Information estimators for weighted observations

Hideitsu Hino*, Noboru Murata

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


The Shannon information content is a valuable numerical characteristic of probability distributions. The problem of estimating the information content from an observed dataset is very important in the fields of statistics, information theory, and machine learning. The contribution of the present paper is in proposing information estimators, and showing some of their applications. When the given data are associated with weights, each datum contributes differently to the empirical average of statistics. The proposed estimators can deal with this kind of weighted data. Similar to other conventional methods, the proposed information estimator contains a parameter to be tuned, and is computationally expensive. To overcome these problems, the proposed estimator is further modified so that it is more computationally efficient and has no tuning parameter. The proposed methods are also extended so as to estimate the cross-entropy, entropy, and Kullback-Leibler divergence. Simple numerical experiments show that the information estimators work properly. Then, the estimators are applied to two specific problems, distribution-preserving data compression, and weight optimization for ensemble regression.

Original languageEnglish
Pages (from-to)260-275
Number of pages16
JournalNeural Networks
Publication statusPublished - 2013 Oct


  • Entropy estimation
  • Information estimation
  • Weighted data

ASJC Scopus subject areas

  • Cognitive Neuroscience
  • Artificial Intelligence


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