the best approximation that is robust to estimation error. Last, we demonstrate the effectiveness of the proposed algorithms through the analysis of both synthetic data and real data from the Twitter network. In the latter case, we identify which news sources influence users in the network by merely analyzing tweet times. Neural message passing algorithms for semi-supervised classification on graphs have recently achieved great success. However, for classifying a node these methods only consider nodes that are a few propagation steps away and the size of this utilized neighborhood is hard to extend. In this paper, we use the relationship between graph convolutional networks (GCN) and PageRank to derive an improved propagation scheme based on personalized PageRank. We utilize this propagation procedure to construct a simple model, personalized propagation of neural predictions (PPNP), and its fast approximation, APPNP. Our model's training time is on par or faster and its number of parameters on par or lower than previous models. It leverages a large, adjustable neighborhood for classification and can be easily combined with any neural network. We show that this model outperforms several recently proposed methods for semi-supervised classification in the most thorough study done so far for GCN-like models. Our implementation is available online. This paper presents two efficient flooding algorithms based on 1-hop neighbor information. In the first part of the paper, we consider sender-based flooding algorithms, specifically the algorithm proposed by In their paper, propose a sender-based flooding algorithm that can achieve local optimality by selecting the minimum number of forwarding nodes in the lowest computational time complexity O(n logn), where n is the number of neighbors. We show that this optimality only holds for a subclass of sender-based algorithms. We propose an efficient sender-based flooding algorithm based on 1-hop neighbor information that reduces the time complexity of computing forwarding nodes to O(n). In Liu's algorithm, n nodes are selected to forward the message in the worst case, whereas in our proposed algorithm, the number of forwarding nodes in the worst case is 11. In the second part of the paper we propose a simple and highly efficient receiver-based flooding algorithm. When nodes are uniformly distributed, we prove that the probability of two neighbor nodes broadcasting the same messageneighbor nodes broadcasting the same message exponentially decreases when the distance between them decreases or when the node density increases. The analytical results are confirmed using simulation. Motivated by the need to understand the algorithmic foundations of distributed large-scale graph computations, we study some fundamental graph problems in a message-passing model for distributed computing where @math machines jointly perform computations on graphs with @math nodes (typically, @math ). The input graph is assumed to be initially randomly partitioned among the @math machines. Communication is point-to-point, and the goal is to minimize the number of communication rounds of the computation. We present (almost) tight bounds for the round complexity of two fundamental graph problems, namely PageRank computation and triangle enumeration. Our tight lower bounds, a main contribution of the paper, are established through an information-theoretic approach that relates the round complexity to the minimal amount of information required by machines for correctly solving a problem. Our approach is generic and might be useful in showing lower bounds in the context of similar problems and similar models. We show a lower bound of @math rounds for computing the PageRank. (Notation @math hides a @math factor.) We also present a simple distributed algorithm that computes the PageRank of all the nodes of a graph in @math rounds (notation @math hides a @math factor and an additive @math term). For triangle enumeration, we show a lower bound of @math rounds, where @math is the number of edges of the graph. Our result implies a lower bound of @math for the congested clique, which is tight up to logarithmic factors. We also present a distributed algorithm that enumerates all the triangles of a graph in @math rounds. In this paper we study gossip based information spreading with bounded message sizes. We use algebraic gossip to disseminate k distinct messages to all n nodes in a network. For arbitrary networks we provide a new upper bound for uniform algebraic gossip of O((k + log n + D)Δ) rounds with high probability, where D and Δ are the diameter and the maximum degree in the network, respectively. For many topologies and selections of k this bound improves previous results, in particular, for graphs with a constant maximum degree it implies that uniform gossip is order optimal and the stopping time is Θ(k + D). To eliminate the factor of Δ from the upper bound we propose a non-uniform gossip protocol, TAG, which is based on algebraic gossip and an arbitrary spanning tree protocol S. The stopping time of TAG is O(k+ log n + d(S) + t(S)), where t(S) is the stopping time of the spanning tree protocol, and d(S) is the diameter of the spanning tree. We provide two general cases in which this bound leads to an order optimal protocol. The first is for k=Ω(n), where, using a simple gossip broadcast protocol that creates a spanning tree in at most linear time, we show that TAG finishes after Θ(n) rounds for any graph. The second uses a sophisticated, recent gossip protocol to build a fast spanning tree on graphs with large weak conductance. In turn, this leads to the optimally