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On the Convergence Rate of Decomposable Submodular Function Minimization [article]

Robert Nishihara, Stefanie Jegelka, Michael I. Jordan
<span title="2014-11-05">2014</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper, we show that the algorithm converges linearly, and we provide upper and lower bounds on the rate of convergence.  ...  Recent work introduced an easy-to-use, parallelizable algorithm for minimizing submodular functions that decompose as the sum of "simple" submodular functions.  ...  We would like to thank Mȃdȃlina Persu for suggesting the use of Cheeger's inequality.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1406.6474v3">arXiv:1406.6474v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ufg3lx3tsnhbhinuybhnzge3ye">fatcat:ufg3lx3tsnhbhinuybhnzge3ye</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200902123326/https://arxiv.org/pdf/1406.6474v3.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/36/e4/36e4cfc7132ee39b1c12eaae84ddae4c6dc667ea.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1406.6474v3" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Random Coordinate Descent Methods for Minimizing Decomposable Submodular Functions [article]

Alina Ene, Huy L. Nguyen
<span title="2015-02-09">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Recent work have used convex optimization techniques to obtain very practical algorithms for minimizing functions that are sums of "simple" functions.  ...  Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision.  ...  We thank Stefanie Jegelka for providing us with some of the data used in our experiments.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1502.02643v1">arXiv:1502.02643v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ei3auk3muzgpdiupnfbad5fi5y">fatcat:ei3auk3muzgpdiupnfbad5fi5y</a> </span>
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Reflection methods for user-friendly submodular optimization [article]

Stefanie Jegelka, Francis Bach , Suvrit Sra
<span title="2013-11-18">2013</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
While general submodular minimization is challenging, we propose a new method that exploits existing decomposability of submodular functions.  ...  In our experiments, we illustrate the benefits of our method on two image segmentation tasks.  ...  To split these intervals, submodular function minimization problems have to be solved on each of these intervals, with total complexity less than a single submodular function optimization problem on the  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1311.4296v1">arXiv:1311.4296v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cyz6xkaskvfmdawpuye4vvtqem">fatcat:cyz6xkaskvfmdawpuye4vvtqem</a> </span>
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Revisiting Decomposable Submodular Function Minimization with Incidence Relations [article]

Pan Li, Olgica Milenkovic
<span title="2018-09-24">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We introduce a new approach to decomposable submodular function minimization (DSFM) that exploits incidence relations.  ...  Incidence relations describe which variables effectively influence the component functions, and when properly utilized, they allow for improving the convergence rates of DSFM solvers.  ...  This work was supported in part by the NSF grant CCF 15-27636, the NSF Purdue 4101-38050 and the NFT STC center Science of Information.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1803.03851v3">arXiv:1803.03851v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cdnxsbn67jaeppci3z2nu2np2i">fatcat:cdnxsbn67jaeppci3z2nu2np2i</a> </span>
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Decomposable Submodular Function Minimization: Discrete and Continuous [article]

Alina Ene and Huy L. Nguyen and László A. Végh
<span title="2017-03-06">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
This paper investigates connections between discrete and continuous approaches for decomposable submodular function minimization.  ...  We also provide a systematic experimental comparison of the two types of methods, based on a clear distinction between level-0 and level-1 algorithms.  ...  A popular model is decomposable submodular functions: these can be written as sums of several "simple" submodular functions defined on small supports.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1703.01830v1">arXiv:1703.01830v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6v7drhaz5jhk3mwtsbncl4slse">fatcat:6v7drhaz5jhk3mwtsbncl4slse</a> </span>
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Algorithms for Approximate Minimization of the Difference Between Submodular Functions, with Applications [article]

Rishabh Iyer, Jeff A. Bilmes
<span title="2014-08-09">2014</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We provide computational bounds and a hardness result on the multiplicative inapproximability of minimizing the dierence between submodular functions.  ...  We extend the work of Narasimhan and Bilmes [30] for minimizing set functions representable as a dierence between submodular functions.  ...  Acknowledgments: We thank Andrew Guillory, Manas Joglekar, Stefanie Jegelka, and the rest of the submodular group at UW for discussions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1408.2051v1">arXiv:1408.2051v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/doric73uhbe2pogy6nv4pqr7mm">fatcat:doric73uhbe2pogy6nv4pqr7mm</a> </span>
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Algorithms for Approximate Minimization of the Difference Between Submodular Functions, with Applications [article]

