NDLI: Information recovery from pairwise measurements

Content Provider	IEEE Xplore Digital Library
Author	Yuxin Chen Goldsmith, A.J.
Copyright Year	2014
Description	Author affiliation: Electr. Eng., Stanford Univ., Stanford, CA, USA (Yuxin Chen; Goldsmith, A.J.)
Abstract	A variety of information processing tasks in practice involve recovering n objects from single-shot graph-based measurements, particularly those taken over the edges of some measurement graph G. This paper concerns the situation where each object takes value over a group of M different values, and where one is interested to recover all these values based on observations of certain pairwise relations over G. The imperfection of measurements presents two major challenges for information recovery: 1) inaccuracy: a (dominant) portion 1 - p of measurements are corrupted; 2) incompleteness: a significant fraction of pairs are unobservable, i.e. G can be highly sparse. Under a natural random outlier model, we characterize the minimax recovery rate, that is, the critical threshold of non-corruption rate p below which exact information recovery is infeasible. This accommodates a very general class of pairwise relations. For various homogeneous random graph models (e.g. Erdös-Rényi random graphs, random geometric graphs, small world graphs), the minimax recovery rate depends almost exclusively on the edge sparsity of the measurement graph G irrespective of other graphical metrics. This fundamental limit decays with the group size M at a square root rate before entering a connectivity-limited regime. Under the Erdös-Rényi random graph, a tractable combinatorial algorithm is proposed to approach the limit for large M (M = $n^{Ω(1)}),$ while order-optimal recovery is enabled by semidefinite programs in the small M regime.
Starting Page	2012
Ending Page	2016
File Size	531721
Page Count	5
File Format	PDF
ISBN	9781479951864
ISSN	21578117
DOI	10.1109/ISIT.2014.6875186
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2014-06-29
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Joints Information theory Electric variables measurement Covariance matrices Robustness Noise measurement
Content Type	Text
Resource Type	Article

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