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Goodness of fit for log-linear network models: dynamic Markov bases using hypergraphs

ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS 2017年第3期69卷 673-704页

作者： Gross, Elizabeth Petrovic, Sonja Stasi, Despina San Jose State Univ Dept Math & Stat One Washington Sq San Jose CA 95192 USA IIT Dept Appl Math Rettaliata Engn Ctr Room 20810 West 32nd St Chicago IL 60616 USA

Social networks and other sparse data sets pose significant challenges for statistical inference, since many standard statistical methods for testing model/data fit are not applicable in such settings. Algebraic statistics offers a theoretically justified approach to goodness-of-fit testing that relies on the theory of Markov bases. Most current practices require the computation of the entire basis, which is infeasible in many practical settings. We present a dynamic approach to explore the fiber of a model, which bypasses this issue, and is based on the combinatorics of hypergraphs arising from the toric algebra structure of log-linear models. We demonstrate the approach on the Holland-Leinhardt model for random directed graphs that allows for reciprocation effects.

关键词： Algebraic statistics Markov basis Hypergraph Toric ideal Contingency table Network model Random graph sampling algorithm

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Polynomial time samplable distributions

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JOURNAL OF COMPLEXITY 1999年第4期15卷 557-574页

作者： Yamakami, T Univ Toronto Dept Comp Sci Toronto ON M5S 3G4 Canada

This paper studies the complexity of the polynomial-time samplable (P-samplable) distributions, which can be approximated within an exponentially small Factor by sampling algorithms in time polynomial in the length of their outputs. The paper shows that common assumptions in complexity theory yield the separation of polynomial-time samplable distributions from the polynomial-lime computable distributions with respect to polynomial domination, average-polynomial domination, polynomial equivalence, and average-polynomial equivalence. (C) 1999 Academic Press.

关键词： average-case complexity sampling algorithm domination condition strong one-way functions

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PSEUDONOISE WITH ARBITRARY AMPLITUDE DISTRIBUTION .1. THEORY

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IEEE TRANSACTIONS ON COMPUTERS 1972年第4期C 21卷 337-+页

作者： SOBOLEWSKI, JS PAYNE, WH Departments of Electrical Engineering and Computer Science and the Computing Center Washington State University Pullman Wash. 9916

Many cases arise in practice where a versatile hardwired pseudorandom number or pseudonoise generator would be extremely useful. General-purpose pseudonoise devices are not available today. We present a new sampling method, conditional bit sampling, which is suited for hardwired sampling devices because of its generality, simplicity, and accuracy. Random variables sampled from an arbitrary distribution are generated bit by bit from high- to low-order bits with the conditional bit algorithm. The result of a comparison of a uniform number to a conditional probability determines whether a bit in the sampled random number is set to one. The conditional probabilities are easily calculated for any probability distribution and must be arranged in special order. Simple Fortran programs make all necessary computations. Agreement between actual and theoretical performance of the conditional bit algorithm was excellent when sampling accuracy was evaluated for several examples of continuous and discrete densities. sampling from empirically known, perhaps erratic-shaped, densities presents no problems. Only a small memory containing the conditional probabilities needs to be changed to alter the sampled distribution. The conditional bit algorithmic process always remains the same.

关键词： Conditional bit sampling cumulative density function probability density function probability distribution function pseudorandom noise pseudorandom variable sampling algorithm

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An improved model combining knowledge graph and GCN for PLM knowledge recommendation

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SOFT COMPUTING 2024年第6期28卷 5557-5575页

作者： Tong, Guoxiang Li, Deyun Liu, Xuemei Univ Shanghai Sci & Technol Sch Opt Elect & Comp Engn Shanghai 200093 Peoples R China Tongji Univ Sch Mech Engn Shanghai 200092 Peoples R China

Faced with the challenges of intelligently managing the entire product lifecycle, traditional management techniques no longer meet the complex demands of modern enterprises. To address it, we employ an ontology modeling method based on a multidimensional view of product information for a knowledge graph, culminating in a comprehensive PLM knowledge system. To better serve PLM users, we propose an intelligent recommendation model based on context and user behavior for knowledge recommendations. This model seamlessly integrates the knowledge storage structure, user preference attributes, and the rich semantics of the knowledge graph. To improve the recommendation capability of the model, we design an improved multi-hop neighbor node sampling algorithm and use a graph convolutional neural network to quantify the target user preference attributes layer by layer. After a series of rigorous validation experiments, our method consistently outperformed competing models across key performance metrics, such as accuracy and recall, underscoring its efficacy and practicality in knowledge recommendation within PLM systems.

