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Abstract: Foreground–background segmentation has recently been applied [S.X. Yu, J. Shi, Object-specific figure-ground segregation, Computer Vision and Pattern Recognition (CVPR), 2003; S. Kumar, M. Hebert, Man-made structure detection in natural images using a causal multiscale random field, Computer Vision and Pattern Recognition (CVPR), 2003] to the detection and segmentation of specific objects or structures of interest from the background as an efficient alternative to techniques such as deformable templates [A.L. Yuille, Deformable templates for face recognition. Journal of Cognitive Neuroscience 3 (1) (1991)]. We introduce a graphical model (i.e. Markov random field)-based formulation of structure-specific figure-ground segmentation based on simple geometric features extracted from an image, such as local configurations of linear features, that are characteristic of the desired figure structure. Our formulation is novel in that it is based on factor graphs, which are graphical models that encode interactions among arbitrary numbers of random variables. The ability of factor graphs to express interactions higher than pairwise order (the highest order encountered in most graphical models used in computer vision) is useful for modeling a variety of pattern recognition problems. In particular, we show how this property makes factor graphs a natural framework for performing grouping and segmentation, and demonstrate that the factor graph framework emerges naturally from a simple maximum entropy model of figure-ground segmentation. We cast our approach in a learning framework, in which the contributions of multiple grouping cues are learned from training data, and apply our framework to the problem of finding printed text in natural scenes. Experimental results are described, including a performance analysis that demonstrates the feasibility of the approach. [Copyright &y& Elsevier]

Location-aware technologies will revolutionize many aspects of commercial, public service, and military sectors, and are expected to spawn numerous unforeseen applications. A new era of highly accurate ubiquitous locationawareness is on the horizon, enabled by a paradigm of cooperation between nodes. In this paper, we give an overview of cooperative localization approaches and apply them to ultrawide bandwidth (UWB) wireless networks. UWB transmission technology is particularly attractive for short- to mediumrange localization, especially in GPS-denied environments: wide transmission bandwidths enable robust communication in dense multipath scenarios, and the ability to resolve subnanosecond delays results in centimeter-level distance resolution. We will describe several cooperative localization algorithms and quantify their performance, based on realistic UWB ranging models developed through an extensive measurement campaign using FCC-compliant UWB radios. We will also present a powerful localization algorithm by mapping a graphical model for statistical inference onto the network topology, which results in a net-factor graph, and by developing a suitable net-message passing schedule. The resulting algorithm (SPAWN) is fully distributed, can cope with a wide variety of scenarios, and requires little communication overhead to achieve accurate and robust localization. [ABSTRACT FROM AUTHOR]

Abstract: Belief propagation over pairwise-connected Markov random fields has become a widely used approach, and has been successfully applied to several important computer vision problems. However, pairwise interactions are often insufficient to capture the full statistics of the problem. Higher-order interactions are sometimes required. Unfortunately, the complexity of belief propagation is exponential in the size of the largest clique. In this paper, we introduce a new technique to compute belief propagation messages in time linear with respect to clique size for a large class of potential functions over real-valued variables. We discuss how this technique can be generalized to still wider classes of potential functions at varying levels of efficiency. Also, we develop a form of nonparametric belief representation specifically designed to address issues common to networks with higher-order cliques and also to the use of guaranteed-convergent forms of belief propagation. To illustrate these techniques, we perform efficient inference in graphical models where the spatial prior of natural images is captured by 2×2 cliques. This approach shows significant improvement over the commonly used pairwise-connected models, and may benefit a variety of applications using belief propagation to infer images or range images, including stereo, shape-from-shading, image-based rendering, segmentation, and matting. [Copyright &y& Elsevier]

We initiate the probabilistic analysis of linear programming (LP) decoding of low-density parity-check (LDPC) codes. Specifically, we show that for a random LDPC code ensemble, the linear programming decoder of Feldman et al. succeeds in correcting a constant fraction of errors with high probability. The fraction of correctable errors guaranteed by our analysis surpasses previous nonasymptotic results for LDPC codes, and in particular, exceeds the best previous finite-length result on LP decoding by a factor greater than ten. This improvement stems in part from our analysis of probabilistic bit-flipping channels, as opposed to adversarial channels. At the core of our analysis is a novel combinatorial characterization of LP decoding success, based on the notion of a flow on the Tanner graph of the code. An interesting by-product of our analysis is to establish the existence of "probabilistic expansion" in random bipartite graphs, in which one requires only that almost every (as opposed to every) set of a certain size expands, for sets much larger than in the classical worst case setting. [ABSTRACT FROM AUTHOR]

