Pub Date : 1994-10-27DOI: 10.1109/WITS.1994.513881
B. Hajek
A load balancing problem is formulated for infinite networks or graphs. There are overlapping sets of locations, each set having an associated possibly random amount of load to be distributed. The total load at a location is the sum of the contributions due to the sets that contain it. Equilibrium is said to hold if the load corresponding to any one set cannot be reassigned to improve the balance of total loads. The set of possible equilibria, or balanced load vectors, is examined. The balanced load vector is shown to be unique for Euclidean lattice networks, in which the sets correspond to pairs of neighboring nodes in a rectangular lattice in finite dimensions. A method for computing the load distribution is explored for tree networks. An FKG type inequality is proved. The concept of load percolation is introduced and is shown to be associated with infinite sets of locations with identical load.
{"title":"Equilibria in infinite random graphs","authors":"B. Hajek","doi":"10.1109/WITS.1994.513881","DOIUrl":"https://doi.org/10.1109/WITS.1994.513881","url":null,"abstract":"A load balancing problem is formulated for infinite networks or graphs. There are overlapping sets of locations, each set having an associated possibly random amount of load to be distributed. The total load at a location is the sum of the contributions due to the sets that contain it. Equilibrium is said to hold if the load corresponding to any one set cannot be reassigned to improve the balance of total loads. The set of possible equilibria, or balanced load vectors, is examined. The balanced load vector is shown to be unique for Euclidean lattice networks, in which the sets correspond to pairs of neighboring nodes in a rectangular lattice in finite dimensions. A method for computing the load distribution is explored for tree networks. An FKG type inequality is proved. The concept of load percolation is introduced and is shown to be associated with infinite sets of locations with identical load.","PeriodicalId":423518,"journal":{"name":"Proceedings of 1994 Workshop on Information Theory and Statistics","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129764456","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1994-10-27DOI: 10.1109/WITS.1994.513853
I. Csiszár
Originally coming from physics, maximum entropy (ME) has been promoted to a general principle of inference primarily by the works of Jaynes. ME applies to the problem of inferring a probability mass (or density) function, or any non-negative function p(x), when the available information specifies a set E of feasible functions, and there is a prior guess q /spl notin/ E. The author will review the arguments that have been put forward for justifying ME. In this author's opinion, the strongest theoretical support to ME is provided by the axiomatic approach. This shows that, in some sense, ME is the only logically consistent method of inferring a function subject to linear constraints.
{"title":"Maximum entropy and related methods","authors":"I. Csiszár","doi":"10.1109/WITS.1994.513853","DOIUrl":"https://doi.org/10.1109/WITS.1994.513853","url":null,"abstract":"Originally coming from physics, maximum entropy (ME) has been promoted to a general principle of inference primarily by the works of Jaynes. ME applies to the problem of inferring a probability mass (or density) function, or any non-negative function p(x), when the available information specifies a set E of feasible functions, and there is a prior guess q /spl notin/ E. The author will review the arguments that have been put forward for justifying ME. In this author's opinion, the strongest theoretical support to ME is provided by the axiomatic approach. This shows that, in some sense, ME is the only logically consistent method of inferring a function subject to linear constraints.","PeriodicalId":423518,"journal":{"name":"Proceedings of 1994 Workshop on Information Theory and Statistics","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129793099","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1994-10-27DOI: 10.1109/WITS.1994.513909
R. Zamir, M. Feder
A matrix form of the Brunn-Minkowski inequality is derived, which may be applied in calculating the uncoded bit rate of lattice quantization and modulation schemes.
导出了布伦-闵可夫斯基不等式的矩阵形式，可用于计算点阵量化和调制方案的非编码比特率。
{"title":"A matrix form of the Brunn-Minkowski inequality and geometric rates","authors":"R. Zamir, M. Feder","doi":"10.1109/WITS.1994.513909","DOIUrl":"https://doi.org/10.1109/WITS.1994.513909","url":null,"abstract":"A matrix form of the Brunn-Minkowski inequality is derived, which may be applied in calculating the uncoded bit rate of lattice quantization and modulation schemes.","PeriodicalId":423518,"journal":{"name":"Proceedings of 1994 Workshop on Information Theory and Statistics","volume":"91 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126292862","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1994-10-27DOI: 10.1109/WITS.1994.513923
F. Muller
Asymptotic (high rate) quantization theory is applied to the multivariate mismatch problem. The question of how much is lost if a vector quantizer which is matched to a specific source with given parameters is used for quantization of a source with different parameters, is addressed. For parameterization of the sources sub-Gaussian processes are employed.
