Nonbacktracking operator for the Ising model and its applications in systems with multiple states

Zhang, Pan

doi:10.1103/physreve.91.042120

Cited by 10 publications

(13 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Our experiments also show that CoreHD outperforms centrality measures using left and right eigenvector of the non-backtracking matrix18, an idea that originally inspired us to propose the CoreHD algorithm. More detailed understanding of why this is the best performing strategy is let for future work.…”

Section: Discussionmentioning

confidence: 67%

Fast and simple decycling and dismantling of networks

Zdeborová

Zhang

Zhou

2016

Sci Rep

Self Cite

129

105

View full text Add to dashboard Cite

Decycling and dismantling of complex networks are underlying many important applications in network science. Recently these two closely related problems were tackled by several heuristic algorithms, simple and considerably sub-optimal, on the one hand, and involved and accurate message-passing ones that evaluate single-node marginal probabilities, on the other hand. In this paper we propose a simple and extremely fast algorithm, CoreHD, which recursively removes nodes of the highest degree from the 2-core of the network. CoreHD performs much better than all existing simple algorithms. When applied on real-world networks, it achieves equally good solutions as those obtained by the state-of-art iterative message-passing algorithms at greatly reduced computational cost, suggesting that CoreHD should be the algorithm of choice for many practical purposes.

show abstract

Section: Discussionmentioning

confidence: 67%

Fast and simple decycling and dismantling of networks

Zdeborová

Zhang

Zhou

2016

Sci Rep

Self Cite

129

105

View full text Add to dashboard Cite

show abstract

“…V D. We now turn back to our pedagogical example, the ±J planted spin glass, and related spectral algorithm as described and analyzed in [274]. Related ideas also appeared in [325].…”

Section: A Non-backtracking Spectral Methodsmentioning

confidence: 97%

“…The idea of using the linearization of BP was inspired by the earlier work of [66]. Since then, a considerable number of papers on promising algorithmic applications of the non-backtracking matrix on sparse networks started appearing, see [204,229,325]. Here, we briefly discuss selected contributions in this direction.…”

Section: E More On the Non-backtracking Operatormentioning

confidence: 99%

Statistical physics of inference: thresholds and algorithms

Zdeborová

Krząkała

2016

Advances in Physics

341

443

View full text Add to dashboard Cite

Many questions of fundamental interest in today's science can be formulated as inference problems: Some partial, or noisy, observations are performed over a set of variables and the goal is to recover, or infer, the values of the variables based on the indirect information contained in the measurements. For such problems, the central scientific questions are: Under what conditions is the information contained in the measurements sufficient for a satisfactory inference to be possible? What are the most efficient algorithms for this task? A growing body of work has shown that often we can understand and locate these fundamental barriers by thinking of them as phase transitions in the sense of statistical physics. Moreover, it turned out that we can use the gained physical insight to develop new promising algorithms. The connection between inference and statistical physics is currently witnessing an impressive renaissance and we review here the current state-of-the-art, with a pedagogical focus on the Ising model which, formulated as an inference problem, we call the planted spin glass. In terms of applications we review two classes of problems: (i) inference of clusters on graphs and networks, with community detection as a special case and (ii) estimating a signal from its noisy linear measurements, with compressed sensing as a case of sparse estimation. Our goal is to provide a pedagogical review for researchers in physics and other fields interested in this fascinating topic. arXiv:1511.02476v5 [cond-mat.stat-mech] 22 Jan 2018 2 CONTENTS

show abstract

“…As what has been investigated in [18,24], when a system has permutation symmetry, linearizing the BP equation at the paramagnetic fixed point results to an efficient spectral algorithm using the so-called non-backtracking operator. Again we analyze the stability of the factorized solution by linearizing the cavity marginals:…”

Section: The Non-backtracking Operatormentioning

confidence: 99%

Weighted community detection and data clustering using message passing

Shi¹,

Liu²,

Zhang³

2018

J. Stat. Mech.

Self Cite

View full text Add to dashboard Cite

Grouping objects into clusters based on similarities or weights between them is one of the most important problems in science and engineering. In this work, by extending message passing algorithms and spectral algorithms proposed for unweighted community detection problem, we develop a non-parametric method based on statistical physics, by mapping the problem to Potts model at the critical temperature of spin glass transition and applying belief propagation to solve the marginals corresponding to the Boltzmann distribution. Our algorithm is robust to over-fitting and gives a principled way to determine whether there are significant clusters in the data and how many clusters there are. We apply our method to different clustering tasks. In the community detection problem in weighted and directed networks, we show that our algorithm significantly outperforms existing algorithms. In the clustering problem when the data was generated by mixture models in the sparse regime we show that our method works all the way down to the theoretical limit of detectability and gives accuracy very close to that of the optimal Bayesian inference. In the semi-supervised clustering problem, our method only needs several labels to work perfectly in classic datasets. Finally, we further develop Thouless-Anderson-Palmer equations which reduce heavily the computation complexity in dense-networks but gives almost the same performance as belief propagation.

show abstract

Nonbacktracking operator for the Ising model and its applications in systems with multiple states

Cited by 10 publications

References 38 publications

Fast and simple decycling and dismantling of networks

Fast and simple decycling and dismantling of networks

Statistical physics of inference: thresholds and algorithms

Weighted community detection and data clustering using message passing

Contact Info

Product

Resources

About