关键词： Product lifecycle management Recommendation model Knowledge graph sampling algorithm

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Constructing hierarchical Archimedean copulas with Levy subordinators

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JOURNAL OF MULTIVARIATE ANALYSIS 2010年第6期101卷 1428-1433页

作者： Hering, Christian Hofert, Marius Mai, Jan-Frederik Scherer, Matthias Tech Univ Munich HVB Stiftungsinst Finanzmath D-85748 Garching Germany Univ Ulm Inst Number Theory & Probabil Theory D-89081 Ulm Germany

A probabilistic interpretation for hierarchical Archimedean copulas based on Levy subordinators is given. Independent exponential random variables are divided by group-specific Levy subordinators which are evaluated at a common random time. The resulting random vector has a hierarchical Archimedean survival copula. This approach suggests an efficient sampling algorithm and allows one to easily construct several new parametric families of hierarchical Archimedean copulas. (C) 2009 Elsevier Inc. All rights reserved.

关键词： Hierarchical Archimedean copulas Levy subordinators sampling algorithm

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Collective proposal distributions for nonlinear MCMC samplers: Mean-field theory and fast implementation

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ELECTRONIC JOURNAL OF STATISTICS 2022年第2期16卷 6395-6460页

作者： Clarte, Gregoire Diez, Antoine Feydy, Jean Univ Helsinki Dept Comp Sci FCAI Helsinki Finland Imperial Coll London Dept Math London England Kyoto Univ Inst Adv Study Human Biol ASHBi Kyoto Japan Inria Paris HeKA Team F-75012 Paris France Sorbonne Univ Univ Paris Cite Ctr Rech Cordeliers Inserm F-75006 Paris France

Over the last decades, various "non-linear" MCMC methods have arisen. While appealing for their convergence speed and efficiency, their practical implementation and theoretical study remain challenging. In this paper, we introduce a non-linear generalization of the Metropolis -Hastings algorithm to a proposal that depends not only on the current state, but also on its law. We propose to simulate this dynamics as the mean field limit of a system of interacting particles, that can in turn itself be understood as a generalisation of the Metropolis-Hastings algorithm to a population of particles. Under the double limit in number of iterations and number of particles we prove that this algorithm converges. Then, we propose an efficient GPU implementation and illustrate its performance on various examples. The method is particularly stable on multimodal exam-ples and converges faster than the classical methods.

关键词： sampling algorithm particle method propaga-tion of chaos entropy methods GPU

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Bayesian inversion of piecewise affine operators in a Gaussian framework

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2005年第1期14卷 56-74页

作者： Kolbjornsen, O Omre, H Norwegian Comp Ctr N-0314 Oslo Norway Norwegian Univ Sci & Technol Dept Math Sci N-7491 Trondheim Norway

Piecewise affine inverse problems form a general class of nonlinear inverse problems. In particular inverse problems obeying certain variational structures, such as Fermat's principle in travel time tomography, are of this type. In a piecewise affine inverse problem a parameter is to be reconstructed when its mapping through a piecewise affine operator is observed, possibly with errors. A piecewise affine operator is defined by partitioning the parameter space and assigning a specific affine operator to each part. A Bayesian approach with a Gaussian random field prior on the parameter space is used. Both problems with a discrete finite partition and a continuous partition of the parameter space are considered. The main result is that the posterior distribution is decomposed into a mixture of truncated Gaussian distributions, and the expression for the mixing distribution is partially analytically tractable. The general framework has, to the authors' knowledge, not previously been published, although the result for the finite partition is generally known. Inverse problems are currently of large interest in many fields. The Bayesian approach is popular and most often highly computer intensive. The posterior distribution is frequently concentrated close to high-dimensional nonlinear spaces, resulting in slow mixing for generic sampling algorithms. Inverse problems are, however, often highly structured. In order to develop efficient sampling algorithms for a problem at hand, the problem structure must be exploited. The decomposition of the posterior distribution that is derived in the current work can be used to develop specialized sampling algorithms. The article contains examples of such sampling algorithms. The proposed algorithms are applicable also for problems with exact observations. This is a case for which generic sampling algorithms tend to fail.

