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Updated: April 5th, 2024 06:00

2023 journal article

Identifiability of linear compartmental tree models and a general formula for input-output equations

*ADVANCES IN APPLIED MATHEMATICS*, *146*.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: February 27, 2023

2023 journal article

On mixing behavior of a family of random walks determined by a linear recurrence

*DISCRETE MATHEMATICS*, *346*(1).

author keywords: Random walk; Mixing time; Linear recurrence

Source: Web Of Science

Added: October 31, 2022

2023 journal article

The h*-polynomial of the order polytope of the zig-zag poset

*ELECTRONIC JOURNAL OF COMBINATORICS*, *30*(2).

UN Sustainable Development Goal Categories

4. Quality Education
(OpenAlex)

Source: Web Of Science

Added: July 10, 2023

2022 journal article

Directed Gaussian graphical models with toric vanishing ideals

*ADVANCES IN APPLIED MATHEMATICS*, *138*.

author keywords: Clique sum; d-Separation; t-Separation; Shortest trek map; Safe gluing

TL;DR:
This paper makes an attempt to characterize the DAGs whose vanishing ideals are toric ideals, and gives some combinatorial criteria to construct such D AGs from smaller DAG’s which have toric vanishing ideals.
(via Semantic Scholar)

Source: Web Of Science

Added: August 15, 2022

2022 article

Exchangeable and sampling-consistent distributions on rooted binary trees

Hollering, B., & Sullivant, S. (2022, January 14). *JOURNAL OF APPLIED PROBABILITY*.

author keywords: Beta-splitting model; multinomial model; random trees

TL;DR:
A notion of finite sampling consistency for phylogenetic trees is introduced and it is shown that the set of finitely sampling-consistent and exchangeable distributions on n-leaf phylogenetics trees is a polytope.
(via Semantic Scholar)

Source: Web Of Science

Added: January 24, 2022

2022 journal article

Structural identifiability of series-parallel LCR systems

*JOURNAL OF SYMBOLIC COMPUTATION*, *112*, 79–104.

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: March 14, 2022

2021 journal article

Identifiability in phylogenetics using algebraic matroids

*JOURNAL OF SYMBOLIC COMPUTATION*, *104*, 142–158.

author keywords: Identifiability; Algebraic matroids; Phylogenetics; Group-based models; Mixture models

TL;DR:
A new computational strategy for proving the identifiability of discrete parameters in algebraic statistical models that uses algebraic matroids naturally associated to the models to prove that the tree parameters are generically identifiable for 2-tree CFN and K3P mixtures.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

15. Life on Land
(Web of Science)

Source: Web Of Science

Added: January 19, 2021

2021 journal article

Quasi-independence models with rational maximum likelihood estimator

*JOURNAL OF SYMBOLIC COMPUTATION*, *104*, 917–941.

author keywords: Algebraic statistics; Maximum likelihood estimation; Quasi-independence models; Log-linear models; Maximum likelihood degree

TL;DR:
This work gives a necessary and sufficient condition on the bipartite graph associated to the model for the MLE to be rational, and uses the Horn uniformization to show that for general log-linear models $\mathcal{M}$ with rational MLE, any model obtained by restricting to a face of the cone of sufficient statistics of $M$ also hasrational MLE.
(via Semantic Scholar)

Source: Web Of Science

Added: January 19, 2021

2019 journal article

BOUNDS ON THE EXPECTED SIZE OF THE MAXIMUM AGREEMENT SUBTREE FOR A GIVEN TREE SHAPE

*SIAM JOURNAL ON DISCRETE MATHEMATICS*, *33*(4), 2316–2325.

author keywords: maximum agreement subtree; exchangeability; sampling consistency

UN Sustainable Development Goal Categories

15. Life on Land
(Web of Science)

Source: Web Of Science

Added: June 29, 2020

2019 journal article

Strongly Robust Toric Ideals in Codimension 2

*Journal of Algebraic Statistics*, *10*(1), 128–136.

author keywords: toric ideal; Graver basis; robust; Hilbert basis

Source: Crossref

Added: June 20, 2019

2018 monograph

Algebraic Statistics

Source: Crossref

Added: June 30, 2019

2018 journal article

Identifiability of Phylogenetic Parameters from k-mer Data Under the Coalescent

*Bulletin of Mathematical Biology*, *81*(2), 431–451.

