Title:
Avoiding the curse of dimensionality in high dimensional problems
Abstract:
Capturing a function 
of a large number (perhaps infinite) 
of variables arises
in many application domains. The curse of dimensionality says that the usual
model assumptions based on smoothness and the traditional numerical methods
will suffer the curse of dimensionality. This means using 
samples of the function
or computations will result in an approximation rate which deteriorates severely
with increasing . New ideas to avoid this curse are based on sparsity, compressibility,
and variable reduction. We will discuss how these new ideas avoid the curse and how
numerical methods based on these new ideas should be constructed. For example,
we discuss where one should sample in these scenarios.
of a large number (perhaps infinite) of variables arises
in many application domains. The curse of dimensionality says that the usual
model assumptions based on smoothness and the traditional numerical methods
will suffer the curse of dimensionality. This means using samples of the function
or computations will result in an approximation rate which deteriorates severely
with increasing . New ideas to avoid this curse are based on sparsity, compressibility,
and variable reduction. We will discuss how these new ideas avoid the curse and how
numerical methods based on these new ideas should be constructed. For example,
we discuss where one should sample in these scenarios.