Elements of information theory
Elements of information theory
The Markov chain Monte Carlo method: an approach to approximate counting and integration
Approximation algorithms for NP-hard problems
A general language model for information retrieval (poster abstract)
Proceedings of the 22nd annual international ACM SIGIR conference on Research and development in information retrieval
An empirical study of smoothing techniques for language modeling
ACL '96 Proceedings of the 34th annual meeting on Association for Computational Linguistics
Universal compression of memoryless sources over unknown alphabets
IEEE Transactions on Information Theory
The context-tree weighting method: basic properties
IEEE Transactions on Information Theory
The maximum likelihood probability of skewed patterns
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
The maximum likelihood probability of unique-singleton, ternary, and length-7 patterns
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
Proceedings of the forty-third annual ACM symposium on Theory of computing
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We consider the problem of estimating the distribution underlying an observed sample of data. Instead of maximum likelihood, which maximizes the probability of the observed values, we propose a different estimate, the high-profile distribution, which maximizes the probability of the observed profile---the number of symbols appearing any given number of times. We determine the high-profile distribution of several data samples, establish some of its general properties, and show that when the number of distinct symbols observed is small compared to the data size, the high-profile and maximum-likelihood distributions are roughly the same, but when the number of symbols is large, the distributions differ, and high-profile better explains the data.