of TAG on these graphs for k=Ω(polylog(n)). The technique used in our proofs relies on queuing theory, which is an interesting approach that can be useful in future gossip analysis. Graphical models (e.g., Bayesian and constraint networks, influence diagrams, and Markov decision processes) have become a central paradigm for knowledge representation and reasoning in both artificial intelligence and computer science in general. These models are used to perform many reasoning tasks, such as scheduling, planning and learning, diagnosis and prediction, design, hardware and software verification, and bioinformatics. These problems can be stated as the formal tasks of constraint satisfaction and satisfiability, combinatorial optimization, and probabilistic inference. It is well known that the tasks are computationally hard, but research during the past three decades has yielded a variety of principles and techniques that significantly advanced the state of the art. In this book we provide comprehensive coverage of the primary exact algorithms for reasoning with such models. The main feature exploited by the algorithms is the model's graph. We present inference-based, message-passing schemes (e.g., variable-elimination) and search-based, conditioning schemes (e.g., cycle-cutset conditioning and AND OR search). Each class possesses distinguished characteristics and in particular has different time vs. space behavior. We emphasize the dependence of both schemes on few graph parameters such as the treewidth, cycle-cutset, and (the pseudo-tree) height. We believe the principles outlined here would serve well in moving forward to approximation and anytime-based schemes. The target audience of this book is researchers and students in the artificial intelligence and machine learning area, and beyond. Table of Contents: Preface Introduction What are Graphical Models Inference: Bucket Elimination for Deterministic Networks Inference: Bucket Elimination for Probabilistic Networks Tree-Clustering Schemes AND OR Search Spaces and Algorithms for Graphical Models Combining Search and Inference: Trading Space for Time Conclusion Bibliography Author's Biography Given a metric space G on n nodes, with a start node r and deadlines D(v) for each vertex v, we consider the Deadline-TSP problem of finding a path starting at r that visits as many nodes as possible by their deadlines. We also consider the more general Vehicle Routing with Time-Windows problem, in which each node v also has a release-time R(v) and the goal is to visit as many nodes as possible within their "time-windows" [R(v),D(v)]. No good approximations were known previously for these problems on general metric spaces. We give an O(logn) approximation algorithm for Deadline-TSP, and extend this algorithm to an O(log2n) approximation for the Time-Window problem. We also give a bicriteria approximation algorithm for both problems: Given an e>0, our algorithm produces a (1 e) approximation, while exceeding the deadlines by a factor of 1+e. We use as a subroutine for these results a constant-factor approximation that we develop for a generalization of the orienteering problem in which both the start and the end nodes of the path are fixed. In the process, we give a 3-approximation to the orienteering problem, improving on the previously best known 4-approximation of [6]. In real-world and online social networks, individuals receive and transmit information in real time. Cascading information transmissions (e.g. phone calls, text messages, social media posts) may be understood as a realization of a diffusion process operating on the network, and its branching path can be represented by a directed tree. The process only traverses and thus reveals a limited portion of the edges. The network reconstruction inference problem is to infer the unrevealed connections. Most existing approaches derive a likelihood and attempt to find the network topology maximizing the likelihood, a problem that is highly intractable. In this paper, we focus on the network reconstruction problem for a broad class of real-world diffusion processes, exemplified by a network diffusion scheme called respondent-driven sampling (RDS). We prove that under realistic and general models of network diffusion, the posterior distribution of an observed RDS realization is a Bayesian log-submodular model.We then propose VINE (Variational Inference for Network rEconstruction), a novel, accurate, and computationally efficient variational inference algorithm, for the network reconstruction problem under this model. Crucially, we do not assume any particular probabilistic model for the underlying network. VINE recovers any connected graph with high accuracy as shown by our experimental results on real-life networks. We consider distributed plurality consensus in a complete graph of size @math with @math initial opinions. We design an efficient and simple protocol in the asynchronous communication model that ensures that all nodes eventually agree on the initially most frequent opinion. In this model, each node is equipped with a random Poisson clock with parameter @math . Whenever a node's clock ticks, it samples some neighbors, uniformly at random and with replacement, and adjusts its opinion according to the sample. A prominent example is the so-called two-choices algorithm in the synchronous model, where in each round, every node chooses two neighbors uniformly at random, and if the two sampled opinions coincide, then that opinion is adopted. This protocol is very efficient and well-studied when @math . If @math for some small @math , we show that it converges to the initial