On Modeling Profiles instead of Values
This addresses a fundamental statistical estimation problem, offering an alternative to maximum likelihood for scenarios with many distinct symbols, though it appears incremental as it builds on existing distribution estimation methods.
The paper tackles the problem of estimating the underlying distribution of observed data by proposing the high-profile distribution, which maximizes the probability of the observed profile rather than the values, and shows that it better explains the data when the number of distinct symbols is large.
We consider the problem of estimating the distribution underlying an observed sample of data. Instead of maximum likelihood, which maximizes the probability of the ob served 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.