Global Sufficient Statistics Research Articles

Keynesian Production Networks and the COVID-19 Crisis: A Simple Benchmark

The COVID-19 crisis is a seemingly all-encompassing shock to supply and demand. These negative shocks affected industries differently: some switched to remote work, maintaining employment and production, while others reduced capacity and shed workers. We consider a stripped-down version of the model in Baqaee and Farhi (2020). The model allows for an arbitrary input-output network, complementarities, incomplete markets, downward wage rigidity, and a zero lower bound. Nevertheless, the model has a stark property: factor income shares at the initial equilibrium are global sufficient statistics for the production network, clarifying assumptions that must be broken if the network is to matter.

A novel mobile agent-based distributed evidential expectation maximization algorithm for uncertain sensor networks

In this paper, a novel mobile agent-based distributed evidential expectation maximization (MADEEM) algorithm is presented for sensor networks. The proposed algorithm is used for probability density function estimation and data clustering in the presence of uncertainties in sensor measurements. It is assumed that the sensor measurements are statistically modeled by a common Gaussian mixture model. The proposed algorithm maximizes a new generalized likelihood criterion in an iterative and distributed manner. For this purpose, mobile agents compute some local sufficient statistics by using local measurements of each sensor node. After the local computations, the global sufficient statistics are updated. At the end of iterations, the parameters of the probability density function are updated by using the global sufficient statistics. The mentioned process will be continued until the convergence criterion is satisfied. Convergence analysis of the proposed algorithm is also presented in this paper. After the convergence analysis, the simulation results show the promising performance of the proposed algorithm. Finally, the last part of the paper is devoted to the concluding remarks.

Probability density estimation in sensor networks based on distributed mixture of factor analyzers, mobile agents and stochastic sensor selection

This paper considers the problem of distributed probability density estimation of high-dimensional data in sensor networks. In order to describe and analyze high-dimensional observations, a mixture of factor analyzers can be used instead of Gaussian mixture model. Due to high communication costs between sensor nodes in centralized algorithms, use of these algorithms is not affordable. In this paper, a distributed estimation algorithm is presented based on the mixture of factor analyzers, mobile agents and stochastic sensor selection. In the proposed algorithm, at the beginning of each iteration, a mobile agent is assigned to each independent route of the network which consists of several sensor nodes based on a stochastic sensor selection scheme. The mobile agents calculate local sufficient statistics vector in each sensor node and update global sufficient statistics. At the end of each iteration, the parameters of the mixture model are computed by using global sufficient statistics. Convergence analysis of the proposed distributed algorithm is also presented. Finally, the performance of the proposed algorithm is evaluated by using numerical simulations. Simulation results show the promising performance of the proposed distributed algorithm.

Consensus Filter-Based Distributed Variational Bayesian Algorithm for Flow and Speed Density Prediction With Distributed Traffic Sensors

This paper formulates a consensus filter-based distributed variational Bayesian (CFBDVB) algorithm for density approximation of traffic flow and average traffic speed in a freeway. This algorithm uses traffic measurements, including volume, occupancy rate, and average velocity, collected by some inductive loop sensors. These traffic sensors are settled in sealed spaces in the freeway network, such that they demonstrate a distributed sensor network. It is assumed that measurements of the sensors can be statistically modeled by a common Gaussian mixture model. Using the suggested algorithm, a challenging problem is solved: selection of the right number of components. The algorithm begins with a large number of initialized components. In this algorithm, each sensor client severally computes local sufficient statistics by using local observations. A consensus filter is then used to spread out local sufficient statistics to neighbors and approximate global sufficient statistics in each client. Then, using the global sufficient statistics, irrelevant components are determined and omitted. Then, the remaining components' parameters are estimated. The suggested CFBDVB algorithm is scalable and robust. It estimates the parameters of mixtures and simultaneously selects the number of components. Various simulations of sensor nets have been done to confirm the promising performance of the CFBDVB algorithm.

