We consider universal decentralized estimation of a noise-corrupted signal by a bandwidth constrained sensor network with a fusion center (FC). We show that in a homogeneous sensing environment and under a bandwidth constraint of 1-bit per sample per node, there exist universal decentralized estimation schemes (DES) with a mean squared error (MSE) decreasing at the rate 1/K, where K is the total number of sensors. We extend such 1bit decentralized estimators to the case of inhomogeneous sensing environment, and propose quantization and transmission power control strategies for local sensors in order to minimize the total consumed sensor energy while ensuring a given MSE performance. We also design a DES for the joint estimation of a vector source based on its noisy and linearly distorted observations, and show that to achieve a MSE within a factor of 2 away from the best linear unbiased estimator (BLUE), the local message length has a nice form of being the channel capacity of “a virtual AWGN channel ” from “nature ” to each local sensor. 1.

Signal estimation from a sequential encoding in the form of quantized noisy measurements is considered. As an example context, this problem arises in a number of remote sensing applications, where a central site estimates an information-bearing signal from low-bandwidth digitized information received from remote sensors, and may or may not broadcast feedback information to the sensors. We demonstrate that the use of an appropriately designed and often easily implemented additive control input before signal quantization at the sensor can significantly enhance overall system performance. In particular, we develop efficient estimators in conjunction with optimized random, deterministic, and feedback-based control inputs, resulting in a hierarchy of systems that trade performance for complexity.

Consider a decentralized estimation problem whereby an ad hoc network of K distributed sensors wish to cooperate to estimate an unknown parameter over a bounded interval [−U, U]. Each sensor collects one noise-corrupted sample, performs a local data quantization according to a fixed (but possibly probabilistic) rule, and transmits the resulting discrete message to its neighbors. These discrete messages are then percolated in the network and used by each sensor to form its own minimum mean squared error (MMSE) estimate of the unknown parameter according to a fixed fusion rule. In this paper we propose a simple probabilistic local quantization rule: each sensor quantizes its observation to the first most significant bit (MSB) with probability 1/2, the second MSB with probability 1/4, and so on. Assuming the noises are i.i.d. across sensors and are bounded to [−U, U], we show that this local quantization strategy together with a fusion rule can guarantee a mean squared error of 4U 2 /K, and that the average length of local messages is bounded (no more than 2.5 bits). Compared to the Cramer-Rao lower bound of U 2 /K (even for the centralized counterpart), this is within a factor of at most 4 to the minimum achievable MSE. Moreover, the proposed scheme is isotropic and universal in the sense that the local quantization rules and the final fusion rules are independent of sensor index, noise distribution, network size or topology. In fact, the proposed scheme allows sensors in the network to operate identically and autonomously even when the network undergos changes in size or topology.

A wireless sensor network (WSN) consists of a large number of spatially distributed signal processing devices (nodes), each with finite battery lifetime and thus limited computing and communication capabilities. When properly programmed and networked, nodes in a WSN can cooperate to perform advanced signal processing tasks with unprecedented robustness and versatility, thus making WSN an attractive low-cost technology for a wide range of remote sensing and environmental monitoring applications [1], [32].

Abstract—We consider decentralized estimation of a noise-corrupted deterministic parameter by a bandwidth-constrained sensor network with a fusion center. The sensor noises are assumed to be additive, zero mean, spatially uncorrelated, but otherwise unknown and possibly different across sensors due to varying sensor quality and inhomogeneous sensing environment. The classical best linear unbiased estimator (BLUE) linearly combines the real-valued sensor observations to minimize the mean square error (MSE). Unfortunately, such a scheme cannot be implemented in a practical bandwidth-constrained sensor network due to its requirement to transmit real-valued messages. In this paper, we construct a decentralized estimation scheme (DES) where each sensor compresses its observation to a small number of bits with length proportional to the logarithm of its local signal-to-noise ratio (SNR). The resulting compressed bits from different sensors are then collected and combined by the fusion center to estimate the unknown parameter. The proposed DES is universal in the sense that each sensor compression scheme requires only the knowledge of local SNR, rather than the noise probability distribution functions (pdf), while the final fusion step is also independent of the local noise pdfs. We show that the MSE of the proposed DES is within a constant factor of PS V of that achieved by the classical centralized BLUE estimator. Index Terms—Best linear unbiased estimator (BLUE), bit allocation, distributed estimation, sensor networks, universal randomized quantization. I.

In this paper, we present a general machine learning approach to the problem of deciding when to share probabilistic beliefs between agents for distributed monitoring. Our approach can generally be applied to domains that use a probabilistic model for evaluating hypotheses, and have a method for combining beliefs from multiple agents. We demonstrate the effectiveness of our approach in a concrete application in network intrusion detection as an example of a multi-agent monitoring problem. Based on an evaluation using packet trace data from a real network, we demonstrate that our learning approach can reduce both the delay and communication overhead required to detect network intrusions. 1.

Abstract — Consider a bandwidth constrained sensor network in which a set of distributed sensors and a fusion center (FC) collaborate to estimate an unknown vector. Due to power and cost limitations, each sensor must compress its data in order to minimize the amount of information that need to be communicated to the FC. In this paper, we consider the design of a linear decentralized estimation scheme (DES) whereby each sensor transmits over a noisy channel to the FC a fixed number of real-valued messages which are linear functions of its observations, while the FC linearly combines the received messages to estimate the unknown parameter vector. Assuming each sensor collects data according to a local linear model, we propose to design optimal linear message functions and linear fusion function according to the minimum mean squared error (MMSE) criterion. We show that the resulting design problem is nonconvex and NP-hard in general, and identify two special cases for which the optimal linear DES design problem can be efficiently solved either in closed form or by Semi-definite programming (SDP). I.

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In this paper, we present an information sharing model for distributed intrusion detection systems. The typical challenges faced by distributed intrusion detection systems is what information to share and how to share information. We address these problems by using the Cumulative Sum algorithm to collect statistics at each local system, and use a machine learning approach to coordinate the information sharing among the distributed detection systems. Our major contributions are two-fold. First, we propose a simple but robust scheme to monitor changes in the local statistics. Second, we present a learning algorithm to decide when to share information so that both the communication overhead among the distributed detection systems and the detection delay are minimized. We demonstrate the application of our information sharing model to a specific distributed intrusion detection scenario. We show that our approach is able to optimize the trade-off between the time required to detect an attack, and the volume of communication between the distributed intrusion detection systems. I.

We compare Bayes Model Averaging, BMA, to a non-Bayes form of model averaging called stacking. In stacking, the weights are no longer posterior probabilities of models; they are obtained by a technique based on cross-validation. When the correct data generating model (DGM) is on the list of models under consideration BMA is never worse than stacking and often is demonstrably better, provided that the noise level is of order commensurate with the coefficients and explanatory variables. Here, however, we focus on the case that the correct DGM is not on the model list and may not be well approximated by the elements on the model list. We give a sequence of computed examples by choosing model lists and DGM’s to contrast the risk performance of stacking and BMA. In the first examples, the model lists are chosen to reflect geometric principles that should give good performance. In these cases, stacking typically outperforms BMA, sometimes by a wide margin. In the second set of examples we examine how stacking and BMA perform when the model list includes all subsets of a set of potential predictors. When we standardize the size of terms and coefficients in this setting, we find that BMA outperforms stacking when the deviant terms in the DGM ‘point ’ in directions accommodated by the model list but that when the deviant term points outside the model list stacking seems to do better. Overall, our results suggest the stacking has better robustness properties than BMA in the most important settings.