检索结果-内蒙古大学图书馆

Disordered systems insights on computational hardness

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2022年第11期2022卷 114015-114015页

作者： Gamarnik, David Moore, Cristopher Zdeborova, Lenka MIT Operat Res Ctr Cambridge MA 02139 USA MIT Sloan Sch Management Cambridge MA 02139 USA Santa Fe Inst Santa Fe NM 87501 USA Ecole Polytech Fed Lausanne EPFL SPOC Lab Route Cantonale CH-1015 Lausanne Switzerland

In this review article we discuss connections between the physics of disordered systems, phase transitions in inference problems, and computational hardness. We introduce two models representing the behavior of glassy systems, the spiked tensor model and the generalized linear model. We discuss the random (non-planted) versions of these problems as prototypical optimization problems, as well as the planted versions (with a hidden solution) as prototypical problems in statistical inference and learning. Based on ideas from physics, many of these problems have transitions where they are believed to jump from easy (solvable in polynomial time) to hard (requiring exponential time). We discuss several emerging ideas in theoretical computer science and statistics that provide rigorous evidence for hardness by proving that large classes of algorithms fail in the conjectured hard regime. This includes the overlap gap property, a particular mathematization of clustering or dynamical symmetry-breaking, which can be used to show that many algorithms that are local or robust to changes in their input fail. We also discuss the sum-of-squares hierarchy, which places bounds on proofs or algorithms that use low-degree polynomials such as standard spectral methods and semidefinite relaxations, including the Sherrington-Kirkpatrick model. Throughout the manuscript we present connections to the physics of disordered systems and associated replica symmetry breaking properties.

关键词： cavity and replica method message-passing algorithms statistical inference typical-case computational complexity

来源：评论

学校读者我要写书评

暂无评论

Characterizing and improving generalized belief propagation algorithms on the 2D Edwards-Anderson model

引用

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2011年第12期2011卷

作者： Dominguez, Eduardo Lage-Castellanos, Alejandro Mulet, Roberto Ricci-Tersenghi, Federico Rizzo, Tommaso Univ Havana Dept Theoret Phys Havana Cuba Univ Havana Fac Phys Henri Poincare Grp Complex Syst Havana Cuba Univ Roma La Sapienza Dipartimento Fis Ist Nazl Fis Nucl Sez Roma 1 I-00185 Rome Italy Univ Roma La Sapienza CNR IPCF UOS Roma I-00185 Rome Italy

We study the performance of different message passing algorithms in the two-dimensional Edwards-Anderson model. We show that the standard belief propagation (BP) algorithm converges only at high temperature to a paramagnetic solution. Then, we test a generalized belief propagation (GBP) algorithm, derived from a cluster variational method (CVM) at the plaquette level. We compare its performance with BP and with other algorithms derived under the same approximation: double loop (DL) and a two-way message passing algorithm (HAK). The plaquette-CVM approximation improves BP in at least three ways: the quality of the paramagnetic solution at high temperatures, a better estimate (lower) for the critical temperature, and the fact that the GBP message passing algorithm converges also to nonparamagnetic solutions. The lack of convergence of the standard GBP message passing algorithm at low temperatures seems to be related to the implementation details and not to the appearance of long range order. In fact, we prove that a gauge invariance of the constrained CVM free energy can be exploited to derive a new message passing algorithm which converges at even lower temperatures. In all its region of convergence this new algorithm is faster than HAK and DL by some orders of magnitude.

关键词： cavity and replica method disordered systems (theory) message-passing algorithms statistical inference

来源：评论

学校读者我要写书评

暂无评论

The cavity method to protein design problem

引用

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2022年第10期2022卷 103403-103403页

作者： Takahashi, Tomoei Chikenji, George Tokita, Kei Nagoya Univ Grad Sch Informat Nagoya Aichi 4648601 Japan Nagoya Univ Grad Sch Engn Nagoya Aichi 4648603 Japan

In this study, we propose an analytic statistical mechanics approach to solve a fundamental problem in biological physics called protein design. Protein design is an inverse problem of protein structure prediction, and its solution is the amino acid sequence that best stabilizes a given conformation. Despite recent rapid progress in protein design using deep learning, the challenge of exploring protein design principles remains. Contrary to previous computational physics studies, we used the cavity method, an extension of the mean-field approximation that becomes rigorous when the interaction network is a tree. We found that for small two-dimensional lattice hydrophobic-polar protein models, the design by the cavity method yields results almost equivalent to those from the Markov chain Monte Carlo method with lower computational cost.

