Results 1 
8 of
8
About Adaptive Coding on Countable Alphabets
, 2012
"... This paper sheds light on universal coding with respect to classes of memoryless sources over a countable alphabet defined by an envelope function with finite and nondecreasing hazard rate. We prove that the autocensuring (AC) code introduced by Bontemps (2011) is adaptive with respect to the coll ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
(Show Context)
This paper sheds light on universal coding with respect to classes of memoryless sources over a countable alphabet defined by an envelope function with finite and nondecreasing hazard rate. We prove that the autocensuring (AC) code introduced by Bontemps (2011) is adaptive with respect to the collection of such classes. The analysis builds on the tight characterization of universal redundancy rate in terms of metric entropy by Haussler and Opper (1997) and on a careful analysis of the performance of the ACcoding algorithm. The latter relies on nonasymptotic bounds for maxima of samples from discrete distributions with finite and nondecreasing hazard rate.
Poissonization and universal compression of envelope classes
"... Abstract—Poisson sampling is a method for eliminating dependence among symbols in a random sequence. It helps improve algorithm design, strengthen bounds, and simplify proofs. We relate the redundancy of fixedlength and Poissonsampled sequences, use this result to derive a simple formula for the ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
Abstract—Poisson sampling is a method for eliminating dependence among symbols in a random sequence. It helps improve algorithm design, strengthen bounds, and simplify proofs. We relate the redundancy of fixedlength and Poissonsampled sequences, use this result to derive a simple formula for the redundancy of general envelope classes, and apply this formula to obtain simple and tight bounds on the redundancy of powerlaw and exponential envelope classes, in particular answering a question posed in [1]. I.
1Large Alphabet Compression and Predictive Distributions through Poissonization and Tilting
"... This paper introduces a convenient strategy for coding and predicting sequences of independent, identically distributed random variables generated from a large alphabet of size m. In particular, the size of the sample is allowed to be variable. The employment of a Poisson model and tilting method si ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
This paper introduces a convenient strategy for coding and predicting sequences of independent, identically distributed random variables generated from a large alphabet of size m. In particular, the size of the sample is allowed to be variable. The employment of a Poisson model and tilting method simplifies the implementation and analysis through independence. The resulting strategy is optimal within the class of distributions satisfying a moment condition, and is close to optimal for the class of all i.i.d distributions on strings of a given length. Moreover, the method can be used to code and predict strings with a condition on the tail of the ordered counts. It can also be applied to distributions in an envelope class.
Universal Compression of Envelope Classes: Tight Characterization via Poisson Sampling∗
, 2014
"... ar ..."
(Show Context)
TABLE OF CONTENTS
, 2014
"... Copyright Jayadev Acharya, 2014 All rights reserved. The dissertation of Jayadev Acharya is approved, and it is acceptable in quality and form for publication on microfilm and electronically: ..."
Abstract
 Add to MetaCart
(Show Context)
Copyright Jayadev Acharya, 2014 All rights reserved. The dissertation of Jayadev Acharya is approved, and it is acceptable in quality and form for publication on microfilm and electronically:
Universal Compression of Envelope Classes: Tight Characterization via Poisson Sampling∗
, 2014
"... ar ..."
(Show Context)
1 About Adaptive Coding on Countable Alphabets §
, 2014
"... Abstract—This paper sheds light on adaptive coding with respect to classes of memoryless sources over a countable alphabet defined by an envelope function with finite and nondecreasing hazard rate (logconcave envelope distributions). We prove that the autocensuring (AC) code introduced by Bontemp ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract—This paper sheds light on adaptive coding with respect to classes of memoryless sources over a countable alphabet defined by an envelope function with finite and nondecreasing hazard rate (logconcave envelope distributions). We prove that the autocensuring (AC) code introduced by Bontemps (2011) is adaptive with respect to the collection of such classes. The analysis builds on the tight characterization of universal redundancy rate in terms of metric entropy by Haussler and Opper (1997) and on a careful analysis of the performance of the ACcoding algorithm. The latter relies on nonasymptotic bounds for maxima of samples from discrete distributions with finite and nondecreasing hazard rate. Index Terms—countable alphabets, redundancy, adaptive compression, minimax.