Abstract: Belief Propagation algorithms acting on Graphical Models of classical probability distributions, such as Markov Networks, Factor Graphs and Bayesian Networks, are amongst the most powerful known methods for deriving probabilistic inferences amongst large numbers of random variables. This paper presents a generalization of these concepts and methods to the quantum case, based on the idea that quantum theory can be thought of as a noncommutative, operator-valued, generalization of classical probability theory. Some novel characterizations of quantum conditional independence are derived, and definitions of Quantum n-Bifactor Networks, Markov Networks, Factor Graphs and Bayesian Networks are proposed. The structure of Quantum Markov Networks is investigated and some partial characterization results are obtained, along the lines of the Hammersley–Clifford theorem. A Quantum Belief Propagation algorithm is presented and is shown to converge on 1-Bifactor Networks and Markov Networks when the underlying graph is a tree. The use of Quantum Belief Propagation as a heuristic algorithm in cases where it is not known to converge is discussed. Applications to decoding quantum error correcting codes and to the simulation of many-body quantum systems are described. [Copyright &y& Elsevier]

In structured classification problems, there is a direct conflict between expressive models and efficient inference: while graphical models such as Markov random fields or factor graphs can represent arbitrary dependences among instance labels, the cost of inference via belief propagation in these models grows rapidly as the graph structure becomes more complicated. One important source of complexity in belief propagation is the need to marginalize large factors to compute messages. This operation takes time exponential in the number of variables in the factor, and can limit the expressiveness of the models we can use. In this paper, we study a new class of potential functions, which we call decomposable k-way potentials, and provide efficient algorithms for computing messages from these potentials during belief propagation. We believe these new potentials provide a good balance between expressive power and efficient inference in practical structured classification problems. We discuss three instances of decomposable potentials: the associative Markov network potential, the nested junction tree, and a new type of potential which we call the voting potential. We use these potentials to classify images of protein subcellular location patterns in groups of cells. Classifying subcellular location patterns can help us answer many important questions in computational biology, including questions about how various treatments affect the synthesis and behavior of proteins and networks of proteins within a cell. Our new representation and algorithm lead to substantial improvements in both inference speed and classification accuracy. [ABSTRACT FROM AUTHOR]

In this paper, a vector-form factor graph representation is derived for intersymbol interference (ISI) channels. The resultant graphs have a tree-structure that avoids the short cycle problem in existing graph approaches. Based on a joint Gaussian approximation, we establish a connection between the LLR (log-likelihood ratio) estimator for a linear system driven by binary inputs and the LMMSE (linear minimum mean-square error) estimator for a linear system driven by Gaussian inputs. This connection facilitates the application of the recently proposed Gaussian message passing technique to the cycle-free graphs for ISI channels. We also show the equivalence between the proposed approach and the Wang-Poor approach based on the LMMSE principle. An attractive advantage of the proposed approach is its intrinsic parallel structure. Simulation results are provided to demonstrate this property. [ABSTRACT FROM AUTHOR]

Satellite channels are generally nonlinear and dispersive in nature, due to amplifiers being driven close to saturation. These effects can cause significant degradations when they are not taken into account at either the receiver (equalization) or at the transmitter (pre-distortion). State-of-the-art equalizers rely on the forward-backward algorithm and yield excellent performance. However, they have unreasonable complexity and storage requirements, especially for highly dispersive channels and/or large constellations. In this paper, we derive an equalization strategy for nonlinear channels based on Monte Carlo methods. We present a detailed performance, complexity and storage analysis. A significant performance gain compared to the linear equalizer is reported, and the proposed technique results in a significant reduction in both complexity and storage, compared to the forward-backward equalizer. [ABSTRACT FROM AUTHOR]

