Proceedings ArticleDOI
Sequential functional quantization
Vinith Misra,Krishnamurthy Viswanathan +1 more
- pp 2359-2363
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TLDR
In this article, the authors consider the problem of companding quantization under non-difference distortion measures, and derive the optimal distortion-rate exponent for quantization with sensitivity matrices.Abstract:
We consider the problem of lossy estimation of an arbitrary smooth function of correlated data in a stream. In this problem, a user sequentially observes correlated random variables and wants to construct an estimate of the specified function so that the mean squared estimation error is small. Techniques from high resolution quantization theory are applied and expanded for this problem, and the optimal distortion-rate exponent for companding quantization is determined. In the process, connections are established to sufficient statistics and to sensitivity matrices, as introduced by Linder et al. in the context of companding quantization under non-difference distortion measures. These results are applied to several example statistical functions, including the sample mean, sample variance, and the p-th order statistic.read more
Citations
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Journal ArticleDOI
Rate Distortion for Lossy In-Network Linear Function Computation and Consensus: Distortion Accumulation and Sequential Reverse Water-Filling
TL;DR: This work quantifies the accumulation of information loss in distributed computing, and obtains fundamental limits on network computation rate as a function of incremental distortions (and hence incremental loss of information) along the edges of the network.
Proceedings ArticleDOI
Towards optimal quantization of neural networks
TL;DR: This work develops an approach to quantizing deep networks using functional high-rate quantization theory and leads to an optimal quantizer that is computed using the celebrated backpropagation algorithm.
Dissertation
Quantization in acquisition and computation networks
TL;DR: This thesis characterize fundamental trade-offs when the desired computation is incorporated into the compression design and the code length is one, and determines the optimal quantizer for expected relative error (ERE), a measure that is widely useful but is often neglected in the source coding community.
Proceedings ArticleDOI
Coding for lossy function computation: Analyzing sequential function computation with distortion accumulation
TL;DR: The key in applying the analysis of Distortion Accumulation is showing that the random-coding based codeword on the receiver side is close in mean-square sense to the MMSE estimate of the sources, even if the knowledge of the source distribution is not fully accurate.
Proceedings ArticleDOI
Information dissipation in noiseless lossy in-network function computation
TL;DR: Lower bounds on the rate-distortion function are obtained that are tighter than classical cut-set bounds by a difference which can be arbitrarily large in both data aggregation and consensus.
References
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