Sequential importance sampling of binary sequences

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.

[1]  Mark Huber,et al.  Fast perfect sampling from linear extensions , 2006, Discret. Math..

[2]  Yuguo Chen,et al.  Sequential Monte Carlo Methods for Statistical Analysis of Tables , 2005 .

[3]  Peng Wang,et al.  Recent developments in exponential random graph (p*) models for social networks , 2007, Soc. Networks.

[4]  Tim Hesterberg,et al.  Monte Carlo Strategies in Scientific Computing , 2002, Technometrics.

[5]  T. Snijders.  Enumeration and simulation methods for 0–1 matrices with given marginals , 1991 .

[6]  P. Matthews.  Generating a Random Linear Extension of a Partial Order , 1991 .

[7]  Martina Morris,et al.  ergm: A Package to Fit, Simulate and Diagnose Exponential-Family Models for Networks. , 2008, Journal of statistical software.

[8]  H. Othmer,et al.  The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in Drosophila melanogaster. , 2003, Journal of theoretical biology.

[9]  Alan Agresti,et al.  Exact Inference for Contingency Tables with Ordered Categories , 1990 .

[10]  R. Rubinstein.  Randomized Algorithms with Splitting: Why the Classic Randomized Algorithms Do Not Work and How to Make them Work , 2010 .

[11]  Hans Schönemann,et al.  SINGULAR: a computer algebra system for polynomial computations , 2001, ACCA.

[12]  Yuguo Chen,et al.  Conditional Inference on Tables With Structural Zeros , 2007 .

[13]  Jun S. Liu,et al.  SEQUENTIAL MONTE CARLO METHODS FOR PERMUTATION TESTS ON TRUNCATED DATA , 2007 .

[14]  H. Wynn,et al.  Algebraic Statistics: Computational Commutative Algebra in Statistics , 2000 .

[15]  Persi Diaconis,et al.  A Sequential Importance Sampling Algorithm for Generating Random Graphs with Prescribed Degrees , 2011, Internet Math..

[16]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[17]  L. Grippo,et al.  A nonmonotone line search technique for Newton's method , 1986 .

[18]  Ronald L. Graham,et al.  Statistical Problems Involving Permutations With Restricted Positions , 1999 .

[19]  José Mario Martínez,et al.  Spectral residual method without gradient information for solving large-scale nonlinear systems of equations , 2006, Math. Comput..

[20]  Leo Breiman,et al.  A deterministic algorithm for global optimization , 1993, Math. Program..

[21]  Steven M. Goodreau,et al.  Advances in exponential random graph (p*) models applied to a large social network , 2007, Soc. Networks.

[22]  Petra Mutzel,et al.  Computational Molecular Biology , 1996 .

[23]  Ravi Varadhan,et al.  BB: An R Package for Solving a Large System of Nonlinear Equations and for Optimizing a High-Dimensional Nonlinear Objective Function , 2009 .

[24]  E. Álvarez-Buylla,et al.  Dynamics of the genetic regulatory network for Arabidopsis thaliana flower morphogenesis. , 1998, Journal of theoretical biology.

[25]  Russ Bubley,et al.  Randomized algorithms , 1995, CSUR.

[26]  J. Aracena.  Maximum Number of Fixed Points in Regulatory Boolean Networks , 2008, Bulletin of mathematical biology.

[27]  Fred S. Roberts,et al.  Applied Combinatorics , 1984 .

[28]  P. Pevzner,et al.  Computational Molecular Biology , 2000 .

[29]  Martin Kreuzer,et al.  Computational Commutative Algebra 1 , 2000 .

[30]  Ian H. Dinwoodie,et al.  Polynomials for classification trees and applications , 2010, Stat. Methods Appl..

[31]  Mark S Handcock,et al.  networksis: A Package to Simulate Bipartite Graphs with Fixed Marginals Through Sequential Importance Sampling. , 2008, Journal of statistical software.

[32]  Ravi Varadhan,et al.  Solving and Optimizing Large-Scale Nonlinear Systems , 2014 .