2,667 research outputs found

    Monte Carlo optimization of decentralized estimation networks over directed acyclic graphs under communication constraints

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    Motivated by the vision of sensor networks, we consider decentralized estimation networks over bandwidth–limited communication links, and are particularly interested in the tradeoff between the estimation accuracy and the cost of communications due to, e.g., energy consumption. We employ a class of in–network processing strategies that admits directed acyclic graph representations and yields a tractable Bayesian risk that comprises the cost of communications and estimation error penalty. This perspective captures a broad range of possibilities for processing under network constraints and enables a rigorous design problem in the form of constrained optimization. A similar scheme and the structures exhibited by the solutions have been previously studied in the context of decentralized detection. Under reasonable assumptions, the optimization can be carried out in a message passing fashion. We adopt this framework for estimation, however, the corresponding optimization scheme involves integral operators that cannot be evaluated exactly in general. We develop an approximation framework using Monte Carlo methods and obtain particle representations and approximate computational schemes for both the in–network processing strategies and their optimization. The proposed Monte Carlo optimization procedure operates in a scalable and efficient fashion and, owing to the non-parametric nature, can produce results for any distributions provided that samples can be produced from the marginals. In addition, this approach exhibits graceful degradation of the estimation accuracy asymptotically as the communication becomes more costly, through a parameterized Bayesian risk

    An efficient Monte Carlo approach for optimizing communication constrained decentralized estimation networks

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    We consider the design problem of a decentralized estimation network under communication constraints. The underlying low capacity links are modeled by introducing a directed acyclic graph where each node corresponds to a sensor platform. The operation of the platforms are constrained by the graph such that each node, based on its measurement and incoming messages from parents, produces a local estimate and outgoing messages to children. A Bayesian risk that captures both estimation error penalty and cost of communications, e.g. due to consumption of the limited resource of energy, together with constraining the feasible set of strategies by the graph, yields a rigorous problem definition. We adopt an iterative solution that converges to an optimal strategy in a person-byperson sense previously proposed for decentralized detection networks under a team theoretic investigation. Provided that some reasonable assumptions hold, the solution admits a message passing interpretation exhibiting linear complexity in the number of nodes. However, the corresponding expressions in the estimation setting contain integral operators with no closed form solutions in general. We propose particle representations and approximate computational schemes through Monte Carlo methods in order not to compromise model accuracy and achieve an optimization method which results in an approximation to an optimal strategy for decentralized estimation networks under communication constraints. Through an example, we present a quantification of the trade-off between the estimation accuracy and the cost of communications where the former degrades as the later is increased

    Sigma Point Belief Propagation

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    The sigma point (SP) filter, also known as unscented Kalman filter, is an attractive alternative to the extended Kalman filter and the particle filter. Here, we extend the SP filter to nonsequential Bayesian inference corresponding to loopy factor graphs. We propose sigma point belief propagation (SPBP) as a low-complexity approximation of the belief propagation (BP) message passing scheme. SPBP achieves approximate marginalizations of posterior distributions corresponding to (generally) loopy factor graphs. It is well suited for decentralized inference because of its low communication requirements. For a decentralized, dynamic sensor localization problem, we demonstrate that SPBP can outperform nonparametric (particle-based) BP while requiring significantly less computations and communications.Comment: 5 pages, 1 figur

    Monte Carlo optimization approach for decentralized estimation networks under communication constraints

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    We consider designing decentralized estimation schemes over bandwidth limited communication links with a particular interest in the tradeoff between the estimation accuracy and the cost of communications due to, e.g., energy consumption. We take two classes of in–network processing strategies into account which yield graph representations through modeling the sensor platforms as the vertices and the communication links by edges as well as a tractable Bayesian risk that comprises the cost of transmissions and penalty for the estimation errors. This approach captures a broad range of possibilities for “online” processing of observations as well as the constraints imposed and enables a rigorous design setting in the form of a constrained optimization problem. Similar schemes as well as the structures exhibited by the solutions to the design problem has been studied previously in the context of decentralized detection. Under reasonable assumptions, the optimization can be carried out in a message passing fashion. We adopt this framework for estimation, however, the corresponding optimization schemes involve integral operators that cannot be evaluated exactly in general. We develop an approximation framework using Monte Carlo methods and obtain particle representations and approximate computational schemes for both classes of in–network processing strategies and their optimization. The proposed Monte Carlo optimization procedures operate in a scalable and efficient fashion and, owing to the non-parametric nature, can produce results for any distributions provided that samples can be produced from the marginals. In addition, this approach exhibits graceful degradation of the estimation accuracy asymptotically as the communication becomes more costly, through a parameterized Bayesian risk