plurality opinion within @math rounds, w.h.p., as long as the initial difference between the largest and second largest opinion is @math . On the other side, we show that there are cases in which @math rounds are needed, w.h.p. One can beat this lower bound in the synchronous model by combining the two-choices protocol with randomized broadcasting. Our main contribution is a non-trivial adaptation of this approach to the asynchronous model. If the support of the most frequent opinion is at least @math times that of the second-most frequent one and @math , then our protocol achieves the best possible run time of @math , w.h.p. We relax full synchronicity by allowing @math nodes to be poorly synchronized, and the well synchronized nodes are only required to be within a certain time difference from one another. We enforce this synchronicity by introducing a novel gadget into the protocol. Given a network represented by a graph @math G=V,E, we consider a dynamical process of influence diffusion in G that evolves as follows: Initially only the nodes of a given @math S⊆V are influenced; subsequently, at each round, the set of influenced nodes is augmented by all the nodes in the network that have a sufficiently large number of already influenced neighbors. The question is to determine a small subset of nodes Sa target set that can influence the whole network. This is a widely studied problem that abstracts many phenomena in the social, economic, biological, and physical sciences. It is known [6] that the above optimization problem is hard to approximate within a factor of @math 2log1-∈|V|, for any @math ∈>0. In this paper, we present a fast and surprisingly simple algorithm that exhibits the following features: 1 when applied to trees, cycles, or complete graphs, it always produces an optimal solution i.e., a minimum size target set; 2 when applied to arbitrary networks, it always produces a solution of cardinality matching the upper bound given in [1], and proved therein by means of the probabilistic method; 3 when applied to real-life networks, it always produces solutions that substantially outperform the ones obtained by previously published algorithms for which no proof of optimality or performance guarantee is known in any class of graphs. We consider broadcasting in radio networks, modeled as undirected graphs, whose nodes know only their own label and labels of their neighbors. In every step every node acts either as a transmitter or as a receiver. A node acting as a transmitter sends a message which can potentially reach all of its neighbors. A node acting as a receiver in a given step gets a message if and only if exactly one of its neighbors transmits in this step. Bar-Yehuda, Goldreich, and Itai [J. Comput. System Sci., 45 (1992), pp. 104--126] considered broadcasting in this model. They claimed a linear lower bound on the time of deterministic broadcasting in such radio networks of diameter 3. This claim turns out to be incorrect in this model (although it is valid in a more pessimistic model [R. Bar-Yehuda, O. Goldreich, and A. Itai, Errata Regarding "On the time complexity of broadcast in radio networks: An exponential gap between determinism and randomization," http: www.wisdom.weizmann.ac.il mathusers oded p .html, 2002]). We construct an algorithm that broadcasts in logarithmic time on all graphs from the Bar-Yehuda, Goldreich, and Itai paper (BGI). Moreover, we show how to broadcast in sublinear time on all n-node graphs of diameter @math . On the other hand, we construct a class of graphs of diameter 4, such that every broadcasting algorithm requires time @math on these graphs. In view of the randomized algorithm from BGI, running in expected time @math on all @math -node graphs of diameter D (cf. also a recent @math -time algorithm from [D. Kowalski and A. Pelc, Proceedings of the 22nd Annual ACM Symposium on Principles of Distributed Computing, Boston, 2003, pp. 73--82; A. Czumaj and W. Rytter, Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science, Cambridge, MA, 2003, pp. 492--501]), our lower bound gives the first correct proof of an exponential gap between determinism and randomization in the time of radio broadcasting, under the considered model of radio communication. We consider the problem of estimating a rank-one matrix in Gaussian noise under a probabilistic model for the left and right factors of the matrix. The probabilistic model can impose constraints on the factors including sparsity and positivity that arise commonly in learning problems. We propose a simple iterative procedure that reduces the problem to a sequence of scalar estimation computations. The method is similar to approximate message passing techniques based on Gaussian approximations of loopy belief propagation that have been used recently in compressed sensing. Leveraging analysis methods by Bayati and Montanari, we show that the asymptotic behavior of the estimates from the proposed iterative procedure is described by a simple scalar equivalent model, where the distribution of the estimates is identical to certain scalar estimates of the variables in Gaussian noise. Moreover, the effective Gaussian noise level is described by a set of state evolution equations. The proposed method thus provides a computationally simple and general method for rank-one estimation problems with a precise analysis in certain high-dimensional settings. Given a set of plausible detections, detected at each time instant independently, we investigate how to associate them across time. This is done by propagating labels on a set of graphs that capture how the spatio-temporal and the appearance