Novel conditions are derived that guarantee convergence of the Sum-Product Algorithm (also known as Loopy Belief Propagation or simply Belief Propagation (BP)) to a unique fixed point, irrespective of the initial messages, for parallel (synchronous) updates. The computational complexity of the conditions is polynomial in the number of variables. In contrast with previously existing conditions, our results are directly applicable to arbitrary factor graphs (with discrete variables) and are shown to be valid also in the case of factors containing zeros, under some additional conditions. The conditions are compared with existing ones, numerically and, if possible, analytically. For binary variables with pairwise interactions, sufficient conditions are derived that take into account local evidence (i.e., single-variable factors) and the type of pair interactions (attractive or repulsive). It is shown empirically that this bound outperforms existing bounds. [ABSTRACT FROM AUTHOR]

Factor graph (FG) is a recently developed graphical model. It subsumes many other graphical models, including Bayesian networks and Markov networks. This paper presents a multilevel probabilistic meta-model based on FGs - factor metanetwork. The model is a kind of context-enabled networks, and assumes that interoperability between component networks can be also modelled by another FG. It is composed of a set of FGs, which are put on each other in such a way that the probability distributions of single or multiple variables (function nodes) of every previous network (factor graph) depend on probability distributions associated with nodes of the next network. We assume parameters of function nodes in a FG as random variables, and allow all kinds of conditional dependencies between these probability functions. Several cases of two-level factor metanetworks are presented, and an example is presented to show the model's application. [ABSTRACT FROM AUTHOR]

A large number of stochastic networks including loss networks and certain queueing networks have product-form steady-state probabilities. However, for most practical networks, evaluating the system performance is a difficult task due to the presence of a normalization constant. We propose a new framework based on probabilistic graphical models to tackle this task. Specifically, we use factor graphs to model the stationary distribution of a network. For networks with arbitrary topology, we can apply efficient message-passing algorithms like the sum-product algorithm to compute the exact or approximate marginal distributions of all state variables and related performance measures such as blocking probabilities. Through extensive numerical experiments, we show that the sum-product algorithm returns very accurate blocking probabilities and greatly outperforms the reduced load approximation for loss networks with a variety of topologies. The factor graph model also provides a promising approach for analyzing product-form queueing networks. [ABSTRACT FROM AUTHOR]

A built-in self-test (BIST) technique is presented for testing analog iterative decoders. Catastrophic circuit faults are detected by temporarily operating the analog soft gates in a digital mode. Self-testing operations are performed in the digital domain, thereby lowering the cost and complexity compared to alternative mixed-signal BIST approaches. A proof-of-concept CMOS integrated circuit realization of the BIST is also presented. BER measurements show that the added circuits do not interfere with the decoder's performance during normal operation. [ABSTRACT FROM AUTHOR]

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We propose a method to improve approximate inference methods by correcting for the influence of loops in the graphical model. The method is a generalization and alternative implementation of a recent idea from Montanari and Rizzo (2005). It is applicable to arbitrary factor graphs, provided that the size of the Markov blankets is not too large. It consists of two steps: (i) an approximate inference method, for example, belief propagation, is used to approximate cavity distributions for each variable (i.e., probability distributions on the Markov blanket of a variable for a modified graphical model in which the factors involving that variable have been removed); (ii) all cavity distributions are improved by a message-passing algorithm that cancels out approximation errors by imposing certain consistency constraints. This loop correction (LC) method usually gives significantly better results than the original, uncorrected, approximate inference algorithm that is used to estimate the effect of loops. Indeed, we often observe that the loop-corrected error is approximately the square of the error of the uncorrected approximate inference method. In this article, we compare different variants of the loop correction method with other approximate inference methods on a variety of graphical models, including "real world" networks, and conclude that the LC method generally obtains the most accurate results. [ABSTRACT FROM AUTHOR]

In this paper, we use the factor-graph framework to describe the statistical relationships that arise in the equalization of data transmitted over an intersymbol interference channel, and use it to develop several new algorithms for linear and decision feedback approaches. Specifically, we examine both unconstrained and constrained linear equalization and decision feedback equalization of a sequence of nonidentically distributed symbols that are transmitted over a linear, possibly time-varying, finite-length channel and then corrupted by additive white noise. Factor graphs are used to derive algorithms for each of these equalization tasks, including fast implementations. One important application of these algorithms is linear turbo equalization, which requires a linear equalizer that can process observations of nonidentically distributed transmitted symbols. We show how the output of these factor-graph-based algorithms can be used in an efficient implementation of a linear turbo equalizer [ABSTRACT FROM PUBLISHER]

