Results 1  10
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47
Algebraic Algorithms for Sampling from Conditional Distributions
 Annals of Statistics
, 1995
"... We construct Markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic. Examples include generating tables with fixed row and column sums and higher dimensional analogs. The algorithms involve finding bases for associated polynomial ideals and so a ..."
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Cited by 192 (16 self)
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We construct Markov chain algorithms for sampling from discrete exponential families conditional on a sufficient statistic. Examples include generating tables with fixed row and column sums and higher dimensional analogs. The algorithms involve finding bases for associated polynomial ideals and so an excursion into computational algebraic geometry.
Multiresolution image classification by hierarchical modeling with two dimensional hidden Markov models
 IEEE TRANS. INFORMATION THEORY
, 2000
"... This paper treats a multiresolution hidden Markov model for classifying images. Each image is represented by feature vectors at several resolutions, which are statistically dependent as modeled by the underlying state process, a multiscale Markov mesh. Unknowns in the model are estimated by maximum ..."
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Cited by 49 (9 self)
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This paper treats a multiresolution hidden Markov model for classifying images. Each image is represented by feature vectors at several resolutions, which are statistically dependent as modeled by the underlying state process, a multiscale Markov mesh. Unknowns in the model are estimated by maximum likelihood, in particular by employing the expectationmaximization algorithm. An image is classified by finding the optimal set of states with maximum a posteriori probability. States are then mapped into classes. The multiresolution model enables multiscale information about context to be incorporated into classification. Suboptimal algorithms based on the model provide progressive classification that is much faster than the algorithm based on singleresolution hidden Markov models.
B lymphocytes may escape tolerance by revising their antigen receptors
, 1993
"... To explore mechanisms that prevent autoreactivity in nonautoimmune mice, endogenous immunoglobulin (Ig) light (L) chains that associate with a transgenic antiDNA heavy chain were analyzed. The antibodies from splenic B cell hybridomas of such mice did not bind doublestranded DNA (dsDNA) and their L ..."
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Cited by 48 (12 self)
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To explore mechanisms that prevent autoreactivity in nonautoimmune mice, endogenous immunoglobulin (Ig) light (L) chains that associate with a transgenic antiDNA heavy chain were analyzed. The antibodies from splenic B cell hybridomas of such mice did not bind doublestranded DNA (dsDNA) and their L chain sequences showed a biased use of V ~ and J ~ gene segments. The 44 L chains in this survey were coded for by just 18 germline genes. Six of the genes, each belonging to a different V ~ group, were used more than once and accounted for three fourths of all sequences. Based on the distribution of V ~ genes, the L chain repertoire in this line of transgenic mice was estimated at 37 V ~ genes. The most frequently observed gene, a member of the V ~ 12/13 group, was identified in 16 hybrids. In addition, the majority of V ~ genes used J~5. We interpret the skewed representation of V ~ and J ~ gene segments to result from negative selection. Based on the data, we suggest that V ~ rearrangements giving rise to antidsDNA reactivity are removed from the repertoire by a corrective mechanism capable of editing selfreactive Ig. T olerance to self has been studied in Ig transgenic models
Some characterizations of minimal Markov basis for sampling from discrete conditional distributions
 Annals of the Institute of Statistical Mathematics
, 2002
"... this paper we give some basic characterizations of minimal Markov basis for a connected Markov chain, which is used for performing exact tests in discrete exponential families given a sufficient statistic. We also give a necessary and sufficient condition for uniqueness of minimal Markov basis. A ge ..."
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Cited by 28 (17 self)
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this paper we give some basic characterizations of minimal Markov basis for a connected Markov chain, which is used for performing exact tests in discrete exponential families given a sufficient statistic. We also give a necessary and sufficient condition for uniqueness of minimal Markov basis. A general algebraic algorithm for constructing a connected Markov chain was given by Diaconis and Sturmfels (1998). Their algorithm is based on computing Grobner basis for a certain ideal in a polynomial ring, which can be carried out by using available computer algebra packages. However structure and interpretation of Grobner basis produced by the packages are not necessarily clear, due to the lack of symmetry and minimality inherent in Grobner basis computation. Our approach clarifies partially ordered structure of minimal Markov basis
The complexity of threeway statistical tables
 SIAM J. COMPUT
, 2004
"... Multiway tables with specified marginals arise in a variety of applications in statistics and operations research. We provide a comprehensive complexity classification of three fundamental computational problems on tables: existence, counting, and entrysecurity. One outcome of our work is that eac ..."
