Analyzing Product-Form Stochastic Networks Via Factor Graphs and the Sum-Product Algorithm

Realizing accurate detection of an unknown radio transmitter (URT) has become a challenging problem due to its unknown parameter information. A method based on received signal strength difference (RSSD) fingerprint positioning technique and using factor graph (FG) for 2-D scenario has been developed. However, the URT positioning under 3-D scenario is more difficult with the large number of unknown parameters and has greater practical significance. In addition, the previous RSSD-based FG model is not accurate enough to express the relationship between the RSSD and corresponding location coordinates since the RSSD variances of reference points are different in practice. This paper proposes a more accurate 3-D FG model to reduce the influence of difference of RSSD measurement variances on positioning accuracy effectively by utilizing weighted least square (WLS). With the proposed RSSD-based 3-D WLSFG model and sum-product rule, positioning process of the proposed 3-D RSSD-WLSFG algorithm is derived. To verify the feasibility of the proposed method, we also explores the effects of different signal receiver numbers and grid distances on positioning accuracy. The simulation experiment results show that the proposed algorithm can obtain the best positioning performance compared with the conventional K nearest neighbor (KNN) algorithm and RSSD-FG algorithm under different grid distances and signal receiver numbers.

<p>Location awareness has been widely used for cooperative localization of target in wireless sensor networks (WSN). But as the number of agent node increases, cooperative localization based on nonparametric belief propagation (BP) causes high communication and computation burden. In addition, high localization accuracy is also the goal of this paper. To this end, this paper based on parameterized BP strategy proposed a distributed cubature Kalman filter (DCKF) algorithm named BP-DCKF. Firstly, basing on joint posterior probability density function of all nodes, this paper constructs a factor graph (FG) model, then the edge posterior distribution of the nodes is obtained by BP strategy. Secondly, considering Gaussian parameterized BP which reconstruct the parameterized message of agents transmitting, this paper proposed the improved DCKF method, moreover, obtaining the locating model of agent node related to posterior distribution of each node in the FG. Finally, based on the localization model, the location estimation of mobile agent node can be obtained utilizing DCKF method to iteratively solve the edge posterior distribution of agent node. Simulation results show that comparing with traditional algorithm, the proposed algorithm is higher on localization accuracy, lower on communication burden.</p> <p> </p>

The ability to reason over partially observable networks of interacting states is a fundamental competency in probabilistic robotics. While the well-known factor graph and Gaussian process models provide flexible and computationally efficient solutions for this inference problem in the special cases in which all of the hidden states are either finite-dimensional parameters or real-valued functions, respectively, in many cases we are interested in reasoning about heterogeneous networks whose hidden states are comprised of both finite-dimensional parameters and functions. To that end, in this paper we propose a novel probabilistic generative model that incorporates both factor graphs and Gaussian processes to model these heterogeneous systems. Our model improves upon prior approaches to inference within these networks by removing the assumption of any specific set of conditional independences amongst the modeled states, thereby significantly expanding the class of systems that can be represented. Furthermore, we show that inference within this model can always be performed by means of a two-stage procedure involving inference within a factor graph followed by inference over a Gaussian process; by exploiting fast inference methods for the individual factor graph and Gaussian process models to solve each of these subproblems in succession, we thus obtain a general framework for computationally efficient inference over heterogeneous finite-/infinite-dimensional systems.

We consider belief propagation (BP) as an efficient and scalable tool for state estimation and optimization problems in supply networks such as power grids. BP algorithms make use of factor graph representations, whose assignment to the problem of interest is not unique. It depends on the state variables and their mutual interdependencies. Many short loops in factor graphs may impede the accuracy of BP. We propose a systematic way to cluster loops of naively assigned factor graphs such that the resulting transformed factor graphs have no additional loops as compared to the original network. They guarantee an accurate performance of BP with only slightly increased computational effort, as we demonstrate by a concrete and realistic implementation for power grids. The method outperforms existing alternatives to handle the loops. We point to other applications to supply networks such as gas-pipeline or other flow networks that share the structure of constraints in the form of analogues to Kirchhoff’s laws. Whenever small and abundant loops in factor graphs are systematically generated by constraints between variables in the original network, our factor-graph assignment in BP complements other approaches. It provides a fast and reliable algorithm to perform marginalization in tasks like state determination, estimation, or optimization issues in supply networks.Graphical abstract

Molecular dynamics (MD) simulations provide a wealth of high-dimensional data at all-atom and femtosecond resolution but deciphering mechanistic information from this data is an ongoing challenge in physical chemistry and biophysics. Theoretically speaking, joint probabilities of the equilibrium distribution contain all thermodynamic information, but they prove increasingly difficult to compute and interpret as the dimensionality increases. Here, inspired by tools in probabilistic graphical modeling, we develop a factor graph trained through belief propagation that helps factorize the joint probability into an approximate tractable form that can be easily visualized and used. We validate the study through the analysis of the conformational dynamics of two small peptides with five and nine residues. Our validations include testing the conditional dependency predictions through an intervention scheme inspired by Judea Pearl. Second, we directly use the belief propagation-based approximate probability distribution as a high-dimensional static bias for enhanced sampling, where we achieve spontaneous back-and-forth motion between metastable states that is up to 350 times faster than unbiased MD. We believe this work opens up useful ways to thinking about and dealing with high-dimensional molecular simulations.

