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Randomized Greedy Sensor Selection: Leveraging Weak Submodularity [article]

Abolfazl Hashemi, Mahsa Ghasemi, Haris Vikalo, Ufuk Topcu
2018 arXiv   pre-print
We develop an efficient randomized greedy algorithm for sensor selection and establish guarantees on the estimator's performance in this setting.  ...  For the MMSE estimation criterion we show that the maximum element-wise curvature of the objective function satisfies a certain upper-bound constraint and is, therefore, weak submodular.  ...  SENSOR SELECTION VIA OPTIMIZING A WEAK SUBMODULAR OBJECTIVE Leveraging the idea of weak submodularity, in this section we propose a new formulation of the sensor selection problem concerned with minimizing  ... 
arXiv:1807.08627v1 fatcat:ca6q27wwrzdyvlmqcbrwlozw4m

A Randomized Greedy Algorithm for Near-Optimal Sensor Scheduling in Large-Scale Sensor Networks [article]

Abolfazl Hashemi, Mahsa Ghasemi, Haris Vikalo, Ufuk Topcu
2018 arXiv   pre-print
(MSE) of the estimator that uses the selected sensors in terms of the optimal MSE.  ...  We propose a randomized greedy algorithm that is significantly faster than state-of-the-art methods.  ...  by leveraging the idea of weak submodularity.  ... 
arXiv:1709.08823v2 fatcat:jziwyc2xwzc2rfcoa3pjbcqss4

Causal meets Submodular: Subset Selection with Directed Information

Yuxun Zhou, Costas J. Spanos
2016 Neural Information Processing Systems  
Two typical tasks, causal sensor placement and covariate selection, are correspondingly formulated into cardinality constrained directed information maximizations.  ...  Moreover, we show that based on SmI, greedy algorithm has performance guarantee for the maximization of possibly non-monotonic and non-submodular functions, justifying its usage for a much broader class  ...  Yet one may wonder that if the conditional dependence is weak or sparse, possibly a greedy selection still works to some extent because the submodularity is not severely deteriorated.  ... 
dblp:conf/nips/ZhouS16 fatcat:mdkovi2xvncuhpxvriwo3x7tki

Determinant-based Fast Greedy Sensor Selection Algorithm [article]

Yuji Saito, Taku Nonomura, Keigo Yamada, Keisuke Asai, Yasuo Sasaki, Daisuke Tsubakino
2020 arXiv   pre-print
determinant-based greedy method which is accelerated by both determinant formula and matrix inversion lemma.  ...  Then, the unified formulation of both algorithms is derived, and the lower bound of the objective function given by this algorithm is shown using the monotone submodularity.  ...  A random selection and the convex approximation method [13] are evaluated as the references in addition to greedy methods.  ... 
arXiv:1911.08757v4 fatcat:rrfw7z4gb5d7ba7ncpamgoyjk4

Greedy Dictionary Selection for Sparse Representation

Volkan Cevher, Andreas Krause
2011 IEEE Journal on Selected Topics in Signal Processing  
We exploit this property to develop SDSOMP and SDSMA, two greedy algorithms with approximation guarantees.  ...  We show that if the available dictionary column vectors are incoherent, our objective function satisfies approximate submodularity.  ...  In sensor networks, multiple sensors simultaneously observe a sparse signal over a noisy channel.  ... 
doi:10.1109/jstsp.2011.2161862 fatcat:wppvskirxvdn3oas6ca6df2qii

Lazy FSCA for Unsupervised Variable Selection [article]

Federico Zocco, Marco Maggipinto, Gian Antonio Susto, Seán McLoone
2022 arXiv   pre-print
Theoretical results exist that provide performance bounds and enable "lazy greedy" efficient implementations for selection criteria that satisfy a diminishing returns property known as submodularity.  ...  Various unsupervised greedy selection methods have been proposed as computationally tractable approximations to the NP-hard subset selection problem.  ...  [12] Based on weak submodularity [13] PFS [10] FSCA [11] Based on submodularity [12] Based on weak submodularity Finding the optimal subset of variables from a set of candidate variables is  ... 
arXiv:2103.02687v2 fatcat:kiiw2cpuzjdzhcav4ylq2pxxgi

Performance-Complexity Tradeoffs in Greedy Weak Submodular Maximization with Random Sampling [article]

Abolfazl Hashemi, Haris Vikalo, Gustavo de Veciana
2021 arXiv   pre-print
For such problems, a simple greedy algorithm (Greedy) is guaranteed to find a solution achieving the objective with a value no worse than 1-e^-1/c of the optimal, where c is the multiplicative weak-submodularity  ...  Many problems in signal processing and machine learning can be formalized as weak submodular optimization tasks.  ...  [41] analyze STOCHASTIC-GREEDY for weak submodular functions and show that it Algorithm 2 GREEDY with Random Sampling 1: Input: Weak submodular function f , ground set X , number of elements to be selected  ... 
arXiv:1907.09064v3 fatcat:5li7u52irzh43flokvaojfeyti

Greedy Sensor Selection for Weighted Linear Least Squares Estimation under Correlated Noise [article]

