On modeling profiles instead of values

  • Authors:
  • Alon Orlitsky;Narayana P. Santhanam;Krishnamurthy Viswanathan;Junan Zhang

  • Affiliations:
  • University of California, San Diego, La Jolla, CA;University of California, San Diego, La Jolla, CA;University of California, San Diego, La Jolla, CA;University of California, San Diego, La Jolla, CA

  • Venue:
  • UAI '04 Proceedings of the 20th conference on Uncertainty in artificial intelligence
  • Year:
  • 2004

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Abstract

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.