cues promote the assignment of identical or distinct labels to a pair of nodes. The graph construction is driven by the locally linear embedding (LLE) of either the spatio-temporal or the appearance features associated to the detections. Interestingly, the neighborhood of a node in each appearance graph is defined to include all nodes for which the appearance feature is available (except the ones that coexist at the same time). This allows to connect the nodes that share the same appearance even if they are temporally distant, which gives our framework the uncommon ability to exploit the appearance features that are available only sporadically along the sequence of detections. Once the graphs have been defined, the multi-object tracking is formulated as the problem of finding a label assignment that is consistent with the constraints captured by each of the graphs. This results into a difference of convex program that can be efficiently solved. Experiments are performed on a basketball and several well-known pedestrian datasets in order to validate the effectiveness of the proposed solution. In this paper, we propose an efficient method to detect the underlying structures in data. The same as RANSAC, we randomly sample MSSs (minimal size samples) and generate hypotheses. Instead of analyzing each hypothesis separately, the consensus information in all hypotheses is naturally fused into a hypergraph, called random consensus graph, with real structures corresponding to its dense subgraphs. The sampling process is essentially a progressive refinement procedure of the random consensus graph. Due to the huge number of hyperedges, it is generally inefficient to detect dense subgraphs on random consensus graphs. To overcome this issue, we construct a pairwise graph which approximately retains the dense subgraphs of the random consensus graph. The underlying structures are then revealed by detecting the dense subgraphs of the pair-wise graph. Since our method fuses information from all hypotheses, it can robustly detect structures even under a small number of MSSs. The graph framework enables our method to simultaneously discover multiple structures. Besides, our method is very efficient, and scales well for large scale problems. Extensive experiments illustrate the superiority of our proposed method over previous approaches, achieving several orders of magnitude speedup along with satisfactory accuracy and robustness. In this paper, we propose a general framework for graph matching which is suitable for different problems of pattern recognition. The pattern representation we assume is at the same time highly structured, like for classic syntactic and structural approaches, and of subsymbolic nature with real-valued features, like for connectionist and statistic approaches. We show that random walk based models, inspired by Google's PageRank, give rise to a spectral theory that nicely enhances the graph topological features at node level. As a straightforward consequence, we derive a polynomial algorithm for the classic graph isomorphism problem, under the restriction of dealing with Markovian spectrally distinguishable graphs (MSD), a class of graphs that does not seem to be easily reducible to others proposed in the literature. The experimental results that we found on different test-beds of the TC-15 graph database show that the defined MSD class "almost always" covers the database, and that the proposed algorithm is significantly more efficient than top scoring VF algorithm on the same data. Most interestingly, the proposed approach is very well-suited for dealing with partial and approximate graph matching problems, derived for instance from image retrieval tasks. We consider the objects of the COIL-100 visual collection and provide a graph-based representation, whose node's labels contain appropriate visual features. We show that the adoption of classic bipartite graph matching algorithms offers a straightforward generalization of the algorithm given for graph isomorphism and, finally, we report very promising experimental results on the COIL-100 visual collection. A new scheme to sample signals defined on the nodes of a graph is proposed. The underlying assumption is that such signals admit a sparse representation in a frequency domain related to the structure of the graph, which is captured by the so-called graph-shift operator. Instead of using the value of the signal observed at a subset of nodes to recover the signal in the entire graph, the sampling scheme proposed here uses as input observations taken at a single node. The observations correspond to sequential applications of the graph-shift operator, which are linear combinations of the information gathered by the neighbors of the node. When the graph corresponds to a directed cycle (which is the support of time-varying signals), our method is equivalent to the classical sampling in the time domain. When the graph is more general, we show that the Vandermonde structure of the sampling matrix, critical when sampling time-varying signals, is preserved. Sampling and interpolation are analyzed first in the absence of noise, and then noise is considered. We then study the recovery of the sampled signal when the specific set of frequencies that is active is not known. Moreover, we present a more general sampling scheme, under which, either our aggregation approach or the alternative approach of sampling a graph signal by observing the value of the signal at a subset of nodes can be both viewed as particular cases. Numerical experiments illustrating the results in both synthetic and real-world graphs close the paper.