关键词： message-passing algorithms cavity and replica method protein function and design

来源：评论

学校读者我要写书评

暂无评论

Survey propagation as local equilibrium equations

引用

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2004年第6期2004卷

作者： Braunstein, A Zecchina, R SISSA I-34100 Trieste Italy Abdus Salaam Int Ctr Theoret Phys I-34100 Trieste Italy

It has been shown experimentally that a decimation algorithm based on survey propagation (SP) equations allows one to solve efficiently some combinatorial problems over random graphs. We show that these equations can be derived as sum - product equations for the computation of marginals in an extended space where the variables are allowed to take an additional value - - when they are not forced by the combinatorial constraints. An appropriate 'local equilibrium condition' cost/energy function is introduced and its entropy is shown to coincide with the expected logarithm of the number of clusters of solutions as computed by SP. These results may help to clarify the geometrical notion of clusters assumed by SP for random K-SAT or random graph colouring ( where it is conjectured to be exact) and help to explain which kind of clustering operation or approximation is enforced in general/small sized models in which it is known to be inexact.

关键词： cavity and replica method message-passing algorithms source and channel coding

来源：评论

学校读者我要写书评

暂无评论

Fermions and loops on graphs: I. Loop calculus for determinants

引用

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2008年第12期2008卷

作者： Chernyak, Vladimir Y. Chertkov, Michael Wayne State Univ Dept Chem Detroit MI 48202 USA Los Alamos Natl Lab Div Theoret Los Alamos NM 87545 USA Los Alamos Natl Lab Ctr Nonlinear Studies Los Alamos NM 87545 USA

This paper is the first in a series devoted to evaluation of the partition function in statistical models on graphs with loops in terms of the Berezin/fermion integrals. The paper focuses on a representation of the determinant of a square matrix in terms of a finite series, where each term corresponds to a loop on the graph. The representation is based on a fermion version of the loop calculus, previously introduced by the authors for graphical models with finite alphabets. Our construction contains two levels. First, we represent the determinant in terms of an integral over anti-commuting Grassmann variables, with some reparametrization/gauge freedom hidden in the formulation. Second, we show that a special choice of the gauge, called the BP (Bethe-Peierls or belief propagation) gauge, yields the desired loop representation. The set of gauge. xing BP conditions is equivalent to the Gaussian BP equations, discussed in the past as efficient (linear scaling) heuristics for estimating the covariance of a sparse positive matrix.

关键词： rigorous results in statistical mechanics message-passing algorithms gauge theories

来源：评论

学校读者我要写书评

暂无评论

Centrality metrics and localization in core-periphery networks

引用

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2016年第2期2016卷

作者： Barucca, Paolo Tantari, Daniele Lillo, Fabrizio Scuola Normale Super Pisa Piazza Cavalieri 7 I-56126 Pisa PI Italy Ctr Ric Matemat Ennio De Giorgi Piazza Cavalieri 3 Pisa PI Italy

Two concepts of centrality have been defined in complex networks. The first considers the centrality of a node and many different metrics for it have been defined (e.g. eigenvector centrality, PageRank, non-backtracking centrality, etc). The second is related to large scale organization of the network, the core-periphery structure, composed by a dense core plus an outlying and loosely-connected periphery. In this paper we investigate the relation between these two concepts. We consider networks generated via the stochastic block model, or its degree corrected version, with a core-periphery structure and we investigate the centrality properties of the core nodes and the ability of several centrality metrics to identify them. We find that the three measures with the best performance are marginals obtained with belief propagation, PageRank, and degree centrality, while non-backtracking and eigenvector centrality (or MINRES [10], showed to be equivalent to the latter in the large network limit) perform worse in the investigated networks.