    Approximate Decentralized Bayesian Inference

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    This paper presents an approximate method for performing Bayesian inference in models with conditional independence over a decentralized network of learning agents. The method first employs variational inference on each individual learning agent to generate a local approximate posterior, the agents transmit their local posteriors to other agents in the network, and finally each agent combines its set of received local posteriors. The key insight in this work is that, for many Bayesian models, approximate inference schemes destroy symmetry and dependencies in the model that are crucial to the correct application of Bayes' rule when combining the local posteriors. The proposed method addresses this issue by including an additional optimization step in the combination procedure that accounts for these broken dependencies. Experiments on synthetic and real data demonstrate that the decentralized method provides advantages in computational performance and predictive test likelihood over previous batch and distributed methods.Comment: This paper was presented at UAI 2014. Please use the following BibTeX citation: @inproceedings{Campbell14_UAI, Author = {Trevor Campbell and Jonathan P. How}, Title = {Approximate Decentralized Bayesian Inference}, Booktitle = {Uncertainty in Artificial Intelligence (UAI)}, Year = {2014}

    Monte Carlo optimization approach for decentralized estimation networks under communication constraints

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    We consider designing decentralized estimation schemes over bandwidth limited communication links with a particular interest in the tradeoff between the estimation accuracy and the cost of communications due to, e.g., energy consumption. We take two classes of in–network processing strategies into account which yield graph representations through modeling the sensor platforms as the vertices and the communication links by edges as well as a tractable Bayesian risk that comprises the cost of transmissions and penalty for the estimation errors. This approach captures a broad range of possibilities for “online” processing of observations as well as the constraints imposed and enables a rigorous design setting in the form of a constrained optimization problem. Similar schemes as well as the structures exhibited by the solutions to the design problem has been studied previously in the context of decentralized detection. Under reasonable assumptions, the optimization can be carried out in a message passing fashion. We adopt this framework for estimation, however, the corresponding optimization schemes involve integral operators that cannot be evaluated exactly in general. We develop an approximation framework using Monte Carlo methods and obtain particle representations and approximate computational schemes for both classes of in–network processing strategies and their optimization. The proposed Monte Carlo optimization procedures operate in a scalable and efficient fashion and, owing to the non-parametric nature, can produce results for any distributions provided that samples can be produced from the marginals. In addition, this approach exhibits graceful degradation of the estimation accuracy asymptotically as the communication becomes more costly, through a parameterized Bayesian risk

    An efficient Monte Carlo approach for optimizing decentralized estimation networks constrained by undirected topologies

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    We consider a decentralized estimation network subject to communication constraints such that nearby platforms can communicate with each other through low capacity links rendering an undirected graph. After transmitting symbols based on its measurement, each node outputs an estimate for the random variable it is associated with as a function of both the measurement and incoming messages from neighbors. We are concerned with the underlying design problem and handle it through a Bayesian risk that penalizes the cost of communications as well as estimation errors, and constraining the feasible set of communication and estimation rules local to each node by the undirected communication graph. We adopt an iterative solution previously proposed for decentralized detection networks which can be carried out in a message passing fashion under certain conditions. For the estimation case, the integral operators involved do not yield closed form solutions in general so we utilize Monte Carlo methods. We achieve an iterative algorithm which yields an approximation to an optimal decentralized estimation strategy in a person by person sense subject to such constraints. In an example, we present a quantification of the trade-off between the estimation accuracy and cost of communications using the proposed algorithm
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