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Sharper lower bounds on the performance of the empirical risk minimization algorithm
empirical risk minimization learning theory lower bound multidimensional central limit theorem uniform central limit theorem
2011/3/24
We present an argument based on the multidimensional and the uniform central limit theorems, proving that, under some geometrical assumptions between the target function $T$ and the learning class $F$...
Empirical risk minimization in inverse problems
Deconvolution empirical risk minimization multivariate density estimation nonparametric function estimation Radon transform tomography
2010/3/9
We study estimation of a multivariate function f :Rd
!R when
the observations are available from the function Af, where A is a
known linear operator. Both the Gaussian white noise model and
densit...
Penalized empirical risk minimization over Besov spaces
Penalized empirical risk Besov spaces
2009/9/16
Kernel methods are closely related to the notion of reproducing kernel Hilbert space (RKHS). A kernel machine is based on the minimization of an empirical cost and a stabilizer (usually the norm in th...
Suboptimality of Penalized Empirical Risk Minimization in Classification
Suboptimality Penalized Empirical Risk Minimization Classification
2010/4/27
Let F be a set of M classification procedures with values in
[−1, 1]. Given a loss function, we want to construct a procedure which
mimics at the best possible rate the best procedure in F. Th...