Mobile‐agent‐based distributed variational Bayesian algorithm for density estimation in sensor networks

This study considers the problem of probability density estimation and model order selection in distributed sensor networks. For this purpose, a mobile-agent-based distributed variational Bayesian algorithm is proposed. It is assumed that the measurements can be statistically modelled by a common Gaussian mixture model. In the proposed algorithm, the problems of model order selection and probability density estimation will be considered simultaneously using mobile agents and the variational concept. Initially, considering a component number greater than the true one, the variational Bayesian algorithm will be executed in different nodes. In other words, the mobile agents move through different routes in the network and compute the local sufficient statistics. Afterwards, the global sufficient statistics will be updated using these values and finally the parameters of the probability density function will be calculated. This procedure will be repeated until convergence is reached. At this moment, the component whose mixture probability is lower than a threshold value will be removed. The mentioned steps will continue until the true component number is reached. Convergence of the proposed method will also be analytically studied. Finally, the proposed algorithm will be applied to synthetic and also real-world data sets to show its promising performance.

A novel distributed variational approximation method for density estimation in sensor networks

In this paper, a consensus filter based distributed variational Bayesian (CFBDVB) algorithm is developed for distributed density estimation. Sensor measurements are assumed to be statistically modeled by a finite mixture model for which the CFBDVB algorithm is used to estimate the parameters, including means, covariances and weights of components. This algorithm is based on three steps: (1) calculating local sufficient statistics at every node, (2) estimating a global sufficient statistics vector using a consensus filter, (3) updating parameters of the finite mixture model based on the global sufficient statistics vector. Scalability and robustness are two advantages of the proposed algorithm. Convergence of the CFBDVB algorithm is also proved using Robbins–Monro stochastic approximation method. Finally, to verify performance of CFBDVB algorithm, we perform several simulations of sensor networks. Simulation results are very promising.

Distributed Data Clustering Using Mobile Agents and EM Algorithm

In this paper, mobile agents are used for density estimation and data clustering in sensor networks. It has been assumed that sensor measurements can be statistically modeled by a common Gaussian mixture model. Here, a new data clustering method will be proposed for sensor networks in which some agents will move in different routes and collect the local necessary sufficient statistics by executing expectation maximization (EM) algorithm locally in each node. Then, the mobile agents will combine the local sufficient statistics in a fusion center and calculate a global sufficient statistics vector. This process will be repeated until convergence is reached. This algorithm not only executes the EM algorithm in a distributed manner but also reduces the number of iterations of the EM algorithm and increases its convergence rate. Convergence of the proposed method will be also analytically studied, and it will be shown that the estimated parameters will eventually converge to their true values. Finally, the proposed method will be applied to synthetic and real data sets in order to show its promising performance.

Distributed Consensus <formula formulatype="inline"><tex Notation="TeX">$+$</tex></formula> Innovation Particle Filtering for Bearing/Range Tracking With Communication Constraints

A constrained sufficient statistic (CSS)-based distributed particle filter (CSS/DPF) implementation is proposed for nonlinear bearing-only and joint bearing/range tracking applications in sensor networks. The CSS/DPF runs localized particle filters at nodes constituting the sensor network and uses the resulting local sufficient statistics (LSS) to compute the global sufficient statistics (GSS) for the overall system. The CSS/DPF is, therefore, a two-step procedure: i) the means of the LSSs for the local filters are computed by running average consensus algorithms, which are then used to derive the corresponding GSSs, and ii) each node renews the local weights of the localized particle filters using the updated GSSs. The attractive feature of the CSS/DPF is the reduced number of consensus runs as compared with the state-of-art consensus-based DPF implementations. To further reduce the consensus overhead, we couple the CSS/DPF with the distributed unscented particle filter (DUPF), collectively referred to as the CSS/DUPF, which extends the linear consensus and innovation framework to nonlinear distributed estimation. Our Monte Carlo simulations show that the performance of the CSS/DUPF follows that of the centralized particle filter, even with a limited number of iterations per consensus run.

Decentralized Data Reduction With Quantization Constraints

A guiding principle for data reduction in statistical inference is the sufficiency principle. This paper extends the classical sufficiency principle to decentralized inference, i.e., data reduction needs to be achieved in a decentralized manner. We examine the notions of local and global sufficient statistics and the relationship between the two for decentralized inference under different observation models. We then consider the impacts of quantization on decentralized data reduction which is often needed when communications among sensors are subject to finite capacity constraints. The central question we intend to ask is: if each node in a decentralized inference system has to summarize its data using a finite number of bits, is it still optimal to implement data reduction using global sufficient statistics prior to quantization? We show that the answer is negative using a simple example and proceed to identify conditions under which sufficiency based data reduction followed by quantization is indeed optimal. They include the well known case when the data at decentralized nodes are conditionally independent as well as a class of problems with conditionally dependent observations that admit conditional independence structure through the introduction of an appropriately chosen hidden variable.

