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Uniform Sampling through the Lovász Local Lemma [article]

Heng Guo, Mark Jerrum, Jingcheng Liu
2019 arXiv   pre-print
Our framework builds (perhaps surprising) new connections between the variable framework of the Lov\'asz Local Lemma and some classical sampling algorithms such as the "cycle-popping" algorithm for rooted  ...  We propose a new algorithmic framework, called "partial rejection sampling", to draw samples exactly from a product distribution, conditioned on none of a number of bad events occurring.  ...  This work was done (in part) while the authors were visiting the Simons Institute for the Theory of Computing. HG was also supported by a Google research fellowship in the Simons Institute.  ... 
arXiv:1611.01647v4 fatcat:s64hjs2eancw7pa4jtdxh5yy2y

Uniform Sampling Through the Lovász Local Lemma

Heng Guo, Mark Jerrum, Jingcheng Liu
2019 Journal of the ACM  
Our framework builds new connections between the variable framework of the Lovász Local Lemma and some classical sampling algorithms such as the "cycle-popping" algorithm for rooted spanning trees.  ...  We propose a new algorithmic framework, called "partial rejection sampling", to draw samples exactly from a product distribution, conditioned on none of a number of bad events occurring.  ...  This work was done (in part) while the authors were visiting the Simons Institute for the Theory of Computing. HG was also supported by a Google research fellowship in the Simons Institute.  ... 
doi:10.1145/3310131 fatcat:wop4gymc4vajvplk6a4qcgxxqu

Uniform sampling through the Lovasz local lemma

Heng Guo, Mark Jerrum, Jingcheng Liu
2017 Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing - STOC 2017  
Our framework builds (perhaps surprising) new connections between the variable framework of the Lovász Local Lemma and some classical sampling algorithms such as the "cycle-popping" algorithm for rooted  ...  We propose a new algorithmic framework, called "partial rejection sampling", to draw samples exactly from a product distribution, conditioned on none of a number of bad events occurring.  ...  We write A i ⇠ A j if the vertices i and j are adjacent in G. The asymmetric Lovász Local Lemma [9] states the following. T 2.1.  ... 
doi:10.1145/3055399.3055410 dblp:conf/stoc/GuoJ017 fatcat:cdnhx6mlofeinoun2jhm63roc4

Sampling Partial Acyclic Orientations in Chordal Graphs by the Lovasz Local Lemma (Student Abstract)

Wenbo Sun, Ivona Bezáková
2021 AAAI Conference on Artificial Intelligence  
In this work we investigate the use of the recently proposed general partial rejection sampling technique of Guo, Jerrum, and Liu, based on the Lovász Local Lemma, for sampling partial acyclic orientations  ...  We show how the technique can be used to sample partial acyclic orientations of chordal graphs fast and with a clearly specified underlying distribution.  ...  Acknowledgments This work was supported by the NSF, award DUE-1819546.  ... 
dblp:conf/aaai/SunB21a fatcat:yya37ny4dzgw3dgfiucqktzf5y

Sampling Constraint Satisfaction Solutions in the Local Lemma Regime [article]

Weiming Feng, Kun He, Yitong Yin
2021 arXiv   pre-print
Assuming a canonical setting for the Lovász local lemma, where each constraint is violated by a small number of forbidden local configurations, our sampling algorithm is accurate in a local lemma regime  ...  Our main approach is a new technique called state compression, which generalizes the "mark/unmark" paradigm of Moitra (Moitra, JACM, 2019), and can give fast local-lemma-based sampling algorithms.  ...  By Lovász local lemma ( eorem 2.1), the set M exist if e · 2 exp − ( − ) 2 2 · ≤ 1.  ... 
arXiv:2011.03915v2 fatcat:6hbzoi5snnegbhhqw6gey6v5y4

Approximate Counting, the Lovasz Local Lemma and Inference in Graphical Models [article]

Ankur Moitra
2017 arXiv   pre-print
Moreover our algorithm extends straightforwardly to approximate sampling, which shows that under Lovász Local Lemma-like conditions it is not only possible to find a satisfying assignment, it is also possible  ...  Finally, we give an application of our results to show that it is algorithmically possible to sample from the posterior distribution in an interesting class of graphical models.  ...  Under the conditions of the Lovász Local Lemma (i.e. when k is logarithmic in d) is it possible to approximately sample from the uniform distribution on satisfying assignments?  ... 
arXiv:1610.04317v2 fatcat:cay6gygb3besllzgdvtxbcogzi

Approximate counting, the Lovasz local lemma, and inference in graphical models

Ankur Moitra
2017 Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing - STOC 2017  
Moreover our algorithm extends straightforwardly to approximate sampling, which shows that under Lovász Local Lemma-like conditions it is not only possible to find a satisfying assignment, it is also possible  ...  Finally, we give an application of our results to show that it is algorithmically possible to sample from the posterior distribution in an interesting class of graphical models.  ...  We thank Heng Guo and anonymous referees for pointing out typos in some inequalities in a preliminary version, fixing which required increasing the constants in the main theorems by roughly a factor of  ... 
doi:10.1145/3055399.3055428 dblp:conf/stoc/Moitra17 fatcat:bfex4bj3craarjcllgeldilgli

Counting Candy Crush Configurations [article]