author keywords: k-mer method; Coalescent; Algebraic geometry

MeSH headings : Algorithms; Computational Biology; Evolution, Molecular; Markov Chains; Mathematical Concepts; Models, Genetic; Models, Statistical; Mutation; Phylogeny; Probability; Sequence Alignment / statistics & numerical data; Stochastic Processes

TL;DR:
Using the multispecies coalescent model as a basis, model-based moment formulas that involve the species divergence times and the coalescent parameters are derived that prove identifiability results for the tree and branch length parameters under the Jukes–Cantor model of sequence mutations.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

15. Life on Land
(Web of Science)

Sources: Web Of Science, Crossref

Added: February 11, 2019

2018 journal article

The maximum likelihood threshold of a graph

*BERNOULLI*, *24*(1), 386–407.

Source: Web Of Science

Added: August 6, 2018

2017 journal article

Normal Binary Hierarchical Models

*EXPERIMENTAL MATHEMATICS*, *26*(2), 153–164.

author keywords: algebraic statistics; contingency tables; Hilbert basis; Groebner basis; combinatorics

TL;DR:
This work studies the normality of these vector configurations including a description of operations on simplicial complexes that preserve normality, constructions of families of minimally nonnormal complexes, and computations classifying all of the normal complexes on up to six vertices.
(via Semantic Scholar)

Source: Web Of Science

Added: August 6, 2018

2017 journal article

Statistically Consistent k-mer Methods for Phylogenetic Tree Reconstruction

*JOURNAL OF COMPUTATIONAL BIOLOGY*, *24*(2), 153–171.

author keywords: phylogenetic trees; alignment-free methods; k-mer

MeSH headings : Algorithms; Base Sequence; Computer Simulation; Evolution, Molecular; Models, Genetic; Phylogeny; Sequence Alignment; Sequence Analysis, DNA

TL;DR:
It is shown that a standard approach of using the squared Euclidean distance between k-mer vectors to approximate a tree metric can be statistically inconsistent, and model-based distance corrections for orthologous sequences without gaps are derived, which lead to consistent tree inference.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

15. Life on Land
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2017 journal article

Unimodular binary hierarchical models

*JOURNAL OF COMBINATORIAL THEORY SERIES B*, *123*, 97–125.

author keywords: Graver basis; Algebraic statistics; Log-linear models; Hierarchical models; Toric ideal

TL;DR:
The main theorem provides both a construction of all unimodular binary hierarchical models and a characterization in terms of excluded minors, where the definition of a minor allows the taking of links and induced complexes.
(via Semantic Scholar)

Source: Web Of Science

Added: August 6, 2018

2016 journal article

Lifting Markov bases and higher codimension toric fiber products

*Journal of Symbolic Computation*, *74*, 276–307.

author keywords: Markov bases; Toric fiber product; Lifting; Grobner bases

TL;DR:
A lifting algorithm is given that allows to compute Markov bases of the factor ideals that satisfy the compatible projection property and implies new finiteness results for iterated toric fiber products.
(via Semantic Scholar)

Source: Crossref

Added: June 30, 2019

2016 journal article

Matrix Schubert varieties and Gaussian conditional independence models

*JOURNAL OF ALGEBRAIC COMBINATORICS*, *44*(4), 1009–1046.

Source: Web Of Science

Added: August 6, 2018

2015 journal article

BOUNDS ON THE EXPECTED SIZE OF THE MAXIMUM AGREEMENT SUBTREE

*SIAM JOURNAL ON DISCRETE MATHEMATICS*, *29*(4), 2065–2074.

author keywords: random trees; agreement subtrees; Yule-Harding distribution

TL;DR:
It is proved polynomial upper and lower bounds on the expected size of the maximum agreement subtree of two random binary phylogenetic trees under both the uniform distribution and Yule-Harding distribution are positive.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

15. Life on Land
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2015 journal article

Identifiability Results for Several Classes of Linear Compartment Models

*BULLETIN OF MATHEMATICAL BIOLOGY*, *77*(8), 1620–1651.

author keywords: Identifiability; Linear compartment models; Identifiable functions; Differential algebra

MeSH headings : Animals; Endosomes / metabolism; Humans; Linear Models; Manganese / pharmacokinetics; Mathematical Concepts; Models, Biological; Rats

