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The Minimax Distortion Redundancy in Empirical Quantizer Design

Peter L. Bartlett, Tamas Linder, Gábor Lugosi
1997 Social Science Research Network  
We obtain minimax lower and upper bounds for the expected distortion redundancy of empirically designed vector quantizers.  ...  T ogether with existing upper bounds this result shows that the minimax distortion redundancy for empirical quantizer design, as a function of the size of the training data, is asymptotically on the order  ...  In addition to this general lower bound, a new minimax upper bound for the empirically optimal quantizer is derived in Theorem 2. The bound is a constant times q k 1;2=d log n n .  ... 
doi:10.2139/ssrn.46990 fatcat:s5zbxs7mi5eapjxe246ldqb4um

The minimax distortion redundancy in empirical quantizer design

P.L. Bartlett, T. Linder, G. Lugosi
1998 IEEE Transactions on Information Theory  
We obtain minimax lower and upper bounds for the expected distortion redundancy of empirically designed vector quantizers.  ...  T ogether with existing upper bounds this result shows that the minimax distortion redundancy for empirical quantizer design, as a function of the size of the training data, is asymptotically on the order  ...  In addition to this general lower bound, a new minimax upper bound for the empirically optimal quantizer is derived in Theorem 2. The bound is a constant times q k 1;2=d log n n .  ... 
doi:10.1109/18.705560 fatcat:azumcd6k7za4lmqo7g6fpmejvq

Individual Convergence Rates in Empirical Vector Quantizer Design

A. Antos, L. Gyorfi, A. Gyorgy
2005 IEEE Transactions on Information Theory  
We prove that for any fixed distribution supported on a given finite set the convergence rate is (1 ) (faster than the minimax lower bound), where the corresponding constant depends on the source distribution  ...  Index Terms-Convergence rates, fixed-rate quantization, empirical design, individual convergence rate, log-concave densities.  ...  ACKNOWLEDGMENT The authors wish to thank Zsolt Bihary and Tamás Linder for useful discussions.  ... 
doi:10.1109/tit.2005.856976 fatcat:gf4vhrew2jbalit7alsiopctu4

Page 4364 of Mathematical Reviews Vol. , Issue 2001F [page]

2001 Mathematical Reviews  
Summary: “We obtain minimax lower and upper bounds for the expected distortion redundance of empirically designed vec- tor quantizers.  ...  We also derive a new upper bound for the performance of the empirically optimal quantizer.” 2001f:94007 94A40 94A24 Pazizin, S. V.  ... 

Nonasymptotic bounds for vector quantization in Hilbert spaces

Clément Levrard
2015 Annals of Statistics  
The dependency of the distortion on other parameters of distributions is then discussed, in particular through a minimax lower bound.  ...  Statist. 27 (1999) 1808-1829], under which a nonasymptotic upper bound on the expected distortion rate of the empirically optimal quantizer is derived.  ...  This minimax lower bound has to be compared to the upper risk bound obtained in Theorem 3.1 for the empirical risk minimizerĉ n over the set of distributions D(c 1 / √ n).  ... 
doi:10.1214/14-aos1293 fatcat:qvaqujdygnbllattbge4tf2coe

Efficient Adaptive Algorithms and Minimax Bounds for Zero-Delay Lossy Source Coding

A. Gyorgy, T. Linder, G. Lugosi
2004 IEEE Transactions on Signal Processing  
These bounds are based on learning-theoretic analyses of the minimax distortion redundancy in the design of empirically optimal quantizers [6] , [7] .  ...  By introducing a simplistic scheme and proving a lower bound, we show that for the class of bounded memoryless sources, the minimax expected distortion redundancy is upper and lower bounded by constant  ...  András György (S'01-A'03-M'04) was born in Budapest, Hungary, in 1976. He received the M.Sc. degree (with distinction) in technical informatics from the Technical University of Budapest, the M.Sc. de  ... 
doi:10.1109/tsp.2004.831128 fatcat:jozgifzzk5atzayypvmn5646qy

Page 6067 of Mathematical Reviews Vol. , Issue 98I [page]

1998 Mathematical Reviews  
Summary: “We obtain a minimax lower bound for the expected distortion of empirically designed vector quantizers.  ...  John Karlof (1-NCW; Wilmington, NC) 98i1:94009 94A29 Bartlett, Peter (S-ANUIF-SE; Canberra); Linder, Tamas (1-UCSD-EE; La Jolla, CA); Lugosi, Gabor A minimax lower bound for empirical quantizer design.  ... 

