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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Statistical theory for deep neural networks with R
eLU activation function - Johannes Schmidt-hieber
(Universiteit Leiden)
DTSTART;TZID=Europe/London:20180321T113000
DTEND;TZID=Europe/London:20180321T123000
UID:TALK102739AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/102739
DESCRIPTION:The universal approximation theorem states that ne
ural networks are capable of approximating any con
tinuous function up to a small error that depends
on the size of the network. The expressive power o
f a network does\, however\, not guarantee that de
ep networks perform well on data. For that\, contr
ol of the statistical estimation risk is needed. I
n the talk\, we derive statistical theory for fitt
ing deep neural networks to data generated from th
e multivariate nonparametric regression model. It
is shown that estimators based on sparsely connect
ed deep neural networks with ReLU activation funct
ion and properly chosen network architecture achie
ve the minimax rates of convergence (up to logarit
hmic factors) under a general composition assumpti
on on the regression function. The framework inclu
des many well-studied structural constraints such
as (generalized) additive models. While there is a
lot of flexibility in the network architecture\,
the tuning parameter is the sparsity of the n etwo
rk. Specifically\, we consider large networks with
number of potential parameters being much bigger
than the sample size. Interestingly\, the depth (n
umber of layers) of the neural network architectur
es plays an important role and our theory suggests
that scaling the network depth with the logarithm
of the sample size is natural.

Related Lin
ks
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:info@newton.ac.uk
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