TL;DR:
This work shows how to modify identifiable cycle models by adding inputs, adding outputs, or removing leaks, in such a way that they obtain an identifiable model and proves a constructive result on how to combine identifiable models, each corresponding to strongly connected graphs, into a larger identifiable model.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2015 journal article

Identifiability of 3-class Jukes-Cantor mixtures

*ADVANCES IN APPLIED MATHEMATICS*, *64*, 89–110.

author keywords: Phylogenetic mixture models; Identifiability; Tropical geometry; Disentangling number

TL;DR:
The proof uses ideas from algebraic statistics, in particular: finding phylogenetic invariants that separate the varieties associated to different triples of trees; computing dimensions of the resulting phylogenetic varieties; and using the disentangling number to reduce to trees with a small number of leaves.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

15. Life on Land
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2015 journal article

Tying up loose strands: Defining equations of the strand symmetric model

*Journal of Algebraic Statistics*, *6*(1), 17–23.

Source: NC State University Libraries

Added: August 6, 2018

2014 journal article

Distance-Based Phylogenetic Methods Around a Polytomy

*IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS*, *11*(2), 325–335.

author keywords: Neighbor-joining; phylogeny; polyhedra; polytomy; UPGMA

MeSH headings : Algorithms; Computational Biology / methods; Evolution, Molecular; Models, Genetic; Phylogeny

TL;DR:
Polyhedral geometry is used to compare the local nature of the subdivisions induced by least-squares phylogeny, UPGMA, and neighbor-joining when the true tree has a single polytomy with exactly four neighbors.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

15. Life on Land
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2014 journal article

Identifiable reparametrizations of linear compartment models

*JOURNAL OF SYMBOLIC COMPUTATION*, *63*, 46–67.

author keywords: Identifiability; Compartment models; Reparametrization

TL;DR:
This work uses commutative algebra and graph theory to study a particular class of unidentifiable models and finds conditions to obtain identifiable scaling reparametrizations of these models, and provides an algorithm for finding these reparamETrizations when they exist and partial results beginning to classify graphs which possess an identifiable scaling re-modelling.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2014 journal article

Multigraded commutative algebra of graph decompositions

*JOURNAL OF ALGEBRAIC COMBINATORICS*, *39*(2), 335–372.

Source: Web Of Science

Added: August 6, 2018

2014 journal article

POSITIVE MARGINS AND PRIMARY DECOMPOSITION

*JOURNAL OF COMMUTATIVE ALGEBRA*, *6*(2), 173–208.

Source: Web Of Science

Added: August 6, 2018

2014 journal article

Structural Identifiability of Viscoelastic Mechanical Systems

*PLOS ONE*, *9*(2).

MeSH headings : Algorithms; Arteries / pathology; Blood Pressure; Computer Simulation; Elasticity; Endothelium, Vascular / pathology; Humans; Models, Cardiovascular; Stress, Mechanical; Viscosity

TL;DR:
A very simple characterization of both local and global structural identifiability based on identifiable tables is proposed, with the purpose of providing a guideline for constructing arbitrarily complex, identifiable spring-dashpot networks.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2013 journal article

Graphical models

*Journal of Software for Algebra and Geometry*, *5*(1), 1–7.

Source: Crossref

Added: June 30, 2019

2013 journal article

Polyhedral combinatorics of UPGMA cones

*ADVANCES IN APPLIED MATHEMATICS*, *50*(2), 327–338.

author keywords: Phylogenetic trees; Polyhedral combinatorics; Partition lattice

TL;DR:
This work uses polyhedral combinatorics to analyze the natural subdivision of the positive orthant induced by classifying the input vectors according to tree topologies returned by the algorithm, and gives a closed form for the extreme rays of UPGMA cones on n taxa.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

15. Life on Land
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2013 journal article

Positivity for Gaussian graphical models

*ADVANCES IN APPLIED MATHEMATICS*, *50*(5), 661–674.

author keywords: Gaussian graphical model; Conditional independence; Determinant; Lindstrom-Gessel-Viennot Lemma

TL;DR:
This work extends trek separation to give explicit cancellation-free formulas for the expansions of non-zero subdeterminants of the Gaussian graphical model.
(via Semantic Scholar)

Source: Web Of Science

Added: August 6, 2018

2012 journal article

Finite Gröbner bases in infinite dimensional polynomial rings and applications

*Advances in Mathematics*, *229*(1), 1–25.