Rishabh Iyer, Jeff Bilmes
<span title="2013-08-24">2013</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We provide computational bounds and a hardness result on the mul- tiplicative inapproximability of minimizing the difference between submodular functions.  ...  We extend the work of Narasimhan and Bilmes [30] for minimizing set functions representable as a difference between submodular functions.  ...  Acknowledgments: We thank Andrew Guillory, Manas Joglekar, Stefanie Jegelka, and the rest of the submodular group at UW for discussions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1207.0560v4">arXiv:1207.0560v4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nhrbsck73jezbkmhqoqgzuijq4">fatcat:nhrbsck73jezbkmhqoqgzuijq4</a> </span>
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Scalable Variational Inference in Log-supermodular Models [article]

Josip Djolonga, Andreas Krause
<span title="2015-02-24">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Furthermore, we show how to perform parallel inference as message passing in a suitable factor graph at a linear convergence rate, without having to sum up over all the configurations of the factor.  ...  This insight sheds light on the nature of the variational approximations produced by L-FIELD.  ...  Exploiting the minimum norm connection, we proved strong convergence rates for a natural parallel approach, with convergence rates dependent on the factor graph structure.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1502.06531v2">arXiv:1502.06531v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kzvpzzl5qre6tighaf5gyk2yye">fatcat:kzvpzzl5qre6tighaf5gyk2yye</a> </span>
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A Submodularity-based Agglomerative Clustering Algorithm for the Privacy Funnel [article]

Ni Ding, Parastoo Sadeghi
<span title="2019-02-12">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
For the privacy funnel (PF) problem, we propose an efficient iterative agglomerative clustering algorithm based on the minimization of the difference of submodular functions (IAC-MDSF).  ...  on I(X; X̂) while minimizing the privacy leakage I(S; X̂).  ...  The following result shows that we can decompose the objective function in (3) into two submodular set functions. The proof of Theorem 1 is in Appendix A. Theorem 1.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1901.06629v2">arXiv:1901.06629v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/r355dwp75bfz5mrmd7ofn7rlmq">fatcat:r355dwp75bfz5mrmd7ofn7rlmq</a> </span>
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Attaining Fairness in Communication for Omniscience [article]

Ni Ding, Parastoo Sadeghi, David Smith, Thierry Rakotoarivelo
<span title="2019-02-11">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The optimal rate region containing all source coding rate vectors that achieve the omniscience with the minimum sum rate is shown to coincide with the core (the solution set) of a coalitional game.  ...  It is shown that the Shapley value assigns each user the source coding rate measured by his/her remaining information of the multiple source given the common randomness that is shared by all users, while  ...  The authors would like to thank Dr. Ali Al-Bashabsheh for his comments on the egalitarian solution in Section V of this paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1902.03706v1">arXiv:1902.03706v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lm7csmhxynehzcv5xdqp5kitou">fatcat:lm7csmhxynehzcv5xdqp5kitou</a> </span>
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Mathematical and Computational Foundations of Learning Theory (Dagstuhl Seminar 15361)

Matthias Hein, Gabor Lugosi, Lorenzo Rosasco, Marc Herbstritt
<span title="2016-01-15">2016</span> <i title="Schloss Dagstuhl Leibniz-Zentrum für Informatik GmbH"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/u2phfyhrhje7xnnubtp3vfklcu" style="color: black;">Dagstuhl Reports</a> </i> &nbsp;
The goal of the seminar was to bring together again experts from computer science, mathematics and statistics to discuss the state of the art in machine learning and identify and formulate the key challenges  ...  The main reasons for the success of machine learning are its strong theoretical foundations and its multidisciplinary approach integrating aspects of computer science, applied mathematics, and statistics  ...  -Mathematical and Computational Foundations of Learning Theory well-studied classes of utility functions, to deal with a misspecified model, and with non-linear prices.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/dagrep.5.8.54">doi:10.4230/dagrep.5.8.54</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/journals/dagstuhl-reports/0001LR15.html">dblp:journals/dagstuhl-reports/0001LR15</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/u63lnb5j4ba3fdgvyes2u3woji">fatcat:u63lnb5j4ba3fdgvyes2u3woji</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220123034313/https://drops.dagstuhl.de/opus/volltexte/2016/5678/pdf/dagrep_v005_i008_p054_s15361.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/7e/1b/7e1b71fe631983708680ac7e8eeca877eae06008.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/dagrep.5.8.54"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

