TY - GEN
T1 - Asymptotically minimax regret for models with hidden variables
AU - Takeuchi, Junnichi
AU - Barron, Andrew R.
PY - 2014/1/1
Y1 - 2014/1/1
N2 - We study the problems of data compression, gambling and prediction of a string xn = x1x2...xn from an alphabet X, in terms of regret with respect to models with hidden variables including general mixture families. When the target class is a non-exponential family, a modification of Jeffreys prior which has measure outside the given family of densities was introduced to achieve the minimax regret [8], under certain regularity conditions. In this paper, we show that the models with hidden variables satisfy those regularity conditions, when the hidden variables' model is an exponential family. In paticular, we do not have to restrict the class of data strings so that the MLE is in the interior of the parameter space for the case of the general mixture family.
AB - We study the problems of data compression, gambling and prediction of a string xn = x1x2...xn from an alphabet X, in terms of regret with respect to models with hidden variables including general mixture families. When the target class is a non-exponential family, a modification of Jeffreys prior which has measure outside the given family of densities was introduced to achieve the minimax regret [8], under certain regularity conditions. In this paper, we show that the models with hidden variables satisfy those regularity conditions, when the hidden variables' model is an exponential family. In paticular, we do not have to restrict the class of data strings so that the MLE is in the interior of the parameter space for the case of the general mixture family.
UR - http://www.scopus.com/inward/record.url?scp=84906539395&partnerID=8YFLogxK
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U2 - 10.1109/ISIT.2014.6875392
DO - 10.1109/ISIT.2014.6875392
M3 - Conference contribution
AN - SCOPUS:84906539395
SN - 9781479951864
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 3037
EP - 3041
BT - 2014 IEEE International Symposium on Information Theory, ISIT 2014
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2014 IEEE International Symposium on Information Theory, ISIT 2014
Y2 - 29 June 2014 through 4 July 2014
ER -