TY - GEN
T1 - A comparison of new and old algorithms for a mixture estimation problem
AU - Helmbold, David P.
AU - Singer, Yoram
AU - Schapire, Robert E.
AU - Warmuth, Manfred K.
N1 - Publisher Copyright:
© 1995 ACM.
PY - 1995/7/5
Y1 - 1995/7/5
N2 - We investigate the problem of estimating the proportion vector which maximizes the likelihood of a given sample for a mixture of given densities. We adapt a framework developed for supervised learning and give simple derivations for many of the standard iterative algorithms like gradient projection and EM. In this framework, the distance between the new and old proportion vectors is used as a penalty term. The square distance leads to the gradient projection update, and the relative entropy to a new update which we call the exponentiated gradient update (EG,). Curiously, when a second order Taylor expansion of the relative entropy is used, we arrive at an update EMη which, for η = 1, gives the usual EM update. Experimentally, both the EMη-update and the EGη-update for η > 1 outperform the EM algorithm and its variants. We also prove a worst-case polynomial bound on the global rate of convergence of the EGη algorithm.
AB - We investigate the problem of estimating the proportion vector which maximizes the likelihood of a given sample for a mixture of given densities. We adapt a framework developed for supervised learning and give simple derivations for many of the standard iterative algorithms like gradient projection and EM. In this framework, the distance between the new and old proportion vectors is used as a penalty term. The square distance leads to the gradient projection update, and the relative entropy to a new update which we call the exponentiated gradient update (EG,). Curiously, when a second order Taylor expansion of the relative entropy is used, we arrive at an update EMη which, for η = 1, gives the usual EM update. Experimentally, both the EMη-update and the EGη-update for η > 1 outperform the EM algorithm and its variants. We also prove a worst-case polynomial bound on the global rate of convergence of the EGη algorithm.
UR - http://www.scopus.com/inward/record.url?scp=85019130815&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85019130815&partnerID=8YFLogxK
U2 - 10.1145/225298.225306
DO - 10.1145/225298.225306
M3 - Conference contribution
AN - SCOPUS:85019130815
T3 - Proceedings of the 8th Annual Conference on Computational Learning Theory, COLT 1995
SP - 69
EP - 78
BT - Proceedings of the 8th Annual Conference on Computational Learning Theory, COLT 1995
PB - Association for Computing Machinery, Inc
T2 - 8th Annual Conference on Computational Learning Theory, COLT 1995
Y2 - 5 July 1995 through 8 July 1995
ER -