Technical Program

Paper Detail

Paper Title Improved MDL Estimators Using Local Exponential Family Bundles Applied to Mixture Families
Paper IdentifierWE1.R3.2
Authors Kohei Miyamoto, Kyushu University, Japan; Andrew Barron, Yale University, United States; Jun'ichi Takeuchi, Kyushu University, Japan
Session Regression and Estimation
Location Monge, Level 3
Session Time Wednesday, 10 July, 09:50 - 11:10
Presentation Time Wednesday, 10 July, 10:10 - 10:30
Manuscript  Click here to download the manuscript
Abstract The MDL estimators for parameter estimation, which are defined by two-part codes for universal coding, are analyzed. We give a two-part code for mixture families whose regret is close to the minimax regret, where regret of a code with respect to a target family M is the difference between the code length of the code and the ideal codelength achieved by an element in M. Our code is constructed using a probability density in an enlarged family of M (a local exponential family bundle ofM) for data description. This result gives a tight upper bound on the risk of the MDL estimator defined by the two-part code, based on the theory introduced by Barron and Cover in 1991.