Abstract
Two sequential methods are described for sampling constrained binary sequences from partial solutions. The backward method computes elimination ideals over finite fields and constructs partial solutions that extend. The forward method uses numerical global optimization to determine which partial solutions extend. The methods are applied to restricted orderings, binary dynamics, and random graphs.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Admiraal, R., Handcock, M.S.: Networksis: a package to simulate bipartite graphs with fixed marginals through sequential importance sampling. J. Stat. Softw. 24, 1–21 (2008)
Agresti, A., Mehta, C.R., Patel, N.R.: Exact inference for contingency tables with ordered categories. J. Am. Stat. Assoc. 85, 453–458 (1990)
Albert, R., Othmer, H.G.: The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in Drosophila melanogaster. J. Theor. Biol. 223, 1–18 (2003)
Aracena, J.: Maximum number of fixed points in regulatory Boolean networks. Bull. Math. Biol. 70, 1398–1409 (2008)
Blitzstein, J., Diaconis, P.: A sequential importance sampling algorithm for generating random graphs with prescribed degrees. Stanford University Technical Report (2006)
Breiman, L., Cutler, A.: A deterministic algorithm for global optimization. Math. Program. 58, 179–199 (1993)
Butts, C.T., Handcock, M.S., Hunter, D.R.: Network: Classes for Relational Data. R package version 1.4-1. Irvine, CA (2008). http://statnet.org/
Chen, Y.: Conditional inference on tables with structural zeros. J. Comput. Graph. Stat. 16, 445–467 (2007)
Chen, Y., Liu, J.S.: Sequential Monte Carlo methods for permutation tests on truncated data. Stat. Sin. 17, 857–872 (2007)
Chen, Y., Diaconis, P., Holmes, S.P., Liu, J.S.: Sequential Monte Carlo methods for statistical analysis of tables. J. Am. Stat. Assoc. 100, 109–120 (2005)
Cox, D., Little, J., O’Shea, D.: Ideal, Varieties, and Algorithms, 2nd edn. Springer, New York (1997)
Diaconis, P., Graham, R., Holmes, S.P.: Statistical problems involving permutations with restricted positions. In: State of the Art in Probability and Statistics, Leiden, 1999. IMS Lecture Notes Monogr. Ser., vol. 36, pp. 195–222. Inst. Math. Statist., Beachwood (2001)
Dinwoodie, I.H.: Polynomials for classification trees and applications. SAMSI Technical Report 2008-7 (2008)
Greuel, G.-M., Pfister, G., Schönemann, H.: Singular 3.0.4. A Computer Algebra System for Polynomial Computations. Centre for Computer Algebra, University of Kaiserslautern (2007). URL http://www.singular.uni-kl.de
Grippo, L., Lampariello, F., Lucidi, S.: A nonmonotone line search technique for Newton’s method. SIAM J. Numer. Anal. 23, 707–716 (1986)
Handcock, M.S., Hunter, D.R., Butts, C.T., Goodreau, S.M., Morris, M.: ergm: A Package to Fit, Simulate and Diagnose Exponential-Family Models for Networks. Version 2.2-1 (2009). Project home page at http://statnetproject.org. URL http://CRAN.R-project.org/package=ergm
Huber, M.: Fast perfect sampling from linear extensions. Discrete Math. 306, 420–428 (2006)
Kreuzer, M., Robbiano, L.: Computational Commutative Algebra I. Springer, New York (2000)
LaCruz, W., Martinez, J.M., Raydan, M.: Spectral residue method without gradient information for solving large-scale nonlinear systems of equations. Math. Comput. 75, 1429–1448 (2006)
Liu, J.S.: Monte Carlo Strategies in Scientific Computing. Springer, New York (2001)
Matthews, P.: Generating a random linear extension of a partial order. Ann. Probab. 19, 1367–1392 (1991)
Mendoza, L., Alvarez-Buylla, E.R.: Dynamics of the genetic regulatory network for Arabidopsis thaliana. J. Theor. Biol. 193, 307–319 (1998)
Motwani, R., Raghavan, P.: Randomized Algorithms. Cambridge University Press, Cambridge (1995)
Pevzner, P.A.: Computational Molecular Biology. MIT Press, Cambridge (2000)
Pistone, G., Riccomagno, E., Wynn, H.: Algebraic Statistics: Computational Commutative Algebra in Statistics. Chapman and Hall, New York (2001)
R Development Core Team: R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna (2009). ISBN 3-900051-07-0, URL http://www.R-project.org
Roberts, F.S., Tesman, B.: Applied Combinatorics. Pearson Prentice Hall, Upper Saddle River (2005)
Robins, G., Snijders, T., Wang, P., Handcock, M., Pattison, P.: Recent developments in exponential random graph (p ∗) models for social networks. Soc. Netw. 29, 192–215 (2007)
Rubinstein, R.: Randomized algorithms with splitting: why the classic randomized algorithms do not work and how to make them work. Methodol. Comput. Appl. Probab. 12, 1–50 (2010)
Snijders, T.A.B.: Enumeration and simulation methods for 0–1 matrices with given marginals. Psychometrika 56, 397–417 (1991)
Varadhan, R., Gilbert, P.D.: BB: An R package for solving a large system of nonlinear equations and for optimizing a high-dimensional nonlinear objective function (version 2010.4-1). J. Stat. Softw. 32, 1–26 (2009)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Dinwoodie, I.H. Sequential importance sampling of binary sequences. Stat Comput 22, 53–63 (2012). https://doi.org/10.1007/s11222-010-9205-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11222-010-9205-0