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Sparsification of Decomposable Submodular Functions
2022
PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE
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The underlying submodular functions for many of these tasks are decomposable, i.e., they are sum of several simple submodular functions. ...
To overcome this issue, we introduce the notion of sparsification for decomposable submodular functions whose objective is to obtain an accurate approximation of the original function that is a (weighted ...
the best of our knowledge there is no prior work on sparsification algorithms for decomposable submodular functions. ...
doi:10.1609/aaai.v36i9.21275
fatcat:4tmtg2ekevd55lsofrk25qtf6m
Sparsification of Decomposable Submodular Functions
[article]
2022
arXiv
pre-print
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The underlying submodular functions for many of these tasks are decomposable, i.e., they are sum of several simple submodular functions. ...
To overcome this issue, we introduce the notion of sparsification for decomposable submodular functions whose objective is to obtain an accurate approximation of the original function that is a (weighted ...
A novel class of submodular functions are decomposable submodular functions. ...
arXiv:2201.07289v1
fatcat:4gqsyaxoincvndnfhqgjz5dt3i
Augmented Sparsifiers for Generalized Hypergraph Cuts with Applications to Decomposable Submodular Function Minimization
[article]
2021
arXiv
pre-print
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Finally, we apply our sparsification techniques to develop approximation algorithms for minimizing sums of cardinality-based submodular functions. ...
This sparsification leads to faster approximate min s-t graph cut algorithms for certain classes of co-occurrence graphs. ...
Decomposable Submodular Function Minimization Any submodular function can be minimized in polynomial time [34, 35, 63] , but the runtimes for general submodular functions are impractical in most cases ...
arXiv:2007.08075v2
fatcat:3zxg6oro6fgi3mpa5656lh7hgi
Hypergraph Cuts with Edge-Dependent Vertex Weights
[article]
2022
arXiv
pre-print
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Moreover, we provide a way to construct submodular EDVWs-based splitting functions and prove that a hypergraph equipped with such splitting functions can be reduced to a graph sharing the same cut properties ...
More precisely, we introduce a new class of hyperedge splitting functions that we call EDVWs-based, where the penalty of splitting a hyperedge depends only on the sum of EDVWs associated with the vertices ...
In this case, the hypergraph minimum s-t cut problem can be solved using general submodular function minimizers [22, 27, 28, 29, 45, 49] or minimizers for decomposable submodular functions [18, 33, ...
arXiv:2201.06084v1
fatcat:khmicchdpvgmdno2zi26ycigeq
Scalable Combinatorial Bayesian Optimization with Tractable Statistical models
[article]
2020
arXiv
pre-print
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We study the problem of optimizing expensive blackbox functions over combinatorial spaces (e.g., sets, sequences, trees, and graphs). ...
First, reformulation of AFO problem as submodular relaxation with some unknown parameters, which can be solved efficiently using minimum graph cut algorithms. ...
The views expressed are those of the authors and do not reflect the official policy or position of the NSF. ...
arXiv:2008.08177v1
fatcat:fadhmgy63vdupacdbmqjcskhfy
Sparsification of influence networks
2011
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '11
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Seeking a practical, scalable approach to sparsification, we devise Spine, a greedy, efficient algorithm with practically little compromise in quality. ...
We claim that sparsification is a fundamental datareduction operation with many applications, ranging from visualization to exploratory and descriptive data analysis. ...
This work was partially supported by the Spanish Centre for the Development of Industrial Technology under the CENIT program, project CEN-20101037, "Social Media" (www.cenitsocialmedia.es). ...
doi:10.1145/2020408.2020492
dblp:conf/kdd/MathioudakisBCGU11
fatcat:v35756h7xndrrgsosrkp63qgha
Maximizing the Weighted Number of Spanning Trees: Near-t-Optimal Graphs
[article]
2016
arXiv
pre-print
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We reveal several new structures, such as the log-submodularity of the weighted number of spanning trees in connected graphs. ...
Our results can be readily applied to a wide verity of applications involving graph synthesis and graph sparsification scenarios. ...
We prove that the (weighted) number of spanning trees in connected graphs can be posed as a monotone log-submodular function. ...
arXiv:1604.01116v2
fatcat:winn2pzyvbhf5gvt43tj6w3ryy
Influence Propagation in Social Networks: A Data Mining Perspective
2011
2011 IEEE/WIC/ACM International Conferences on Web Intelligence and Intelligent Agent Technology
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With the success of online social networks and microblogs such as Facebook, Flickr and Twitter, the phenomenon of influence exerted by users of such platforms on other users, and how it propagates in the ...
