1,666 research outputs found
Decomposing Overcomplete 3rd Order Tensors using Sum-of-Squares Algorithms
Tensor rank and low-rank tensor decompositions have many applications in
learning and complexity theory. Most known algorithms use unfoldings of tensors
and can only handle rank up to for a -th order
tensor in . Previously no efficient algorithm can decompose
3rd order tensors when the rank is super-linear in the dimension. Using ideas
from sum-of-squares hierarchy, we give the first quasi-polynomial time
algorithm that can decompose a random 3rd order tensor decomposition when the
rank is as large as .
We also give a polynomial time algorithm for certifying the injective norm of
random low rank tensors. Our tensor decomposition algorithm exploits the
relationship between injective norm and the tensor components. The proof relies
on interesting tools for decoupling random variables to prove better matrix
concentration bounds, which can be useful in other settings
Synthesis of Attributed Feature Models From Product Descriptions: Foundations
Feature modeling is a widely used formalism to characterize a set of products
(also called configurations). As a manual elaboration is a long and arduous
task, numerous techniques have been proposed to reverse engineer feature models
from various kinds of artefacts. But none of them synthesize feature attributes
(or constraints over attributes) despite the practical relevance of attributes
for documenting the different values across a range of products. In this
report, we develop an algorithm for synthesizing attributed feature models
given a set of product descriptions. We present sound, complete, and
parametrizable techniques for computing all possible hierarchies, feature
groups, placements of feature attributes, domain values, and constraints. We
perform a complexity analysis w.r.t. number of features, attributes,
configurations, and domain size. We also evaluate the scalability of our
synthesis procedure using randomized configuration matrices. This report is a
first step that aims to describe the foundations for synthesizing attributed
feature models
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