2004/11/15 by Imre Csiszár, Paul C. Shields · 1 citation
Mathematics · #Statistics Education and Methodologies #Statistics #Computer science #Data science #Information retrieval #Mathematics
paper · doi:10.1561/0100000004
openalex publication_date 2004/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11
This tutorial is concerned with applications of information theory concepts in statistics, in the finite alphabet setting. The information measure known as information divergence or Kullback-Leibler distance or relative entropy plays a key role, often with a geometric flavor as an analogue of squared Euclidean distance, as in the concepts of I-projection, I-radius and I-centroid. The topics covered include large deviations, hypothesis testing, maximum likelihood estimation in exponential families, analysis of contingency tables, and iterative algorithms with an “information geometry” background. Also, an introduction is provided to the theory of universal coding, and to statistical inference via the minimum description length principle motivated by that theory.