Distributed maximum likelihood estimation for flow and speed density prediction in distributed traffic detectors with Gaussian mixture model assumption

In this study a distributed maximum likelihood estimator (MLE) has been presented to estimate ML function of traffic flow and mean traffic speed in a freeway. This algorithm uses traffic measurements including volume, occupancy and mean speed which gathered by some inductive loop detectors. These traffic detectors (traffic sensors) located in certain distances in the freeway network such that they establish a distributed sensor network (DSN). The presented distributed estimator has employed a distributed expectation maximisation algorithm to calculate MLE. In the E-step of this algorithm, each sensor node independently calculates local sufficient statistics by using local observations. A consensus filter is used to diffuse local sufficient statistics to neighbours and estimate global sufficient statistics in each node. In the M-step of this algorithm, each sensor node uses the estimated global sufficient statistics to update model parameters of the Gaussian mixtures, which can maximise the log-likelihood in the same way as in the standard EM algorithm. As the consensus filter only requires each node to communicate with its neighbours, the distributed algorithm is scalable and robust. A set of field traffic data from Minnesota freeway network has been used to simulate and verify the proposed distributed estimator performance.

Distributed density estimation in sensor networks based on variational approximations

This article presents a peer-to-peer (P2P) distributed variational Bayesian (P2PDVB) algorithm for density estimation and clustering in sensor networks. It is assumed that measurements of the nodes can be statistically modelled by a common Gaussian mixture model. The variational approach allows the simultaneous estimate of the component parameters and the model complexity. In this algorithm, each node independently calculates local sufficient statistics first by using local observations. A P2P averaging approach is then used to diffuse local sufficient statistics to neighbours and estimate global sufficient statistics in each node. Finally, each sensor node uses the estimated global sufficient statistics to estimate the model order as well as the parameters of this model. Because the P2P averaging approach only requires that each node communicate with its neighbours, the P2PDVB algorithm is scalable and robust. Diffusion speed and convergence of the proposed algorithm are also studied. Finally, simulated and real data sets are used to verify the remarkable performance of proposed algorithm.

Distributed Unsupervised Gaussian Mixture Learning for Density Estimation in Sensor Networks

This paper considers the problem of density estimation and clustering in sensor networks. It is assumed that measurements of the sensors can statistically be modeled by a common Gaussian mixture model (GMM). In this paper, a distributed expectation maximization (DEM) algorithm is developed to estimate the model order and the parameters of this model. Scalability and fault tolerance are two important advantages of this method. In the E-step of this algorithm, each node calculates local sufficient statistics using its local observations. A distributed averaging approach is then used to diffuse local sufficient statistics to neighboring nodes and estimate global sufficient statistics in each node. In the M-step, each node updates parameters of the GMM using the estimated global sufficient statistics. Diffusion speed and convergence of the proposed algorithm are also studied. The proposed method is then used for environmental monitoring and also distributed target classification. Simulation results approve the promising performance of this algorithm.

Distributed EM Algorithm for Gaussian Mixtures in Sensor Networks

This paper presents a distributed expectation-maximization (EM) algorithm over sensor networks. In the E-step of this algorithm, each sensor node independently calculates local sufficient statistics by using local observations. A consensus filter is used to diffuse local sufficient statistics to neighbors and estimate global sufficient statistics in each node. By using this consensus filter, each node can gradually diffuse its local information over the entire network and asymptotically the estimate of global sufficient statistics is obtained. In the M-step of this algorithm, each sensor node uses the estimated global sufficient statistics to update model parameters of the Gaussian mixtures, which can maximize the log-likelihood in the same way as in the standard EM algorithm. Because the consensus filter only requires that each node communicate with its neighbors, the distributed EM algorithm is scalable and robust. It is also shown that the distributed EM algorithm is a stochastic approximation to the standard EM algorithm. Thus, it converges to a local maximum of the log-likelihood. Several simulations of sensor networks are given to verify the proposed algorithm.

A note on distributed estimation and sufficiency

In relation to distributed parameter estimation, the notion of local and global sufficient statistics is introduced. It is shown that when a sufficiency condition is satisfied by the probability distribution of a random sample, a global sufficient statistic is obtainable as a function of local sufficient statistics. Several standard distributions satisfy the said sufficiency condition. >