One of the key problems in this area is the identification of influential users, by targeting whom certain desirable marketing outcomes can be achieved. ...
Kempe et al., however, showed that the function σ m (S) is monotone and submodular. ...
doi:10.1109/wi-iat.2011.286
dblp:conf/webi/Bonchi11
fatcat:wutoxda2hrg75iscjwp2hyc6my
Approximate Decomposable Submodular Function Minimization for Cardinality-Based Components
[article]
2021
arXiv
pre-print
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Minimizing a sum of simple submodular functions of limited support is a special case of general submodular function minimization that has seen numerous applications in machine learning. ...
This variant is one of the most widely applied in practice, encompassing, e.g., common energy functions arising in image segmentation and recent generalized hypergraph cut functions. ...
The past decade has witnessed several advances in faster algorithms for decomposable submodular function minimization (DSFM), i.e., minimizing a sum of simpler submodular functions [11, 26, 41, 31, 37 ...
arXiv:2110.14859v1
fatcat:iyrk7mrpj5hmrcs7s7du63k6mu
Influence Propagation in Social Networks: A Data Mining Perspective
2011
2011 IEEE/WIC/ACM International Conferences on Web Intelligence and Intelligent Agent Technology
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With the success of online social networks and microblogs such as Facebook, Flickr and Twitter, the phenomenon of influence exerted by users of such platforms on other users, and how it propagates in the ...
One of the key problems in this area is the identification of influential users, by targeting whom certain desirable marketing outcomes can be achieved. ...
Kempe et al., however, showed that the function σ m (S) is monotone and submodular. ...
doi:10.1109/wi-iat.2011.292
fatcat:gdymrsxd3fgmhhhm5uaox2edbu
Maximizing the Number of Spanning Trees in a Connected Graph
[article]
2018
arXiv
pre-print
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We give both algorithmic and hardness results for this problem: - We give a greedy algorithm that, using submodularity, obtains an approximation ratio of (1 - 1/e - ϵ) in the exponent of the number of ...
of an SDDM matrix. ...
Lemma 3.1. log T (G + P ) is a monotone submodular function. ...
arXiv:1804.02785v2
fatcat:xi7w3e3s3ne7lfnk23tohibiuq
Tractable hypergraph properties for constraint satisfaction and conjunctive queries
[article]
2011
arXiv
pre-print
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Here we introduce a new hypergraph measure called submodular width, and show that bounded submodular width of H implies that CSP(H) is fixed-parameter tractable. ...
In a matching hardness result, we show that if H has unbounded submodular width, then CSP(H) is not fixed-parameter tractable, unless the Exponential Time Hypothesis fails. ...
. • Submodular functions. Submodular width is defined in terms of submodular functions, thus submodular functions defined on hypergraphs is our second natural domain. ...
arXiv:0911.0801v3
fatcat:4hyeugfjovdjja7pfovpvzom34
Tractable hypergraph properties for constraint satisfaction and conjunctive queries
2010
Proceedings of the 42nd ACM symposium on Theory of computing - STOC '10
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of partial solutions can be described by a submodular function. ...
To prove these combinatorial results, we need to develop a theory of (multicommodity) flows on hypergraphs and vertex separators in the case when the function b(S) defining the cost of separator S is submodular ...
-Submodular functions. Submodular width is defined in terms of submodular functions, thus submodular functions defined on hypergraphs is our second natural domain. ...
doi:10.1145/1806689.1806790
dblp:conf/stoc/Marx10
fatcat:rue3f6bjjjgszgs37fq5bzitte
Tractable Hypergraph Properties for Constraint Satisfaction and Conjunctive Queries
2013
Journal of the ACM
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of partial solutions can be described by a submodular function. ...
To prove these combinatorial results, we need to develop a theory of (multicommodity) flows on hypergraphs and vertex separators in the case when the function b(S) defining the cost of separator S is submodular ...
-Submodular functions. Submodular width is defined in terms of submodular functions, thus submodular functions defined on hypergraphs is our second natural domain. ...
doi:10.1145/2535926
fatcat:z663q2gyc5a3fp4r26fnp4ivgi
Variational Graph Methods for Efficient Point Cloud Sparsification
[article]
2019
arXiv
pre-print
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approximation based on the chosen regularization functional. ...
The main contribution in this paper is a novel coarse-to-fine optimization scheme for point cloud sparsification, inspired by the efficiency of the recently proposed Cut Pursuit algorithm for total variation ...
parameter, D is a differentiable, convex data fidelity term with the original data given as g, and R is a convex regularization functional, which is decomposable into differentiable and non-differentiable ...
arXiv:1903.02858v3
fatcat:52zqly764fgadckm4ph5h2ep7i
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