Over-the-Air Statistical Estimation

Lee, Chuan-Zheng; Barnes, Leighton Pate; Özgür, Ayfer

doi:10.1109/globecom42002.2020.9322345

Cited by 9 publications

(4 citation statements)

References 4 publications

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“…Similar ideas have been applied to Single Input Single Output (SISO) fading channels [13], and to Multiple Input Multiple Output (MIMO) channels [14]. More recent algorithms in this area include those described in [15,16,17,18,19] and the references therein.…”

Section: A Federated Learning and Over-the-air Federated Learningmentioning

confidence: 99%

PolarAir: A Compressed Sensing Scheme for Over-the-Air Federated Learning

Gkagkos¹,

Narayanan²,

Jean-Francois³

et al. 2023

Preprint

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We explore a scheme that enables the training of a deep neural network in a Federated Learning configuration over an additive white Gaussian noise channel. The goal is to create a low complexity, linear compression strategy, called PolarAir, that reduces the size of the gradient at the user side to lower the number of channel uses needed to transmit it. The suggested approach belongs to the family of compressed sensing techniques, yet it constructs the sensing matrix and the recovery procedure using multiple access techniques. Simulations show that it can reduce the number of channel uses by ∼30% when compared to conveying the gradient without compression. The main advantage of the proposed scheme over other schemes in the literature is its low time complexity. We also investigate the behavior of gradient updates and the performance of PolarAir throughout the training process to obtain insight on how best to construct this compression scheme based on compressed sensing.

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Section: A Federated Learning and Over-the-air Federated Learningmentioning

confidence: 99%

PolarAir: A Compressed Sensing Scheme for Over-the-Air Federated Learning

Gkagkos¹,

Narayanan²,

Jean-Francois³

et al. 2023

Preprint

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“…To get (8) we have used the Cauchy-Schwarz inequality, and (9) follows by using the sub-Gaussianity of each of the (dB) 2 different terms in S θ (X) 4 2 to bound their fourth moments. Combining ( 7) and (9),…”

Section: Fisher Information Boundmentioning

confidence: 99%

“…Other works such as [8] have also considered statistical inference under communication and privacy constraints, but have not considered the more general class of mutual information constrained channels. One application where general mutual information constrained channels are needed is when communication of statistical samples is done over an analog channel such as an additive white Gaussian noise channel or Gaussian multiple access channel, such as in recent works [9] and [10] which seek to jointly study the communication and estimation problem.…”

Section: Introductionmentioning

confidence: 99%

Fisher Information and Mutual Information Constraints

Barnes¹,

Özgür²

2021

Preprint

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We consider the processing of statistical samples X ∼ P θ by a channel p(y|x), and characterize how the statistical information from the samples for estimating the parameter θ ∈ R d can scale with the mutual information or capacity of the channel. We show that if the statistical model has a sub-Gaussian score function, then the trace of the Fisher information matrix for estimating θ from Y can scale at most linearly with the mutual information between X and Y . We apply this result to obtain minimax lower bounds in distributed statistical estimation problems, and obtain a tight preconstant for Gaussian mean estimation. We then show how our Fisher information bound can also imply mutual information or Jensen-Shannon divergence based distributed strong data processing inequalities.

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“…All nodes, synchronized with the sink, transmit their signals simultaneously, which are added together in the air by exploiting the superposition property of wireless communication. Although analog communication seems to be error prone, actually it can achieve much smaller computation error than its digital counterpart when using the same amount of resources [5].…”

Section: Introductionmentioning

confidence: 99%

Miso: Misalignment Allowed Optimization for Multiantenna Over-the-Air Computation

Tang

Zhang

et al. 2024

IEEE Internet Things J.

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Over-the-air computation (AirComp), as an effective method to wireless data aggregation, has attracted much attention recently. It helps to improve network efficiency and scalability by integrating communication and computation in the air. In AirComp, both signal magnitude misalignment and noise lead to computation error. In the single antenna case, by allowing misalignment in signal magnitude, a good tradeoff can be achieved between signal distortion and noise power, which leads to a minimal error. In the multi-antenna case, usually the zeroforcing policy is used to enforce signal magnitude alignment (no distortion), which, however, increases noise and affects the overall computation error. To better exploit multiple antennas at the sink, in this paper, we propose a misalignment allowed optimization (Miso) method for AirComp. Specifically, a group of nodes whose signals may be misaligned are dynamically selected, and other signals are aligned to a higher level with higher quality. On this basis, the optimization of multi-antenna AirComp is converted to a difference of convex problem and is solved iteratively. Simulations confirm that the proposed method greatly reduces computation error and scales better with the number of nodes, compared with previous methods.

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Over-the-Air Statistical Estimation

Cited by 9 publications

References 4 publications

PolarAir: A Compressed Sensing Scheme for Over-the-Air Federated Learning

PolarAir: A Compressed Sensing Scheme for Over-the-Air Federated Learning

Fisher Information and Mutual Information Constraints

Miso: Misalignment Allowed Optimization for Multiantenna Over-the-Air Computation

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