{"title":"Asymptotic performance evaluation of mismatched vector quantizers using sub-Gaussian sources","authors":"F. Muller","doi":"10.1109/WITS.1994.513923","DOIUrl":"https://doi.org/10.1109/WITS.1994.513923","url":null,"abstract":"Asymptotic (high rate) quantization theory is applied to the multivariate mismatch problem. The question of how much is lost if a vector quantizer which is matched to a specific source with given parameters is used for quantization of a source with different parameters, is addressed. For parameterization of the sources sub-Gaussian processes are employed.","PeriodicalId":423518,"journal":{"name":"Proceedings of 1994 Workshop on Information Theory and Statistics","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127839789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1994-10-27DOI: 10.1109/WITS.1994.513907
A. Tsybakov, E. van der Meulen
We consider a truncated version of the entropy estimator and prove the mean square /spl radic/n-consistency of this estimator for a class of densities with unbounded support, including the Gaussian density.
{"title":"Root-N consistent estimators of entropy for densities with unbounded support","authors":"A. Tsybakov, E. van der Meulen","doi":"10.1109/WITS.1994.513907","DOIUrl":"https://doi.org/10.1109/WITS.1994.513907","url":null,"abstract":"We consider a truncated version of the entropy estimator and prove the mean square /spl radic/n-consistency of this estimator for a class of densities with unbounded support, including the Gaussian density.","PeriodicalId":423518,"journal":{"name":"Proceedings of 1994 Workshop on Information Theory and Statistics","volume":"307 9","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120986556","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1994-10-27DOI: 10.1109/WITS.1994.513932
A.T. Murgan, R. Radescu
Lempel-Ziv-Welch methods and their variations are all based on the principle of using a prescribed parsing rule to find duplicate occurrences of data and encoding the repeated strings with some sort of special code word identifying the data to be replaced. This paper includes a general presentation of five existing lossless compression methods used in any application of digital signal processing. The comparisons are made experimentally by computer simulation.
{"title":"A comparison of algorithms for lossless data compression using the Lempel-Ziv-Welch type methods","authors":"A.T. Murgan, R. Radescu","doi":"10.1109/WITS.1994.513932","DOIUrl":"https://doi.org/10.1109/WITS.1994.513932","url":null,"abstract":"Lempel-Ziv-Welch methods and their variations are all based on the principle of using a prescribed parsing rule to find duplicate occurrences of data and encoding the repeated strings with some sort of special code word identifying the data to be replaced. This paper includes a general presentation of five existing lossless compression methods used in any application of digital signal processing. The comparisons are made experimentally by computer simulation.","PeriodicalId":423518,"journal":{"name":"Proceedings of 1994 Workshop on Information Theory and Statistics","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124347125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1994-10-27DOI: 10.1109/WITS.1994.513926
L. Talbot, H. Tolley, B. Talbot, H.D. Mecham
We have elucidated the position of Woodbury's (1974) statistical fuzzy grade-of-membership (GoM) model in the unsupervised clustering domain. This implementation of the model is shown to operate not only on multivariate categorical data, but on permuted, or encoded, data as well.