We show that for low-density parity-check (LDPC) codes whose Tanner graphs have sufficient expansion, the linear programming (LP) decoder of Feldman, Karger, and Wainwright can correct a constant fraction of errors. A random graph will have sufficient expansion with high probability, and recent work shows that such graphs can be constructed efficiently. A key element of our method is the use of a dual witness: a zero-valued dual solution to the decoding linear program whose existence proves decoding success. We show that as long as no more than a certain constant fraction of the bits are flipped by the channel, we can find a dual witness. This new method can be used for proving bounds on the performance of any LP decoder, even in a probabilistic set- ting. Our result implies that the word error rate of the LP decoder decreases exponentially in the code length under the binary-symmetric channel (BSC). This is the first such error bound for LDPC codes using an analysis based on "pseudocodewords." Recent work by Koetter and Vontobel shows that LP decoding and min-sum decoding of LDPC codes are closely related by the "graph cover" structure of their pseudocodewords; in their terminology, our result implies that that there exist families of LDPC codes where the minimum BSC pseudoweight grows linearly in the block length. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new Bayesian receiver for signal detection in flat-fading channels. First, the detection problem is formulated as an inference problem in a graphical model that models a hybrid dynamic system with both continuous and discrete variables. Then, based on the expectation propagation (EP) framework, we develop a smoothing algorithm to address the inference problem and visualize this algorithm using factor graphs. As a generalization of loopy belief propagation, EP efficiently approximates Bayesian estimation by iteratively propagating information between different nodes in the graphical model and projecting the posterior distributions into the exponential family. We use window-based EP smoothing for online estimation as in the signal detection problem. Window-based EP smoothing achieves accuracy similar to that obtained by batch EP smoothing, as shown in our simulations, while reducing delay time. Compared to sequential Monte Carlo filters and smoothers, the new method has lower computational complexity since it makes analytically deterministic approximation instead of Monte Carlo approximations. Our simulations demonstrate that the new receiver achieves accurate detection without the aid of any training symbols or decision feedbacks. Furthermore, the new receiver achieves accuracy comparable to that achieved by sequential Monte Carlo methods, but with less than one-tenth computational cost [ABSTRACT FROM PUBLISHER]

Estimation and detection algorithms for orthogonal frequency division multiplexing (OFDM) systems can be developed based on the sum-product algorithms, which operate by message passing in factor graphs. In this paper, we apply the sampling method (Monte Carlo) to factor graphs, and then the integrals in the sum-product algorithm can be approximated by sums, which results in complexity reduction. The blind receiver for OFDM systems can be derived via Sequential Monte Carlo (SMC) in factor graphs, the previous SMC blind receiver can be regarded as the special case of the sum-product algorithms using sampling methods. The previous SMC blind receiver for OFDM systems needs generating samples of the channel vector assuming the channel has an a priori Gaussian distribution. In the newly-built blind receiver, we generate samples of the virtual-pilots instead of the channel vector, with channel vector which can be easily computed based on virtual-pilots. As the size of the virtual-pilots space is much smaller than the channel vector space, only small number of samples are necessary, with the blind detection being much simpler. Furthermore, only one pilot tone is needed to resolve phase ambiguity and differential encoding is not used anymore. Finally, the results of computer simulations demonstrate that the proposal can perform well while providing significant complexity reduction. [ABSTRACT FROM AUTHOR]

A low-complexity high-accuracy algorithm is proposed to estimate the location of a target MS based on network-side time-of-arrival (TOA) measurements. Under a factor graph framework, the proposed algorithm first constructs a graphical model for the mobile position location problem by dividing the problem into many mutually-interactive local constraints. Each local constraint is enforced by a separate local processing unit. Efficient exchange of soft-information among local processing units in the mobile switching center (MSC) then iteratively purifies the estimate of the MS location. Numerical results show that the proposed algorithm not only enjoys low complexity, suitable for integrated-circuit implementation, but it is also able to achieve performance very close to the optimum achievable solution accuracy, the maximum likelihood (ML) solution accuracy [ABSTRACT FROM PUBLISHER]

