TY - GEN
T1 - Improved MDL Estimators Using Local Exponential Family Bundles Applied to Mixture Families
AU - Miyamoto, Kohei
AU - Barron, Andrew R.
AU - Takeuchi, Jun'ichi
N1 - Funding Information:
ACKNOWLEDGMENT This research was partially supported by JSPS KAKENHI Grant Number 18H03291.
Publisher Copyright:
© 2019 IEEE.
PY - 2019/7
Y1 - 2019/7
N2 - The MDL estimators for density 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 is the difference between the codelength of the code and the ideal codelength achieved by an element in . Our code is constructed using a probability density in an enlarged family of (a bundle of local exponential families of ) 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.
AB - The MDL estimators for density 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 is the difference between the codelength of the code and the ideal codelength achieved by an element in . Our code is constructed using a probability density in an enlarged family of (a bundle of local exponential families of ) 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.
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U2 - 10.1109/ISIT.2019.8849350
DO - 10.1109/ISIT.2019.8849350
M3 - Conference contribution
AN - SCOPUS:85073159101
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 1442
EP - 1446
BT - 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2019 IEEE International Symposium on Information Theory, ISIT 2019
Y2 - 7 July 2019 through 12 July 2019
ER -