Keigo Yamada, Yuji Saito, Taku Nonomura, Keisuke Asai
2022 arXiv   pre-print
An algorithm for greedy sensor selection is presented under the assumption of correlated noise in the sensor signals.  ...  Optimization of sensor selection has been studied to monitor complex and large-scale systems with data-driven linear reduced-order modeling.  ...  Thus, the sensor selection problem Eq. ( 6 ) with a greedy method generally has no performance guarantee based on submodularity or supermodularity.  ... 
arXiv:2104.12951v2 fatcat:c2sjovz6rbdddjamyt27efbj74

Sensor Selection via Randomized Sampling [article]

Shaunak D. Bopardikar
2018 arXiv   pre-print
First, we present a randomized algorithm that samples the sensors with replacement as per specified distributions.  ...  Second, with a different distribution, we derive high probability bounds on other standard metrics used in sensor selection, including the minimum eigenvalue or the trace of the Gramian inverse.  ...  With a fixed budget on the number of sensors that can be used, recent work [11] addresses the use of randomization for sensor scheduling and uses weak submodularity to performance guarantees on the mean  ... 
arXiv:1712.06511v3 fatcat:mrrwwbvy4fek3o7piyfaoaivrq

Near-optimal Nonmyopic Value of Information in Graphical Models [article]

Andreas Krause, Carlos E. Guestrin
2012 arXiv   pre-print
The algorithm leverages the theory of submodular functions, in combination with a polynomial bound on sample complexity.  ...  A fundamental issue in real-world systems, such as sensor networks, is the selection of observations which most effectively reduce uncertainty.  ...  In this paper, by leveraging the theory of submodular functions [16] , we present the first efficient randomized algorithm providing a constant factor (1 − 1/e − ε) approximation guarantee for any ε >  ... 
arXiv:1207.1394v1 fatcat:6m7nwn67trhozcxlelnfz6wahe

Sampling and Reconstruction of Graph Signals via Weak Submodularity and Semidefinite Relaxation [article]

Abolfazl Hashemi, Rasoul Shafipour, Haris Vikalo, Gonzalo Mateos
2017 arXiv   pre-print
Moreover, we provide an alternative formulation based on maximizing a monotone weak submodular function and propose a randomized-greedy algorithm to find a sub-optimal subset.  ...  Notably, the randomized greedy algorithm yields an order-of-magnitude speedup over state-of-the-art greedy sampling schemes, while incurring only a marginal MSE performance loss.  ...  Our proposed algorithms are based on semidefinite and weak submodular optimization techniques that have recently shown superior performance in applications such as sensor selection [21] , graph sketching  ... 
arXiv:1711.00142v1 fatcat:ykku6nwkjbdlhascabh3vuirae

Near-Optimal Distributed Estimation for a Network of Sensing Units Operating Under Communication Constraints [article]

Abolfazl Hashemi, Osman Fatih Kilic, Haris Vikalo
2018 arXiv   pre-print
By leveraging the notion of weak submodularity, we develop an efficient greedy algorithm for the proposed formulation and show that the greedy algorithm achieves a constant factor approximation of the  ...  Our extensive simulation studies illustrate the efficacy of the proposed formulation and the greedy algorithm.  ...  A randomized greedy approach proposed in [8] leverages the weak submodularity of the mean-square error (MSE) objective in the sensor selection problem.  ... 
arXiv:1807.07650v1 fatcat:axv7cuazcnbczijibegkb7kjva

Approximate Submodular Functions and Performance Guarantees [article]

Gaurav Gupta and Sergio Pequito and Paul Bogdan
2018 arXiv   pre-print
Nonetheless, often we leverage the greedy algorithms used in submodular functions to determine a solution to the non-submodular functions.  ...  Furthermore, submodular functions are known to lead to different sub-optimality guarantees, so we generalize those dependencies upon a δ-approximation into the notion of greedy curvature.  ...  A comparison of the performance of Greedy and random selection of sensors for all 4 tasks is presented in (c) with box plots for random selection. .  ... 
arXiv:1806.06323v1 fatcat:7xwha2stcvbwdhpm7kaep4t73m

Submodular Sparse Sensing for Gaussian Detection With Correlated Observations

Mario Coutino, Sundeep Prabhakar Chepuri, Geert Leus
2018 IEEE Transactions on Signal Processing  
In this work, different from the widely used convex relaxation of the problem, we leverage submodularity, the diminishing returns property, to provide practical near optimal algorithms suitable for large-scale  ...  ., either physical, economical or computational constraints, the selection of a subset of available sensors, referred to as sparse sensing, that meets both the budget and performance requirements is highly  ...  For random Fig. 4 : 4 (a) KL divergence of the different sensor selection methods for different subset sizes K for random covariance matrices.  ... 
doi:10.1109/tsp.2018.2846220 fatcat:4rstpaxtdbbwdoviz2zomgdhoa

Submodularity in Action: From Machine Learning to Signal Processing Applications [article]

Ehsan Tohidi, Rouhollah Amiri, Mario Coutino, David Gesbert, Geert Leus, Amin Karbasi
2020 arXiv   pre-print
We introduce a variety of submodular-friendly applications, and elucidate the relation of submodularity to convexity and concavity which enables efficient optimization.  ...  Submodular functions exhibit strong structure that lead to efficient optimization algorithms with provable near-optimality guarantees.  ...  This setting is similar to that of [6] , where the approximate submodularity of the signalto-noise ratio (same functional form as (12) ) is leveraged in sensor selection for detection of signals under  ... 
arXiv:2006.09905v1 fatcat:ksn2bqbdczechktpa6ivcpwcau
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