It has been observed that a linear-feedback shift-register (LFSR) sequence can be synchronized by feeding the modulated sequence into a ‘soft’ (or ‘analog’) version of the LFSR. In this correspondence, the ‘soft LFSR’ is derived as forward-only message passing in the corresponding factor graph. A continuous-time analog (suitable fur realization as a clockless electronic circuit) is then given of both the LFSR and the soft LFSR. A connection is thus established between statistical state estimation and the phenomenon of entrainment of dynamical systems, which opens the prospect of deriving dynamical systems (such as electronic circuits) with strong entrainment capabilities from more powerful message passing algorithms. [ABSTRACT FROM AUTHOR]

We study the computational and sample complexity of parameter and structure learning in graphical models. Our main result shows that the class of factor graphs with bounded degree can be learned in polynomial time and from a polynomial number of training examples, assuming that the data is generated by a network in this class. This result covers both parameter estimation for a known network structure and structure learning. It implies as a corollary that we can learn factor graphs for both Bayesian networks and Markov networks of bounded degree, in polynomial time and sample complexity. Importantly, unlike standard maximum likelihood estimation algorithms, our method does not require inference in the underlying network, and so applies to networks where inference is intractable. We also show that the error of our learned model degrades gracefully when the generating distribution is not a member of the target class of networks. In addition to our main result, we show that the sample complexity of parameter learning in graphical models has an O(1) dependence on the number of variables in the model when using the KL-divergence normalized by the number of variables as the performance criterion. [ABSTRACT FROM AUTHOR]

This contribution deals with two hypothesis testing problems for digital receivers: frame synchronization and phase ambiguity resolution. As current receivers use powerful error-correcting codes and operate at low signal-to-noise ratio (SNR), these problems have become increasingly challenging: one is forced either to waste a part of the bandwidth on training symbols or to consider novel hypothesis testing techniques. We will consider five algorithms for hypothesis testing that exploit properties of the underlying channel code: a re-encoding (REEN) technique, an algorithm we previously derived from the expectation-maximization (EM) algorithm, two recently proposed algorithms known as mode separation (MS) and pseudo-ML (PML), and a technique where all hypotheses are tested simultaneously by applying the sum-product algorithm (SPA) to the overall factor graph of the system. These techniques will be compared in terms of their computational complexity, the class of problems to which they can be applied and their error rate performance. Through computer simulations we show that the EM-based and the PML algorithms have excellent performance. The MS, PML, REEN, and EM-based algorithms all have similar complexity, but the latter algorithm is suitable for a much wider range of applications. The SPA has the lowest computational complexity, but might yield poor performance. [ABSTRACT FROM AUTHOR]

This paper presents a novel self-organizing distributed algorithm for finding a broadcasting schedule in a packet radio network via only local collaborative interactions among neighboring network stations. Inspired by the huge success of the low density parity check (LDPC) codes in the field of error control coding, we transform the broadcast scheduling problem (BSP) into an LDPC-like problem through a factor graph. In the proposed algorithm, the constraint rules of the BSP are divided into many simple local rules, each of which is enforced by a local processing unit in the factor graph. The soft-information, describing the probability that each station will transmit a data packet, is then efficiently exchanged among the local processing units by using the sum-product algorithm to iteratively optimize the broadcasting schedule. Simulation results indicate that the proposed algorithm performs better than the other existing central-processing algorithms in terms of the channel utilization and the average packet delay. This is true especially when the network scenario is very complex. Furthermore, the proposed algorithm is both low in complexity and completely distributed, which makes it suitable for implementation in practical network applications [ABSTRACT FROM PUBLISHER]

This paper presents the systolic array implementation of a real-time symbol-optimum multiuser detection (MUD) algorithm for a direct-sequence code-division multiple-access system by truncating the backward recursions in the generalized forward/backward schedule. Simulation results show that the real-time algorithm provides negligible performance loss compared to the original symbol-optimum detection algorithm. The systolic array implementation is derived in this paper through the factor graph language of the real-time algorithm in order to exploit the suitability of the algorithm for parallel signal processing. [ABSTRACT FROM AUTHOR]

