SCHEDULE: NOV 15-20, 2015

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A Kernel-Independent FMM in General Dimensions

SESSION: Applications: Folding, Imaging, and Proteins

EVENT TYPE: Papers

EVENT TAG(S): Applications

TIME: 4:00PM - 4:30PM

SESSION CHAIR(S): Evelyn Duesterwald

AUTHOR(S):William B. March, Bo Xiao, Sameer Tharakan, Chenhan D. Yu, George Biros

ROOM:18AB

ABSTRACT:

We introduce a general-dimensional, kernel-independent, algebraic
fast multipole method and apply it to kernel regression. The
motivation for this work is the approximation of
kernel matrices, which appear in mathematical
physics, approximation theory, non-parametric statistics, and machine
learning. Existing fast multipole methods are asymptotically optimal,
but the underlying constants scale quite badly with the ambient space
dimension. We introduce a method that mitigates this shortcoming; it
only requires kernel evaluations and scales well with the problem
size, the number of processors, and the ambient dimension---as long as
the intrinsic dimension of the dataset is small. We test the
performance of our method on several synthetic datasets. As a
highlight, our largest run was on an image dataset with 10 million
points in 246 dimensions.

Chair/Author Details:

Evelyn Duesterwald (Chair) - IBM Corporation|

William B. March - The University of Texas at Austin

Bo Xiao - The University of Texas at Austin

Sameer Tharakan - The University of Texas at Austin

Chenhan D. Yu - The University of Texas at Austin

George Biros - The University of Texas at Austin

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Paper provided by the ACM Digital Library

Paper also available from IEEE Computer Society