M-user Gaussian Interference Channels: To Decode the Interference or To Consider it as Noise

Abolfazl S. Motahari, Amir K. Khandani
<span title="">2007</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ux5tf45dtrgptnezraiii73msm" style="color: black;">2007 IEEE International Symposium on Information Theory</a> </i> &nbsp;
Given any ordering of users, we characterize an achievable rate vector in which users' rates are successively maximized based on the ordering.  ...  We first present a polynomial-time algorithm for finding the maximum decodable subset among interfering users, provided the users' rates and powers are given.  ...  However, the following algorithm can find some fixed points of the function by updating just one rate at each iteration. ] T and let π be a permutation on users. 2) Do the following until converges: For  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/isit.2007.4557546">doi:10.1109/isit.2007.4557546</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/isit/MotahariK07.html">dblp:conf/isit/MotahariK07</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vqj7ojaoxvhuzpi64binamz6jq">fatcat:vqj7ojaoxvhuzpi64binamz6jq</a> </span>
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Quadratic Decomposable Submodular Function Minimization [article]

Pan Li, Niao He, Olgica Milenkovic
<span title="2018-10-11">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We introduce a new convex optimization problem, termed quadratic decomposable submodular function minimization.  ...  The problem is closely related to decomposable submodular function minimization and arises in many learning on graphs and hypergraphs settings, such as graph-based semi-supervised learning and PageRank  ...  Acknowledgement The authors gratefully acknowledge many useful suggestions by the reviewers. This work was supported in part by the NIH grant 1u01 CA198943A and the NSF grant CCF 15-27636.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1806.09842v3">arXiv:1806.09842v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lkgwmp4w7zay3n3jcsqd2x5r2y">fatcat:lkgwmp4w7zay3n3jcsqd2x5r2y</a> </span>
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Learning with Submodular Functions: A Convex Optimization Perspective [article]

Francis Bach
<span title="2013-10-08">2013</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Submodular functions are relevant to machine learning for at least two reasons: (1) some problems may be expressed directly as the optimization of submodular functions and (2) the lovasz extension of submodular  ...  This allows the derivation of new efficient algorithms for approximate and exact submodular function minimization with theoretical guarantees and good practical performance.  ...  The author would like to thank Rodolphe Jenatton, Armand Joulin, Simon Lacoste-Julien, Julien Mairal and Guillaume Obozinski for discussions related to submodular functions and convex optimization.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1111.6453v2">arXiv:1111.6453v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qsbgrxoot5f7jhss4otffr3izy">fatcat:qsbgrxoot5f7jhss4otffr3izy</a> </span>
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Learning with Submodular Functions: A Convex Optimization Perspective

Francis Bach
<span title="">2013</span> <i title="Now Publishers"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ka2h7lkphrfvjlabybgqbnn2jq" style="color: black;">Foundations and Trends® in Machine Learning</a> </i> &nbsp;
The author would like to thank Thibaut Horel, Stefanie Jegelka, Rodolphe Jenatton, Armand Joulin, Simon Lacoste-Julien, Julien Mairal and Guillaume Obozinski for discussions related to submodular functions  ...  The suggestions of the reviewers were greatly appreciated and have significantly helped improve the manuscript.  ...  at rate O(1/t), which translates through the analysis of Chapter 8 to the same convergence rate of O(1/ √ t) for submodular function minimization, although with improved behavior and better empirical  ... 
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