Factor graphs are important models for succinctly representing probability distributions in machine learning, coding theory, and statistical physics. Several computational problems, such as computing marginals and partition functions, arise naturally when working with factor graphs. Belief propagation is a widely deployed iterative method for solving these problems. However, despite its significant empirical success, not much is known about the correctness and efficiency of belief propagation. Bethe approximation is an optimization-based framework for approximating partition functions. While it is known that the stationary points of the Bethe approximation coincide with the fixed points of belief propagation, in general, the relation between the Bethe approximation and the partition function is not well understood. It has been observed that for a few classes of factor graphs, the Bethe approximation always gives a lower bound to the partition function, which distinguishes them from the general case, where neither a lower bound, nor an upper bound holds universally. This has been rigorously proved for permanents and for attractive graphical models. Here we consider bipartite normal factor graphs and show that if the local constraints satisfy a certain analytic property, the Bethe approximation is a lower bound to the partition function. We arrive at this result by viewing factor graphs through the lens of polynomials. In this process, we reformulate the Bethe approximation as a polynomial optimization problem. Our sufficient condition for the lower bound property to hold is inspired by recent developments in the theory of real stable polynomials. We believe that this way of viewing factor graphs and its connection to real stability might lead to a better understanding of belief propagation and factor graphs in general.

In this paper, we develop a Belief Propagation (BP) algorithm for similarity computation to improve the recommendation accuracy of the neighborhood method, which is one of the most popular Collaborative Filtering (CF) recommendation algorithms. We formulate a probabilistic inference problem as to compute the marginal posterior distributions of similarity variables from their joint posterior distribution given the observed ratings. However, direct computation is prohibitive in large-scale recommender systems. Therefore, we introduce an appropriate chosen factor graph to express the factorization of the joint distribution function, and utilize the BP algorithm that operates in the factor graph to exploit the factorization for efficient inference. In addition, since the high degree at the factor node incurs an exponential increase in computational complexity, we also propose a complexity-reduction technique. The overall complexity of the proposed BP algorithm on a factor graph is linear in the number of variables, which ensures scalability. Finally, through experiments on the MovieLens dataset, we show the superior prediction accuracy of the proposed BP-based similarity computation algorithm for recommendation.

Privacy preserving data releasing is an important problem for reconciling data openness with individual privacy.The state-of-the-art approach for privacy preserving data release is differential privacy, which offers powerful privacy guarantee without confining assumptions about the background knowledge about attackers.For genomic data with huge-dimensional attributes, however, current approaches based on differential privacy are not effective to handle.Specifically, amount of noise is required to be injected to genomic data with tens of million of SNPs (Single Nucleotide Polymorphisms), which would significantly degrade the utility of released data.To address this problem, this paper proposes a differential privacy guaranteed genomic data releasing method.Through executing belief propagation on factor graph, our method can factorize the distribution of sensitive genomic data into a set of local distributions.After injecting differential-privacy noise to these local distributions, synthetic sensitive data can be obtained by sampling on noise distribution.Synthetic sensitive data and factor graph can be further used to construct approximate distribution of non-sensitive data.Finally, non-sensitive genomic data is sampled from the approximate distribution to construct a synthetic genomic dataset.

Cooperative Spectrum Sensing (CSS) is a reliable detection approach that performs better over faded channel. In CSS, all Secondary Users (SU) have equal weight. We have studied performance of Centralized CSS (CCSS) using Normal Factor Graph (NFG) model with logical OR and Neyman-Pearson based Likelihood Ratio Testing (LRT) fusion rules. Here, we have proposed a novel Weighted CCSS (WCCSS) using NFG based probabilistic inference model. Sum Product algorithm (SPA) has been used for message passing and different weight assignment strategies have been used. The performance of WCCSS approach in Cognitive Radio Network (CRN) under different channels have been studied through simulation.

