16,115 research outputs found
Differentially Private Decomposable Submodular Maximization
We study the problem of differentially private constrained maximization of
decomposable submodular functions. A submodular function is decomposable if it
takes the form of a sum of submodular functions. The special case of maximizing
a monotone, decomposable submodular function under cardinality constraints is
known as the Combinatorial Public Projects (CPP) problem [Papadimitriou et al.,
2008]. Previous work by Gupta et al. [2010] gave a differentially private
algorithm for the CPP problem. We extend this work by designing differentially
private algorithms for both monotone and non-monotone decomposable submodular
maximization under general matroid constraints, with competitive utility
guarantees. We complement our theoretical bounds with experiments demonstrating
empirical performance, which improves over the differentially private
algorithms for the general case of submodular maximization and is close to the
performance of non-private algorithms
Self-decomposable Global Constraints
International audienceScalability becomes more and more critical to decision support technologies. In order to address this issue in Constraint Programming, we introduce the family of self-decomposable constraints. These constraints can be satisfied by applying their own filtering algorithms on variable subsets only. We introduce a generic framework which dynamically decompose propagation, by filtering over variable subsets. Our experiments over the CUMULATIVE constraint illustrate the practical relevance of self-decomposition
Distributed Low-rank Subspace Segmentation
Vision problems ranging from image clustering to motion segmentation to
semi-supervised learning can naturally be framed as subspace segmentation
problems, in which one aims to recover multiple low-dimensional subspaces from
noisy and corrupted input data. Low-Rank Representation (LRR), a convex
formulation of the subspace segmentation problem, is provably and empirically
accurate on small problems but does not scale to the massive sizes of modern
vision datasets. Moreover, past work aimed at scaling up low-rank matrix
factorization is not applicable to LRR given its non-decomposable constraints.
In this work, we propose a novel divide-and-conquer algorithm for large-scale
subspace segmentation that can cope with LRR's non-decomposable constraints and
maintains LRR's strong recovery guarantees. This has immediate implications for
the scalability of subspace segmentation, which we demonstrate on a benchmark
face recognition dataset and in simulations. We then introduce novel
applications of LRR-based subspace segmentation to large-scale semi-supervised
learning for multimedia event detection, concept detection, and image tagging.
In each case, we obtain state-of-the-art results and order-of-magnitude speed
ups
On tree decomposability of Henneberg graphs
In this work we describe an algorithm that generates well constrained geometric constraint graphs which are solvable by the tree-decomposition constructive technique. The algorithm is based on Henneberg constructions and would be of help in transforming underconstrained problems into well constrained problems as well as in exploring alternative constructions over a given set of geometric elements.Postprint (published version
The complexity of global cardinality constraints
In a constraint satisfaction problem (CSP) the goal is to find an assignment
of a given set of variables subject to specified constraints. A global
cardinality constraint is an additional requirement that prescribes how many
variables must be assigned a certain value. We study the complexity of the
problem CCSP(G), the constraint satisfaction problem with global cardinality
constraints that allows only relations from the set G. The main result of this
paper characterizes sets G that give rise to problems solvable in polynomial
time, and states that the remaining such problems are NP-complete
FNNC: Achieving Fairness through Neural Networks
In classification models fairness can be ensured by solving a constrained
optimization problem. We focus on fairness constraints like Disparate Impact,
Demographic Parity, and Equalized Odds, which are non-decomposable and
non-convex. Researchers define convex surrogates of the constraints and then
apply convex optimization frameworks to obtain fair classifiers. Surrogates
serve only as an upper bound to the actual constraints, and convexifying
fairness constraints might be challenging.
We propose a neural network-based framework, \emph{FNNC}, to achieve fairness
while maintaining high accuracy in classification. The above fairness
constraints are included in the loss using Lagrangian multipliers. We prove
bounds on generalization errors for the constrained losses which asymptotically
go to zero. The network is optimized using two-step mini-batch stochastic
gradient descent. Our experiments show that FNNC performs as good as the state
of the art, if not better. The experimental evidence supplements our
theoretical guarantees. In summary, we have an automated solution to achieve
fairness in classification, which is easily extendable to many fairness
constraints
A structural Markov property for decomposable graph laws that allows control of clique intersections
We present a new kind of structural Markov property for probabilistic laws on
decomposable graphs, which allows the explicit control of interactions between
cliques, so is capable of encoding some interesting structure. We prove the
equivalence of this property to an exponential family assumption, and discuss
identifiability, modelling, inferential and computational implications.Comment: 10 pages, 3 figures; updated from V1 following journal review, new
more explicit title and added section on inferenc
Nonplanar On-shell Diagrams and Leading Singularities of Scattering Amplitudes
Bipartite on-shell diagrams are the latest tool in constructing scattering
amplitudes. In this paper we prove that a Britto-Cachazo-Feng-Witten
(BCFW)-decomposable on-shell diagram process a rational top-form if and only if
the algebraic ideal comprised of the geometrical constraints is shifted
linearly during successive BCFW integrations. With a proper geometric
interpretation of the constraints in the Grassmannian manifold, the rational
top-form integration contours can thus be obtained, and understood, in a
straightforward way. All rational top-form integrands of arbitrary higher loops
leading singularities can therefore be derived recursively, as long as the
corresponding on-shell diagram is BCFW-decomposable.Comment: 13 pages with 12 figures; final version appeared in Eur.Phys.J. C77
(2017) no.2, 8
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