1,721,020 research outputs found
Detection of Gauss-Markov Random Fields under Routing Energy Constraint
No full textAbstract — The problem of maximizing detection performance subject to an energy constraint is analyzed in an asymptotic setting. The correlation between the sensor measurements is incorporated through the Gauss-Markov random field with Euclidean nearest-neighbor dependency graph. An average energy constraint is imposed on a routing scheme with an approximation factor of two, and the resulting Neyman-Pearson error exponent is optimized with respect to the density of the deployed sensors. It is shown that the behavior of this optimal density crucially depends on the ratio between the measurement variances under the two hypotheses and displays a threshold behavior. Below the threshold value of the variance ratio, the optimal density tends towards infinity for any feasible energy constraint. On the other hand, when the variance ratio is above the threshold, the optimal density is characterized by the energy constraint. Index Terms — detection, Gauss-Markov random fields, Routing, error exponent. I
Energy Efficient Routing for Statistical Inference of Markov Random Fields
No full textAbstract — The problem of routing of sensor observations for optimal detection of a Markov random field (MRF) at a designated fusion center is analyzed. Assuming that the correlation structure of the MRF is defined by the nearestneighbor dependency graph, routing schemes which minimize the total energy consumption are analyzed. It is shown that the optimal routing scheme involves data fusion at intermediate nodes and requires transmissions of two types viz., the raw sensor data and the aggregates of log-likelihood ratio (LLR). The raw data is transmitted among the neighbors in the dependency graph and local contributions to the LLR are computed. These local contributions are then aggregated and delivered to the fusion center. A 2-approximation routing algorithm (DFMRF) is proposed and it has a transmission multidigraph consisting of the dependency graph and the directed minimum spanning tree, with the directions toward the fusion center
Distributed statistical inference using type based random access over multi-access fading channels
No full textAbstract — The problem of distributed detection and estimation in a sensor network over a multiaccess fading channel is considered. A communication scheme known as the Type-Based Random Access (TBRA) is employed and its performance is characterized with respect to the mean transmission rate and the channel coherence index. For extreme values of channel coherence index i.e., 0 and ∞, we give an optimal TBRA scheme which is essentially a sensor activation strategy that achieves the optimal allocation of transmission energy to spatial and temporal domains. For channels with zero coherence index, it is shown that there exists a finite optimal mean transmission rate maximizing performance. This optimal rate can be calculated numerically or estimated using the Gaussian approximation. On the other hand, for channels with infinite coherence index (i.e., no fading) the optimal strategy is to allocate all the energy to the spatial domain. Numerical examples and simulations confirm our theory. Index Terms—Signal Processing for Communications, distributed detection, distributed estimation, multi-sensor systems, performance analysis. I
High-Dimensional Covariance Decomposition into Sparse Markov and Independence Domains
Get PDFIn this paper, we present a novel frame-work incorporating a combination of sparse models in different domains. We posit the observed data as generated from a linear combination of a sparse Gaussian Markov model (with a sparse precision matrix) and a sparse Gaussian independence model (with a sparse covariance matrix). We provide efficient methods for decomposition of the data into two domains, viz., Markov and independence domains. We characterize a set of sufficient conditions for identifiability and model consistency. Our decomposition method is based on a simple modification of the popular `1-penalized maximum-likelihood estimator (`1-MLE). We establish that our estimator is consistent in both the domains, i.e., it successfully recovers the sup-ports of both Markov and independence models, when the number of samples n scales as n = Ω(d2 log p), where p is the number of variables and d is the maximum node degree in the Markov model. Our conditions for recovery are comparable to those of `1-MLE for consistent estimation of a sparse Markov model, and thus, we guarantee successful high-dimensional estimation of a richer class of models under comparable conditions. Our experiments validate these results and also demonstrate that our models have better inference accuracy under simple algorithms such as loopy belief propagation
Latent Graphical Model Selection: Efficient Methods for Locally Tree-like Graphs
No full textGraphical model selection refers to the problem of estimating the unknown graph structure given observations at the nodes in the model. We consider a challenging instance of this problem when some of the nodes are latent or hidden. We characterize conditions for tractable graph estimation and develop efficient methods with provable guarantees. We consider the class of Ising models Markov on locally tree-like graphs, which are in the regime of correlation decay. We propose an efficient method for graph estimation, and establish its structural consistency when the number of samples n scales as n = Ω(θ−δη(η+1)−2min log p), where θmin is the minimum edge potential, δ is the depth (i.e., distance from a hidden node to the nearest observed nodes), and η is a parameter which depends on the minimum and maximum node and edge potentials in the Ising model. The proposed method is practical to implement and provides flexibility to control the number of latent variables and the cycle lengths in the output graph. We also present necessary conditions for graph estimation by any method and show that our method nearly matches the lower bound on sample requirements
Tensor Computing for Internet of Things (Dagstuhl Perspectives Workshop 16152)
No full textThis report documents the program and the outcomes of Dagstuhl Perspectives Workshop 16152 "Tensor Computing for Internet of Things". In an interactive three-day workshop industrial and academic researchers exchanged their multidisciplinary perspectives through impulse talks, panel discussions, and break-out sessions. Internet of Things (IoT) or Cyber-physical systems (CPS) bring out interesting new challenges to tensor computing, such as the need for real-time analytics and control in interconnected dynamic networks, e.g. electricity, transportation, manufacturing. On the other hand, IoT/CPS have characteristics that make tensor methods applicable to extract information very efficiently. During our discussions we identified an action plan to have a structured approach that will enable the multidisciplinary community of domain and control experts, data scientists, and distributed, embedded software developers to share knowledge and best practices, compare and exchange tensor models depending on data types and applications in distinct IoT/CPS scenarios
Tensor Computing for Internet of Things (Dagstuhl Perspectives Workshop 16152)
No full text"The fundamental laws necessary for the mathematical treatment of large part of physics and the whole of chemistry are thus completely known, and the difficulty lies only in the fact that application of these laws leads to equations that are too complex to be solved." - Dirac 1929
The digital world of Internet of Things (IoT) will provide a high-resolution depiction of our physical world through measurements and other data - even high-definition "video," if you consider streaming data frames coming from a myriad of sensors embedded in everything we use. This depiction will have captured our interactions with the physical world and the interactions of digitally enhanced machines and devices. Tensors, as generalizations of vectors and matrices, provide a natural and scalable framework for handling data with such inherent structures and complex dependencies. Scalable tensor methods have attracted considerable amount of attention, with successes in a series of learning tasks, such as learning latent variable models, relational learning, spatio-temporal forecasting as well as training [19] and compression [20] of deep neural networks.
In a Dagstuhl Perspectives Workshop on Tensor Computing for IoT, we validated the fundamental suitability of tensor methods for handling the massive amounts of data coming from connected cyber-physical systems (CPS). The multidisciplinary discourse among academics, industrial researchers and practitioners in the IoT/CPS domain and in the field of machine learning and tensor methods, exposed open issues that need to be addressed to reap value from the technological opportunity. This Manifesto summarizes the immediate action fields for advancement: IoT Tensor Data Benchmarks, Tensor Tools for IoT, and the evolution of a Knowledge Hub. The activities will also be channeled to create best practices and a common tensor language across the disciplines.
In a not so distant future, basic infrastructures for living will be mainly data-driven, automated by digitally enhanced devices and machines. The tools and frameworks used to engineer such systems will ensure production-ready machine learning code which utilizes tensor-based, hence better interpretable, models and runs on distributed, decentralized, and embedded computing resources in a robust and reliable way. We conclude the manifesto with a strategy how to move towards this vision with concrete steps in the identified action fields
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