{"title":"Characteristics of a statistical fuzzy grade-of-membership model in the context of unsupervised data clustering","authors":"L. Talbot, H. Tolley, B. Talbot, H.D. Mecham","doi":"10.1109/WITS.1994.513926","DOIUrl":"https://doi.org/10.1109/WITS.1994.513926","url":null,"abstract":"We have elucidated the position of Woodbury's (1974) statistical fuzzy grade-of-membership (GoM) model in the unsupervised clustering domain. This implementation of the model is shown to operate not only on multivariate categorical data, but on permuted, or encoded, data as well.","PeriodicalId":423518,"journal":{"name":"Proceedings of 1994 Workshop on Information Theory and Statistics","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124437402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1994-10-27DOI: 10.1109/WITS.1994.513904
K. Bell, Y. Steinberg, Y. Ephraim, H. van Trees
The Ziv-Zakai (1969) bounds on the mean square error (MSE) in parameter estimation are some of the tightest available bounds. These bounds relate the MSE in the estimation problem to the probability of error in a binary hypothesis testing problem. The original Bayesian version derived by Ziv and Zakai, and improvements by Chazan, Zakai and Ziv (1975) and Bellini and Tartara (1974) are applicable to scalar random variables with uniform prior distributions. This bound was extended by Bell, Ephraim, Steinberg and Van Trees (see Proceedings of 1994 International Symposium on Information Theory, Trondheim, Norway, June 1994) to vectors of random variables with arbitrary prior distributions. The goal of this paper is to present an improvement to the vector version of Bell et. al., explore some properties of the bounds, and present further generalizations.
{"title":"Improved Ziv-Zakai lower bound for vector parameter estimation","authors":"K. Bell, Y. Steinberg, Y. Ephraim, H. van Trees","doi":"10.1109/WITS.1994.513904","DOIUrl":"https://doi.org/10.1109/WITS.1994.513904","url":null,"abstract":"The Ziv-Zakai (1969) bounds on the mean square error (MSE) in parameter estimation are some of the tightest available bounds. These bounds relate the MSE in the estimation problem to the probability of error in a binary hypothesis testing problem. The original Bayesian version derived by Ziv and Zakai, and improvements by Chazan, Zakai and Ziv (1975) and Bellini and Tartara (1974) are applicable to scalar random variables with uniform prior distributions. This bound was extended by Bell, Ephraim, Steinberg and Van Trees (see Proceedings of 1994 International Symposium on Information Theory, Trondheim, Norway, June 1994) to vectors of random variables with arbitrary prior distributions. The goal of this paper is to present an improvement to the vector version of Bell et. al., explore some properties of the bounds, and present further generalizations.","PeriodicalId":423518,"journal":{"name":"Proceedings of 1994 Workshop on Information Theory and Statistics","volume":"79 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124585533","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1994-10-27DOI: 10.1109/WITS.1994.513884
D. Donoho
Adaptive signal representations in overcomplete libraries of waveforms have been very popular. One naturally expects that in searching through a large number of signal representations for noisy data, one is at risk of identifying apparent structure in the data which turns out to be spurious, noise-induced artifacts. We show how to use penalties based on the logarithm of library complexity to temper the search, preventing such spurious structure, and giving near-ideal behavior.
{"title":"Adaptive signal representations: How much is too much?","authors":"D. Donoho","doi":"10.1109/WITS.1994.513884","DOIUrl":"https://doi.org/10.1109/WITS.1994.513884","url":null,"abstract":"Adaptive signal representations in overcomplete libraries of waveforms have been very popular. One naturally expects that in searching through a large number of signal representations for noisy data, one is at risk of identifying apparent structure in the data which turns out to be spurious, noise-induced artifacts. We show how to use penalties based on the logarithm of library complexity to temper the search, preventing such spurious structure, and giving near-ideal behavior.","PeriodicalId":423518,"journal":{"name":"Proceedings of 1994 Workshop on Information Theory and Statistics","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121211000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1994-10-27DOI: 10.1109/WITS.1994.513883
R. DeVore, V. Temlyakov
A brief discussion is given of the role of approximation and smoothness spaces in algorithms for noise removal and compression. The discussion is limited to cases where approximation takes place in a Hilbert space although the theory applies in far greater generality.
{"title":"The role of approximation and smoothness spaces in compression and noise removal","authors":"R. DeVore, V. Temlyakov","doi":"10.1109/WITS.1994.513883","DOIUrl":"https://doi.org/10.1109/WITS.1994.513883","url":null,"abstract":"A brief discussion is given of the role of approximation and smoothness spaces in algorithms for noise removal and compression. The discussion is limited to cases where approximation takes place in a Hilbert space although the theory applies in far greater generality.","PeriodicalId":423518,"journal":{"name":"Proceedings of 1994 Workshop on Information Theory and Statistics","volume":"93 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123040743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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