We introduce a new class of upper bounds on the log partition function of a Markov random field (MRF). This quantity plays an important role in various contexts, including approximating marginal distributions, parameter estimation, combinatorial enumeration, statistical decision theory, and large-deviations bounds. Our derivation is based on concepts from convex duality and information geometry: in particular, it exploits mixtures of distributions in the exponential domain, and the Legendre mapping between exponential and mean parameters. In the special case of convex combinations of tree-structured distributions, we obtain a family of variational problems, similar to the Bethe variational problem, but distinguished by the following desirable properties: i) they are convex, and have a unique global optimum; and ii) the optimum gives an upper bound on the log partition function. This optimum is defined by stationary conditions very similar to those defining fixed points of the sum-product algorithm, or more generally, any local optimum of the Bethe variational problem. As with sum-product fixed points, the elements of the optimizing argument can be used as approximations to the marginals of the original model. The analysis extends naturally to convex combinations of hypertree-structured distributions, thereby establishing links to Kikuchi approximations and variants. [ABSTRACT FROM AUTHOR]

We introduce the concept of convolutional factor graphs, which represent convolutional factorizations of multivariate functions, just as conventional (multiplicative) factor graphs represent multiplicative factorizations. Convolutional and multiplicative factor graphs arise as natural Fourier transform duals. In coding theory applications, algebraic duality of group codes is essentially an instance of Fourier transform duality. Convolutional factor graphs arise when a code is represented as a sum of subcodes, just as conventional multiplicative factor graphs arise when a code is represented as an intersection of supercodes. With auxiliary variables, convolutional factor graphs give rise to "syndrome realizations" of codes, just as multiplicative factor graphs with auxiliary variables give rise to "state realizations." We introduce normal and coenormal extensions of a multivariate function, which essentially allow a given function to be represented with either a multiplicative or a convolutional factorization, as is convenient. We use these function extensions to derive a number of duality relationships among the corresponding factor graphs, and use these relationships to obtain the duality properties of Forney graphs as a special case. [ABSTRACT FROM AUTHOR]

The highly stochastic nature of wireless environments makes it desirable to monitor link loss rates in wireless sensor networks. In a wireless sensor network, link loss monitoring is particularly supported by the data aggregation communication paradigm of network traffic: the data collecting node can infer link loss rates on all links in the network by exploiting whether packets from various sensors are received, and there is no need to actively inject probing packets for inference purposes. In this paper, we present a low complexity algorithmic framework for link loss monitoring based on the recent modeling and computational methodology of factor graphs. The proposed algorithm iteratively updates the estimates of link losses upon receiving (or detecting the loss of) recently sent packets by the sensors. The algorithm exhibits good performance and scalability, and can be easily adapted to different statistical models of networking scenarios. In particular, due to its low complexity, the algorithm is particularly suitable as a long-term monitoring facility. [ABSTRACT FROM AUTHOR]

Media analysis for video indexing is witnessing an increasing influence of statistical techniques. Examples of these techniques include the use of generative models as well as discriminant techniques for video structuring, classification, summarization, indexing, and retrieval. There is increasing emphasis on reducing the amount of supervision and user interaction needed to construct and utilize the semantic models. This paper highlights the statistical learning techniques in semantic multimedia indexing and retrieval. In particular the gamut of techniques from supervised to unsupervised systems will be demonstrated. [ABSTRACT FROM AUTHOR]

Accurate evaluation of Bayesian model evidence for a given data set is a fundamental problem in model development. Since evidence evaluations are usually intractable, in practice variational free energy (VFE) minimization provides an attractive alternative, as the VFE is an upper bound on negative model log-evidence (NLE). In order to improve tractability of the VFE, it is common to manipulate the constraints in the search space for the posterior distribution of the latent variables. Unfortunately, constraint manipulation may also lead to a less accurate estimate of the NLE. Thus, constraint manipulation implies an engineering trade-off between tractability and accuracy of model evidence estimation. In this paper, we develop a unifying account of constraint manipulation for variational inference in models that can be represented by a (Forney-style) factor graph, for which we identify the Bethe Free Energy as an approximation to the VFE. We derive well-known message passing algorithms from first principles, as the result of minimizing the constrained Bethe Free Energy (BFE). The proposed method supports evaluation of the BFE in factor graphs for model scoring and development of new message passing-based inference algorithms that potentially improve evidence estimation accuracy. [ABSTRACT FROM AUTHOR]