id: 01930608
dt: j
an: 01930608
au: Burnashev, M.V.; Amari, S.
ti: On density estimation under relative entropy loss criterion.
so: Probl. Inf. Transm. 38, No.4, 323-346 (2002); translation from Probl.
Peredachi Inf. 38, No.4, 85-112 (2002).
py: 2002
pu: Springer US, New York, NY; Pleiades Publishing, New York, NY; MAIK
“Nauka/Interperiodica”, Moscow
la: EN
cc: E.4 I.2.6 I.5
ut: relative entropy loss function; density estimation; neural networks;
pattern recognition; learning systems; minimax risk; Bayesian
ci:
li: doi:10.1023/A:1022002029826
ab: From the text: A density estimation problem under a relative entropy loss
criterion is considered. This loss function appears naturally in neural
networks, pattern recognition, and learning systems (see details in
[{\it S. Amari} and {\it N. Murata}, Statistical theory of learning
curves and entropic loss criterion, Neural Comp. 5, 140-153 (1992)]).
When the densities estimated constitute a $d$-dimensional smooth
parameter family, the exact asymptotics of the minimax risk is
established. A Bayesian statement of the problem is also considered.
rv: