25,802 research outputs found
Distributed Smoothed Tree Kernel
In this paper we explore
the possibility to merge the world of
Compositional Distributional Semantic
Models (CDSM) with Tree Kernels
(TK). In particular, we will introduce a
specific tree kernel (smoothed tree kernel,
or STK) and then show that is
possibile to approximate such kernel
with the dot product of two vectors
obtained compositionally from the sentences,
creating in such a way a new
CDSM
Distributed Tree Kernels
In this paper, we propose the distributed tree kernels (DTK) as a novel
method to reduce time and space complexity of tree kernels. Using a linear
complexity algorithm to compute vectors for trees, we embed feature spaces of
tree fragments in low-dimensional spaces where the kernel computation is
directly done with dot product. We show that DTKs are faster, correlate with
tree kernels, and obtain a statistically similar performance in two natural
language processing tasks.Comment: ICML201
Lossy Kernelization
In this paper we propose a new framework for analyzing the performance of
preprocessing algorithms. Our framework builds on the notion of kernelization
from parameterized complexity. However, as opposed to the original notion of
kernelization, our definitions combine well with approximation algorithms and
heuristics. The key new definition is that of a polynomial size
-approximate kernel. Loosely speaking, a polynomial size
-approximate kernel is a polynomial time pre-processing algorithm that
takes as input an instance to a parameterized problem, and outputs
another instance to the same problem, such that . Additionally, for every , a -approximate solution
to the pre-processed instance can be turned in polynomial time into a
-approximate solution to the original instance .
Our main technical contribution are -approximate kernels of
polynomial size for three problems, namely Connected Vertex Cover, Disjoint
Cycle Packing and Disjoint Factors. These problems are known not to admit any
polynomial size kernels unless . Our approximate
kernels simultaneously beat both the lower bounds on the (normal) kernel size,
and the hardness of approximation lower bounds for all three problems. On the
negative side we prove that Longest Path parameterized by the length of the
path and Set Cover parameterized by the universe size do not admit even an
-approximate kernel of polynomial size, for any , unless
. In order to prove this lower bound we need to combine
in a non-trivial way the techniques used for showing kernelization lower bounds
with the methods for showing hardness of approximationComment: 58 pages. Version 2 contain new results: PSAKS for Cycle Packing and
approximate kernel lower bounds for Set Cover and Hitting Set parameterized
by universe siz
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