Minimax Learning for Remote Prediction [article]

Cheuk Ting Li, Xiugang Wu, Ayfer Ozgur, Abbas El Gamal
2018 arXiv   pre-print
We then establish information theoretic bounds on the risk-rate Lagrangian cost and a general method to design a near-optimal descriptor-estimator pair, which can be viewed as a rate-constrained analog  ...  Our results show that a naive estimate-compress scheme for rate-constrained prediction is not in general optimal.  ...  the lower bound given by the minimax risk-information costL * λ , and the upper bound given in Theorem 2.  ... 
arXiv:1806.00071v2 fatcat:y4slvferu5frvad7xtvwi6wyeu

On the training distortion of vector quantizers

T. Linder
2000 IEEE Transactions on Information Theory  
Earlier results provide lower bounds of the same order. Index Terms-Empirical design, training distortion, vector quantization, worst case bounds.  ...  For squared error distortion and independent training data, worst case type upper bounds are derived on the minimum training distortion achieved by an empirically optimal quantizer.  ...  This upper bound was shown to have the right order in a minimax sense in [5] , where it was demonstrated that for any quantizer design method, there exist "bad" source distributions for which the test  ... 
doi:10.1109/18.850705 fatcat:yudrx2n34nbk7hqvaazyvaffyu

Impedance Modeling of Virtual Synchronous Control of Doubly-Fed Wind Power System Under Weak Grid Condition

Tian Yang, Hui Li, Kun Wang, Yu Hu, Zhaosen Chai, Guisen Xia
2019 2019 22nd International Conference on Electrical Machines and Systems (ICEMS)  
We show that for sequences whose empirical distributions are monotonic, individual redundancy bounds even tighter than those in the average case can be obtained.  ...  The results are specifically true for finite entropy monotonic distributions. Finally, we study individual sequence redundancy behavior assuming a sequence is governed by a monotonic distribution.  ...  the individual minimax redundancy for coding a sequence believed to have an empirical monotonic distribution.  ... 
doi:10.1109/icems.2019.8922357 fatcat:lazp5ureqjbtff7r44z4gwmdxa

A low-complexity universal scheme for rate-constrained distributed regression using a wireless sensor network

Avon Loy Fernandes, Maxim Raginsky, Todd Coleman
2008 Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing  
We propose a scheme for rate-constrained distributed nonparametric regression using a wireless sensor network.  ...  dither and message passing between neighboring nodes in the network, and attains minimax optimality for regression functions in common smoothness classes.  ...  ACKNOWLEDGMENT The authors would like to thank the referees for their constructive criticism and for making numerous suggestions, which helped greatly improve the paper.  ... 
doi:10.1109/icassp.2008.4518098 dblp:conf/icassp/FernandesRC08 fatcat:d6ujc6i3bfcbhb3c2sc25o7wci

A Low-Complexity Universal Scheme for Rate-Constrained Distributed Regression Using a Wireless Sensor Network

A.L. Fernandes, M. Raginsky, T.P. Coleman
2009 IEEE Transactions on Signal Processing  
We propose a scheme for rate-constrained distributed nonparametric regression using a wireless sensor network.  ...  dither and message passing between neighboring nodes in the network, and attains minimax optimality for regression functions in common smoothness classes.  ...  ACKNOWLEDGMENT The authors would like to thank the referees for their constructive criticism and for making numerous suggestions, which helped greatly improve the paper.  ... 
doi:10.1109/tsp.2009.2013897 fatcat:x23bdxa2afhihldneqpvadopm4

Efficient Randomized Subspace Embeddings for Distributed Optimization under a Communication Budget [article]

Rajarshi Saha, Mert Pilanci, Andrea J. Goldsmith
2022 arXiv   pre-print
We propose computationally efficient optimization algorithms with convergence rates matching the information-theoretic performance lower bounds for: (i) Smooth and Strongly-Convex objectives with access  ...  The crux of these algorithms is a polynomial complexity source coding scheme that embeds a vector into a random subspace before quantizing it.  ...  and achieves the minimax lower bound to within constant factors.  ... 
arXiv:2103.07578v4 fatcat:3w4nleiw4rabbiegbtky4s52pe

On the MDL principle for i.i.d. sources with large alphabets

G.I. Shamir
2006 IEEE Transactions on Information Theory  
This result is shown to be the lower bound in the minimax and maximin senses, as well as for almost every source in the class.  ...  This bound is shown to be achievable both with two-part codes and with a sequential modification of the KT estimates. For = 2( ), the redundancy is 2(1) bits per symbol.  ...  He also wishes to thank the anonymous reviewers for very helpful suggestions.  ... 
doi:10.1109/tit.2006.872846 fatcat:jw5kxsfc2zgitj4yqywgmenvhu

Pointwise Bounds for Distribution Estimation under Communication Constraints [article]

Wei-Ning Chen, Peter Kairouz, Ayfer Özgür
2021 arXiv   pre-print
We also develop a new local minimax lower bound with (almost) matching ℓ_2 error, showing that any interactive scheme must admit a Ω( ‖ p ‖_(1+δ)/2/n2^b) ℓ_2 error for any δ > 0.  ...  The lower bound is derived by first finding the best parametric sub-model containing p, and then upper bounding the quantized Fisher information under this model.  ...  Acknowledgments This work was supported in part by a Google Faculty Research Award, a National Semiconductor Corporation Stanford Graduate Fellowship, and the National Science Foundation under grants CCF  ... 
arXiv:2110.03189v2 fatcat:llzlfnjwbvfrbi6d3e7xcofpr4
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