关键词： message-passing algorithms random graphs networks clustering techniques

来源：评论

学校读者我要写书评

暂无评论

The number of matchings in random graphs

引用

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2006年第5期2006卷

作者： Zdeborova, Lenka Mezard, Marc Univ Paris 11 CNRS UMR 8626 LPTMS F-91405 Orsay France

We study matchings on sparse random graphs by means of the cavity method. We first show how the method reproduces several known results about maximum and perfect matchings in regular and Erdos-Renyi random graphs. Our main new result is the computation of the entropy, i.e. the leading order of the logarithm of the number of solutions, of matchings with a given size. We derive both an algorithm to compute this entropy for an arbitrary graph with a girth that diverges in the large size limit, and an analytic result for the entropy in regular and Erdos-Renyi random graph ensembles.

关键词： cavity and replica method message-passing algorithms random graphs networks

来源：评论

学校读者我要写书评

暂无评论

Clusters of solutions and replica symmetry breaking in random k-satisfi ability

引用

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2008年第4期2008卷

作者： Montanari, Andrea Ricci-Tersenghi, Federico Semerjian, Guilhem Stanford Univ Dept Elect Engn Stanford CA 94305 USA Stanford Univ Dept Stat Stanford CA 94305 USA Univ Roma La Sapienza Dipartimento Fis I-00185 Rome Italy Univ Roma La Sapienza CNR INFM I-00185 Rome Italy Univ Paris 06 CNRS UMR 8549 LPTENS F-75231 Paris 05 France Univ Paris 06 ENS Associee UPMC F-75231 Paris 05 France

We study the set of solutions of random k-satisfiability formulas through the cavity method. It is known that, for an interval of the clause-to-variables ratio, this decomposes into an exponential number of pure states (clusters). We re. ne substantially this picture by: (i) determining the precise location of the clustering transition;(ii) uncovering a second 'condensation' phase transition in the structure of the solution set for k >= 4. These results both follow from computing the large deviation rate of the internal entropy of pure states. From a technical point of view our main contributions are a simplified version of the cavity formalism for special values of the Parisi replica symmetry breaking parameter m (in particular for m = 1 via a correspondence with the tree reconstruction problem) and new large-k expansions.

关键词： cavity and replica method disordered systems (theory) message-passing algorithms random graphs networks

来源：评论

学校读者我要写书评

暂无评论

The patient-zero problem with noisy observations

引用

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2014年第10期2014卷

作者： Altarelli, Fabrizio Braunstein, Alfredo Dall'Asta, Luca Ingrosso, Alessandro Zecchina, Riccardo Politecn Torino DISAT I-10129 Turin Italy Politecn Torino Ctr Computat Sci I-10129 Turin Italy Coll Carlo Alberto I-10024 Moncalieri Italy Human Genet Fdn I-10126 Turin Italy

A belief propagation approach has been recently proposed for the patient-zero problem in SIR epidemics. The patient-zero problem consists of finding the initial source of an epidemic outbreak given observations at a later time. In this work, we study a more difficult but related inference problem, in which observations are noisy and there is confusion between observed states. In addition to studying the patient-zero problem, we also tackle the problem of completing and correcting the observations to possibly find undiscovered infected individuals and false test results. Moreover, we devise a set of equations, based on the variational expression of the Bethe free energy, to find the patient-zero along with maximum-likelihood epidemic parameters. We show, by means of simulated epidemics, that this method is able to infer details on the past history of an epidemic outbreak based solely on the topology of the contact network and a single snapshot of partial and noisy observations.

关键词： message-passing algorithms network dynamics epidemic modelling statistical inference

来源：评论

学校读者我要写书评

暂无评论

Stability of the replica symmetric solution in diluted perceptron learning

引用

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT 2013年第2期2013卷

作者： Lage-Castellanos, Alejandro Pagnani, Andrea Quintero Angulo, Gretel Univ Havana Fac Phys Dept Theoret Phys Havana 10400 Cuba Univ Havana Fac Phys Henri Poincare Grp Complex Syst Havana Cuba Human Genet Fdn HuGeF Torino I-10122 Turin Italy

We study the role played by dilution in the average behavior of a perceptron model with continuous coupling with the replica method. We analyze the stability of the replica symmetric solution as a function of the dilution field for the generalization and memorization problems. Thanks to a Gardner-like stability analysis we show that at any fixed ratio a between the number of patterns M and the dimension N of the perceptron (alpha = M/N), there exists a critical dilution field h(c) above which the replica symmetric ansatz becomes unstable.

关键词： message-passing algorithms cognitive dynamical networks learning theory statistical inference

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：