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Cited by 26 (7 self)
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Multiway tables with specified marginals arise in a variety of applications in statistics and operations research. We provide a comprehensive complexity classification of three fundamental computational problems on tables: existence, counting, and entrysecurity. One outcome of our work is that each of the following problems is intractable already for “slim” 3tables, with constant number 3 of rows: (1) deciding existence of 3tables with specified 2marginals; (2) counting all 3tables with specified 2marginals; (3) deciding whether a specified value is attained in a specified entry by at least one of the 3tables having the same 2marginals as a given table. This implies that a characterization of feasible marginals for such slim tables, sought by much recent research, is unlikely to exist. Another consequence of our study is a systematic efficient way of embedding the set of 3tables satisfying any given 1marginals and entry upper bounds in a set of slim 3tables satisfying suitable 2marginals with no entry bounds. This provides a valuable tool for studying multiindex transportation problems and multiindex transportation polytopes. Remarkably, it enables us to automatically recover a famous example due to Vlach of a “realfeasible integerinfeasible ” collection of 2marginals for 3tables of smallest possible size (3, 4, 6).
All rational polytopes are transportation polytopes and all polytopal integer sets are contingency tables
 PROC. 10TH
, 2004
"... We show that any rational polytope is polynomialtime representable as a “slim ” r × c × 3 threeway linesum transportation polytope. This universality theorem has important consequences for linear and integer programming and for confidential statistical data disclosure. It provides polynomialtime ..."
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Cited by 22 (5 self)
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We show that any rational polytope is polynomialtime representable as a “slim ” r × c × 3 threeway linesum transportation polytope. This universality theorem has important consequences for linear and integer programming and for confidential statistical data disclosure. It provides polynomialtime embedding of arbitrary linear programs and integer programs in such slim transportation programs and in bipartite biflow programs. It resolves several standing problems on 3way transportation polytopes. It demonstrates that the range of values an entry can attain in any slim 3way contingency table with specified 2margins can contain arbitrary gaps, suggesting that disclosure of kmargins of dtables for 2 ≤ k<dis confidential. Our construction also provides a powerful tool in studying concrete questions about transportation polytopes and contingency tables; remarkably, it enables to automatically recover the famous “realfeasible integerinfeasible” 6×4×3 transportation polytope of M. Vlach, and to produce the first example of 2margins for 6 × 4 × 3 contingency tables where the range of values a specified entry can attain has a gap.
Sampling Contingency Tables
 Random Structures & Algorithms
, 1995
"... this paper, discuss our work counting 4 \Theta 4 contingency tables. 5 4 Sampling Contingency tables : Reduction to continuous sampling This section reduces the problem of sampling from the discrete set of contingency tables to the problem of sampling with nearuniform density from a contingency po ..."
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Cited by 15 (6 self)
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this paper, discuss our work counting 4 \Theta 4 contingency tables. 5 4 Sampling Contingency tables : Reduction to continuous sampling This section reduces the problem of sampling from the discrete set of contingency tables to the problem of sampling with nearuniform density from a contingency polytope. To this end, we first take a natural basis for the lattice of all integer points in
All Linear and Integer Programs are Slim 3way Transportation Programs
"... We show that any rational convex polytope is polynomialtime representable as a threeway linesum transportation polytope of “slim ” (r, c, 3) format. This universality theorem has important consequences for linear and integer programming and for confidential statistical data disclosure. We provide ..."
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Cited by 14 (3 self)
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We show that any rational convex polytope is polynomialtime representable as a threeway linesum transportation polytope of “slim ” (r, c, 3) format. This universality theorem has important consequences for linear and integer programming and for confidential statistical data disclosure. We provide a polynomialtime embedding of arbitrary linear programs and integer programs in such slim transportation programs and in bitransportation programs. Our construction resolves several standing problems on 3way transportation polytopes. For example, it demonstrates that, unlike the case of 2way contingency tables, the range of values an entry can attain in any slim 3way contingency table with specified 2margins can contain arbitrary gaps. Our smallest such example has format (6, 4, 3). Our construction provides a powerful automatic tool for studying concrete questions about transportation polytopes and contingency tables. For example, it automatically provides new proofs for some classical results, including a wellknown “realfeasible integerinfeasible ” (6, 4, 3)transportation polytope of M. Vlach, and bitransportation programs where any feasible bitransportation must have an arbitrarily large prescribed denominator.
Stochastic grammatical inference with Multinomial Tests
, 2002
"... We present a new statistical framework for stochastic grammatical inference algorithms based on a state merging strategy. We propose to use multinomial statistical tests to decide which states should be merged. This approach has three main advantages. First, since it is not based on asymptotic resul ..."
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Cited by 12 (1 self)
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We present a new statistical framework for stochastic grammatical inference algorithms based on a state merging strategy. We propose to use multinomial statistical tests to decide which states should be merged. This approach has three main advantages. First, since it is not based on asymptotic results, small sample case can be specifically dealt with. Second, all the probabilities associated to a state are included in a single test so that statistical evidence is cumulated. Third, a statistical score is associated to each possible merging operation and can be used for bestfirst strategy. Improvement over classical stochastic grammatical inference algorithm is shown on artificial data.