Adam Hamilton, Giang T. Nguyen, Matthew Roughan
2019 arXiv   pre-print
A k-stable c-coloured Candy Crush grid is a weak proper c-colouring of a particular type of k-uniform hypergraph.  ...  We also discuss the applicability of this FPRAS to the problem of counting the number of weak c-colourings of other, more general hypergraphs.  ...  Acknowledgements The second author would like to also acknowledge the support of her ARC DP180103106.  ... 
arXiv:1908.09996v1 fatcat:h6zisjuhxba5dgozgze5zallrm

Sampling Lovász Local Lemma For General Constraint Satisfaction Solutions In Near-Linear Time [article]

Kun He, Chunyang Wang, Yitong Yin
2022 arXiv   pre-print
We give a fast algorithm for sampling uniform solutions of general constraint satisfaction problems (CSPs) in a local lemma regime.  ...  Within a local lemma regime, this marginal sampler can draw a random value for a variable according to its marginal distribution, at a local cost independent of the size of the CSP.  ...  Uniform sampling through the Lovász local lemma. J. ACM, 66(3):Art. 18, 31, 2019. [GLLZ19] Heng Guo, Chao Liao, Pinyan Lu, and Chihao Zhang. Counting hypergraph colorings in the local lemma regime.  ... 
arXiv:2204.01520v2 fatcat:fln2p5q6jzceli3nkiendgtzpi

Global graph kernels using geometric embeddings

Fredrik D. Johansson, Vinay Jethava, Devdatt P. Dubhashi, Chiranjib Bhattacharyya
2014 International Conference on Machine Learning  
This paper presents two graph kernels defined on unlabeled graphs which capture global properties of graphs using the celebrated Lovász number and its associated orthonormal representation.  ...  However, several interesting properties such as girth or chromatic number are global properties of the graph, and are not captured in local substructures.  ...  Acknowledgments The authors would like to thank Jean-Philippe Vert for fruitful discussions and the ICML reviewers for useful comments.  ... 
dblp:conf/icml/JohanssonJDB14 fatcat:gsctumjdljei7cr5d66kw5iy7m

The mixing time of the Dikin walk in a polytope—A simple proof

Sushant Sachdeva, Nisheeth K. Vishnoi
2016 Operations Research Letters  
Bounds on its mixing time are important for algorithms for sampling and optimization over polytopes.  ...  We study the mixing time of the Dikin walk in a polytope - a random walk based on the log-barrier from the interior point method literature.  ...  the local norm.  ... 
doi:10.1016/j.orl.2016.07.005 fatcat:aulnxnbgkjcptbm4wonuqpnnja

An Alternate Proof of the Algorithmic Lovász Local Lemma [chapter]

Ioannis Giotis, Lefteris Kirousis, Kostas I. Psaromiligkos, Dimitrios M. Thilikos
2017 Trends in Mathematics  
We provide new algorithmic proofs for two forms of the Lovász Local Lemma: the Asymmetric version and Shearer's Lemma.  ...  In contrast most extant proofs for the Lovász Local Lemma and its variants use counting arguments that give estimates of only the expectation that the algorithm lasts for at least n steps.  ...  Kirousis' research was partially supported by the Special Account for Research Grants of the National and Kapodistrian University of Athens. K. I.  ... 
doi:10.1007/978-3-319-51753-7_10 fatcat:5lmicllanvcadcncio7oau4qgq

Escaping the Local Minima via Simulated Annealing: Optimization of Approximately Convex Functions [article]

Alexandre Belloni, Tengyuan Liang, Hariharan Narayanan, Alexander Rakhlin
2015 arXiv   pre-print
The problem is reduced to sampling from an approximately log-concave distribution using the Hit-and-Run method, which is shown to have the same O^* complexity as sampling from log-concave distributions  ...  The algorithm then is based on simulated annealing which does not relies on first order conditions which makes it essentially immune to local minima.  ...  We end this section with two useful lemmas that can be found in Lovász and Vempala (2007) . Lemma 3 (Lovász and Vempala (2007) (t ) = {x ∈ R n : h(x) ≥ t }.  ... 
arXiv:1501.07242v2 fatcat:nc3l4akcmvfsha2g4wodgsuj6q

STOCHASTIC ALGORITHM APPLICATION IN PIPELINE JOINT RECOGNITION TASK FOR WELDING ROBOT MANIPULATOR CONTROL

A. A. Piskarev, B. B. Mikhailov, B. I. Shakhtarin
2018 Vestnik komp iuternykh i informatsionnykh tekhnologii  
The problem is reduced to sampling from an approximately log-concave distribution using the Hit-and-Run method, which is shown to have the same O * complexity as sampling from log-concave distributions  ...  The algorithm then is based on simulated annealing which does not relies on first order conditions which makes it essentially immune to local minima.  ...  Choose a random line that passes through x. The direction is uniform from the surface of ellipse given by Σ acting on sphere 2.  ... 
doi:10.14489/vkit.2018.10.pp.022-029 fatcat:sb6lgicngbb5lepkaj4xoag4pq

The Kannan-Lovász-Simonovits Conjecture [article]

Yin Tat Lee, Santosh S. Vempala
2018 arXiv   pre-print
Here we survey the origin and consequences of the conjecture (in geometry, probability, information theory and algorithms) as well as recent progress resulting in the current best bounds.  ...  The conjecture has lead to several techniques of general interest.  ...  It was partially supported by the DIMACS/Simons Collaboration on Bridging Continuous and Discrete Optimization through NSF grant #CCF-1740425.  ... 
arXiv:1807.03465v1 fatcat:y2w7nb6kyfctpo7dokqq7kkxdu
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