关键词： Bayesian inference nonlinear inverse problem piecewise linear inverse problem sampling algorithm

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Truncation invariant copulas and a testing procedure

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2016年第12期86卷 2362-2378页

作者： Di Lascio, F. Marta L. Durante, Fabrizio Jaworski, Piotr Free Univ Bozen Bolzano Fac Econ & Management I-39100 Bolzano Italy Univ Warsaw Inst Math Warsaw Poland

The class of bivariate copulas that are invariant under truncation with respect to one variable is considered. A simulation algorithm for the members of the class and a novel construction method are presented. Moreover, inspired by a stochastic interpretation of the members of such a class, a procedure is suggested to check whether the dependence structure of a given data set is truncation invariant. The overall performance of the procedure has been illustrated on both simulated and real data.

关键词： Copula goodness-of-fit test sampling algorithm truncation invariance

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PSEUDONOISE WITH ARBITRARY AMPLITUDE DISTRIBUTION .2. HARDWARE IMPLEMENTATION

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IEEE TRANSACTIONS ON COMPUTERS 1972年第4期C 21卷 346-+页

作者： SOBOLEWSKI, JS PAYNE, WH Departments of Electrical Engineering and Computer Science and the Computing Center Washington State University Pullman Wash. 9916

A hardwired device that produces a voltage with arbitrary amplitude distribution was constructed using a "conditional bit" algorithm to sample from an arbitrary voltage amplitude distribution. The sampling algorithm and hardware processor are independent of the distribution sampled. Only a small read-only memory ROM needs to be changed to alter the distribution sampled. It is possible to compute the accuracy of the sampled random variables from knowledge of the read-only memory contents. The sampling accuracy of the device may be arbitrarily increased by varying any of several design parameters. Our particular pseudonoise generator produced 200 000 random seven-bit variables/s. Contents of read-only memories for both a Gaussian and an arbitrary density were computed so that the maximum error was less than 2.73 percent. Both the sampling speed and accuracy of a conditional bit pseudonoise generator can be increased much in excess of our implementation.

关键词： Conditional bit sampling hardware sampling device pseudorandom noise pseudorandom variable sampling algorithm shift register sequence

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A fast algorithm to sample the number of vertexes and the area of the random convex hull on the unit square

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COMPUTATIONAL STATISTICS 2014年第5期29卷 1187-1205页

作者： Ng, Chi Tim Lim, Johan Lee, Kyeong Eun Yu, Donghyeon Choi, Sujung Chonnam Natl Univ Dept Stat Kwangju 500757 South Korea Seoul Natl Univ Dept Stat Seoul 151747 South Korea Kyoungpook Natl Univ Dept Stat Taegu 702701 South Korea Univ Texas SW Med Ctr Dallas Dept Clin Sci Dallas TX 75390 USA Ulsan Univ Sci & Technol Sch Technol Management Ulsan 689798 South Korea

We propose an algorithm to sample the area of the smallest convex hull containing sample points uniformly distributed over unit square. To do it, we introduce a new coordinate system for the position of vertexes and re-write joint distribution of the number of vertexes and their locations in the new coordinate system. The proposed algorithm is much faster than existing procedure and has a computational complexity on the order of , where is the number of vertexes. Using the proposed algorithm, we numerically investigate the asymptotic behavior of functionals of the random convex hull. In addition, we apply it to finding pairs of stocks where the returns are dependent on each other on the New York Stock Exchange.

关键词： Area Convex hull Pairwise dependence sampling algorithm Uniform distribution Unit square Vertexes

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