Sparse sensing for distributed gaussian detection

Chepuri, Sundeep Prabhakar; Leus, Geert

doi:10.1109/icassp.2015.7178400

Cited by 14 publications

(9 citation statements)

References 12 publications

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“…It is clear from (25) that when an inactive sensor is made active, the increase in Fisher information leads to an information gain in terms of the rank-one matrix given by (25). Such a phenomenon was also discovered in the calculation of sensor utility for adaptive signal estimation [29] and leader selection in stochastically forced consensus networks [12].…”

Section: B Greedy Algorithmmentioning

confidence: 89%

Sensor Selection for Estimation with Correlated Measurement Noise

Liu

Chepuri

Fardad

et al. 2016

IEEE Trans. Signal Process.

Self Cite

166

107

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Abstract-In this paper, we consider the problem of sensor selection for parameter estimation with correlated measurement noise. We seek optimal sensor activations by formulating an optimization problem, in which the estimation error, given by the trace of the inverse of the Bayesian Fisher information matrix, is minimized subject to energy constraints. Fisher information has been widely used as an effective sensor selection criterion. However, existing information-based sensor selection methods are limited to the case of uncorrelated noise or weakly correlated noise due to the use of approximate metrics. By contrast, here we derive the closed form of the Fisher information matrix with respect to sensor selection variables that is valid for any arbitrary noise correlation regime, and develop both a convex relaxation approach and a greedy algorithm to find near-optimal solutions. We further extend our framework of sensor selection to solve the problem of sensor scheduling, where a greedy algorithm is proposed to determine non-myopic (multi-time step ahead) sensor schedules. Lastly, numerical results are provided to illustrate the effectiveness of our approach, and to reveal the effect of noise correlation on estimation performance.

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Section: B Greedy Algorithmmentioning

confidence: 89%

Sensor Selection for Estimation with Correlated Measurement Noise

Liu

Chepuri

Fardad

et al. 2016

IEEE Trans. Signal Process.

Self Cite

166

107

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show abstract

“…In particular, the Chernoff information [14,15] is asymptotically (in N) relied on the exponential rate of P (N) e . It turns out that the Chernoff information is very useful in many practically important problems as for instance, distributed sparse detection [16], sparse support recovery [17], energy detection [18], multi-input and multi-output (MIMO) radar processing [19,20], network secrecy [21], angular resolution limit in array processing [22], detection performance for informed communication systems [23], just to name a few. In addition, the Chernoff information bound can be tight for a minimal s-divergence over parameter s ∈ (0, 1).…”

Section: State-of-the-art and Problem Statementmentioning

confidence: 99%

“…We can notice that for Q = 1, the result 5 is similar to result 1. However, when Q ≥ 2, the integrals in Equation (16) are not tractable in a closed-form expression. For instance, let Q = 2, we consider the integral…”

Section: Remarkmentioning

confidence: 99%

Computational Information Geometry for Binary Classification of High-Dimensional Random Tensors

Pham

Boyer

Nielsen

2018

Entropy

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Evaluating the performance of Bayesian classification in a high-dimensional random tensor is a fundamental problem, usually difficult and under-studied. In this work, we consider two Signal to Noise Ratio (SNR)-based binary classification problems of interest. Under the alternative hypothesis, i.e., for a non-zero SNR, the observed signals are either a noisy rank-R tensor admitting a Q-order Canonical Polyadic Decomposition (CPD) with large factors of size N q × R, i.e., for 1 ≤ q ≤ Q, where R, N q → ∞ with R 1/q /N q converge towards a finite constant or a noisy tensor admitting TucKer Decomposition (TKD) of multilinear (M 1 ,. .. , M Q)-rank with large factors of size N q × M q , i.e., for 1 ≤ q ≤ Q, where N q , M q → ∞ with M q /N q converge towards a finite constant. The classification of the random entries (coefficients) of the core tensor in the CPD/TKD is hard to study since the exact derivation of the minimal Bayes' error probability is mathematically intractable. To circumvent this difficulty, the Chernoff Upper Bound (CUB) for larger SNR and the Fisher information at low SNR are derived and studied, based on information geometry theory. The tightest CUB is reached for the value minimizing the error exponent, denoted by s. In general, due to the asymmetry of the s-divergence, the Bhattacharyya Upper Bound (BUB) (that is, the Chernoff Information calculated at s = 1/2) cannot solve this problem effectively. As a consequence, we rely on a costly numerical optimization strategy to find s. However, thanks to powerful random matrix theory tools, a simple analytical expression of s is provided with respect to the Signal to Noise Ratio (SNR) in the two schemes considered. This work shows that the BUB is the tightest bound at low SNRs. However, for higher SNRs, the latest property is no longer true.

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“…The key idea of expressing (7) as an explicit function of w is to replace Φ w with w based on their relationship given by (4). Consider a decomposition of the noise covariance matrix [25]…”

Section: B Fisher Information J W As An Explicit Function Of Wmentioning

confidence: 99%

“…given w, enumerate all the inactive sensors in I to determine j ∈ I such that tr(J −1 w ) − tr(J −1 w ) in ( 26) is maximized 3: update w by setting w j = 1, and update J w by adding c j α j α T j in (25) 4:…”

Section: Algorithm 3 Greedy Algorithm For Sensor Selectionmentioning

confidence: 99%

Sensor Selection for Estimation with Correlated Measurement Noise

Liu,

Chepuri,

Fardad

et al. 2015

Preprint

Self Cite

View full text Add to dashboard Cite

In this paper, we consider the problem of sensor selection for parameter estimation with correlated measurement noise. We seek optimal sensor activations by formulating an optimization problem, in which the estimation error, given by the trace of the inverse of the Bayesian Fisher information matrix, is minimized subject to energy constraints. Fisher information has been widely used as an effective sensor selection criterion. However, existing information-based sensor selection methods are limited to the case of uncorrelated noise or weakly correlated noise due to the use of approximate metrics. By contrast, here we derive the closed form of the Fisher information matrix with respect to sensor selection variables that is valid for any arbitrary noise correlation regime, and develop both a convex relaxation approach and a greedy algorithm to find near-optimal solutions. We further extend our framework of sensor selection to solve the problem of sensor scheduling, where a greedy algorithm is proposed to determine non-myopic (multi-time step ahead) sensor schedules. Lastly, numerical results are provided to illustrate the effectiveness of our approach, and to reveal the effect of noise correlation on estimation performance.

show abstract

Sparse sensing for distributed gaussian detection

Cited by 14 publications

References 12 publications

Sensor Selection for Estimation with Correlated Measurement Noise

Sensor Selection for Estimation with Correlated Measurement Noise

Computational Information Geometry for Binary Classification of High-Dimensional Random Tensors

Sensor Selection for Estimation with Correlated Measurement Noise

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