The rapid expansion of Twitter has attracted worldwide attention. With more than 500 million tweets posted per day, Twitter becomes an invaluable information and knowledge source. Many Twitter related tasks have been studied, such as event extraction, hashtag recommendation, and topic detection. A critical step in understanding and mining information from Twitter is to disambiguate entities in tweets, i.e., tweet entity linking. It is a challenging task because tweets are short, noisy, and fresh. Many tweet-specific signals have been found to solve the tweet entity linking problem, such as user interest, temporal popularity, location information and so on. However, two common weaknesses exist in previous work. First, most proposed models are not flexible and extendable to fit new signals. Second, their scalability is not good enough to handle the large-scale social network like Twitter. In this work, we formalize the tweet entity linking problem into a factor graph model which has shown its effectiveness and efficiency in many other applications. We also propose selective attention over entities to increase the scalability of our model, which brings linear complexity. To adopt the attention mechanism in the factor graph, we propose a new type of nodes called pseudo-variable nodes to solve the asymmetry attention problem caused by the undirected characteristic of the factor graph. We evaluated our model on two different manually annotated tweet datasets. The experimental results show that our model achieves better performance in terms of both effectiveness and efficiency compared with the state-of-the-art approaches.

In this paper, we discuss the belief propagation (BP) decoding of polar codes. The performance of polar codes for short lengths is not satisfactory. Therefore, motivated by this we propose a novel technique to improve the performance of polar codes under BP decoding. In order to enhance the reliability of the variable nodes’ propagated messages in BP decoding, the messages are multiplied by previous messages of variable nodes. It is also shown that the BP decoding can be performed on polar codes if the factor graph is constructed according to the parity check matrix of polar codes. Simulation results in binary-input additive white Gaussian noise channel show that using the proposed method a gain of 1–2 dB can be achieved. We also show that the complexity of proposed decoder is same as the complexity of standard BP decoder. Furthermore, we show that the proposed decoder requires about 10–25 iterations less than the standard BP decoder.

This paper explores a belief propagation algorithm approach, for state estimation of thermal states of aggregated populations of thermostatically controlled loads to provide balancing services in power systems. Balancing services such as frequency control require high accuracy and thus estimation is crucial, especially when sensing and communication in real time is not available or partially. We use Markov chain models to describe the thermal states of aggregated thermostatically controlled loads populations and belief propagation for state estimation. Kalman filter, which has been used in similar studies, is known to be an instance of belief propagation framework. This fact motivates us to introduce belief propagation in this framework, and demonstrate that it provides the same results as Kalman filter. Moreover, belief propagation algorithm is fully decentralized, offering higher flexibility of system modeling using factor graphs. Besides demand response, belief propagation can be applied for different purposes in power systems, either in fully distributed or in mixed systems, and is easily integrated with Kalman filter or similar probabilistic frameworks.

A model-based approach to robot kinematics and control using discrete factor graphs with belief propagation

Belief propagation (BP) is widely used to solve the cooperative localization problem due to its excellent performance and natural distributed structure of implementation. For a mobile agent network, its factor graph inevitably encounters loops. In this case, the BP algorithm becomes iterative and can only provide an approximate marginal probability density function of the estimate with finite iterations. We propose an augmented-state BP algorithm for mobile agent networks to alleviate the effect of loops. By performing state augmentation, the messages in the factor graph will actually be allowed to be backward propagated, which reduces the number of loops in the factor graph, increases the available information of agents, and thus, benefits the localization. Experimental results demonstrate the better performance of the proposed algorithm over the original BP method.

Globally referenced and accurate positioning is of great significance for the application of intelligent vehicular systems. The visual and inertial measurement unit (IMU) integrated navigation system (VINS) is widely used in many intelligent positioning-based services. However, VINS are prone to drift over time and their performance is significantly compromised in urban canyons since the numerous outlier visual features caused by moving objects and unstable illuminations. Similarly, the global navigation satellite system (GNSS) is reliable in open areas but struggles with signal obstructions and reflections in urban canyons. To exploit the complementariness of the VINS and GNSS, this paper proposed a sliding window factor graph optimization (FGO)-based GNSS/Visual/IMU/Map (GVIM) integration, which exploits the full suit raw measurements from GNSS, IMU, and visual, together with the prior lightweight map. Unlike the existing tightly-coupled GNSS/Visual/IMU integration schemes, the potential of the carrier-phase measurement is fully explored using the recently developed window carrier phase (WCP) model. To further mitigate the impacts of the GNSS outliers, a novel sliding window (SW)-based map matching model is proposed to correct the states using the lightweight OpenStreetMap (OSM). Different from conventional filtering-based map matching, the states within the sliding window are associated with the lane information from the OSM which effectively exploits the measurement redundancy provided by the factor graph model. The experiments are conducted in the urban canyons of Hong Kong, utilizing a challenging dataset characterized by poor satellite visibility and numerous visual feature outliers, to verify the performance of the proposed method.