Sources: Web Of Science, Crossref

Added: August 6, 2018

2012 journal article

Geodesics in CAT(0) cubical complexes

*ADVANCES IN APPLIED MATHEMATICS*, *48*(1), 142–163.

author keywords: CAT(0); Cubical complex; Partially ordered set; Geodesic; Reconfigurable system; Touring problem

TL;DR:
An algorithm to compute the geodesics in an arbitrary CAT(0) cubical complex using a correspondence between cubical complexes of global non-positive curvature and posets with inconsistent pairs is described.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

11. Sustainable Cities and Communities
(OpenAlex)

Source: Web Of Science

Added: August 6, 2018

2012 journal article

Identifiability of Large Phylogenetic Mixture Models

*BULLETIN OF MATHEMATICAL BIOLOGY*, *74*(1), 212–231.

author keywords: Phylogenetic mixture model; Parameter identifiability

MeSH headings : Evolution, Molecular; Models, Genetic; Models, Statistical; Phylogeny

TL;DR:
It is shown that both numerical and tree parameters are indeed identifiable in these models when all trees are the same, providing a theoretical justification for some current empirical studies, and indicates that extensions to even more mixture components should be theoretically well behaved.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

15. Life on Land
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2012 journal article

THE DISENTANGLING NUMBER FOR PHYLOGENETIC MIXTURES

*SIAM JOURNAL ON DISCRETE MATHEMATICS*, *26*(2), 856–859.

author keywords: phylogenetics; mixture models; contingency tables; trees

TL;DR:
A logarithmic upper bound for the disentangling number on unordered lists of leaf labeled trees is provided, useful for analyzing phylogenetic mixture models.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

15. Life on Land
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2012 journal article

When Do Phylogenetic Mixture Models Mimic Other Phylogenetic Models?

*SYSTEMATIC BIOLOGY*, *61*(6), 1049–1059.

author keywords: Phylogenetic mixture models; parameter identifiability; heterogeneous sequence evolution

MeSH headings : Algorithms; Computer Simulation; Data Interpretation, Statistical; Models, Biological; Phylogeny

TL;DR:
Surveying some of the works on mixture models gives several new results that can serve as a guide to when the use of mixture models in either maximum likelihood or Bayesian frameworks is likely to lead to statistically consistent inference, and when mimicking due to heterogeneity should be considered a realistic possibility.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

15. Life on Land
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2011 journal article

Eulerian-Catalan numbers

*Electronic Journal of Combinatorics*, * 18*(1).

Source: NC State University Libraries

Added: August 6, 2018

2011 journal article

GLOBAL IDENTIFIABILITY OF LINEAR STRUCTURAL EQUATION MODELS

*ANNALS OF STATISTICS*, *39*(2), 865–886.

Source: Web Of Science

Added: August 6, 2018

2011 journal article

Identifiability of Two-Tree Mixtures for Group-Based Models

*IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS*, *8*(3), 710–722.

author keywords: Phylogenetic mixture; group-based model; identifiability of phylogenetic models

MeSH headings : Algorithms; Computational Biology / methods; DNA / genetics; Databases, Nucleic Acid; Markov Chains; Models, Genetic; Models, Statistical; Phylogeny

TL;DR:
It is proved that generic substitution parameters for the JC mixture models are identifiable, and for the K2P and K3P models obtain generic identifiability results for mixtures on the same tree.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

15. Life on Land
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

2010 journal article

Normal binary graph models

*ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS*, *62*(4), 717–726.

author keywords: Marginal cone; Normal semigroup; Algebraic statistics

Source: Web Of Science

Added: August 6, 2018

2010 journal article

Normal binary graph models.

*Annals of the Institute of Statistical Mathematics, Special Issue: Algebraic Methods in Computational Statistics*, *64*(4), 717–726.

Source: NC State University Libraries

Added: July 10, 2019

2010 journal article

TREK SEPARATION FOR GAUSSIAN GRAPHICAL MODELS

*ANNALS OF STATISTICS*, *38*(3), 1665–1685.

author keywords: Graphical model; Bayesian network; Gessel-Viennot-Lindstrom lemma; trek rule; linear regression; conditional independence

TL;DR:
This work gives a precise graph-theoretic characterization of when submatrices of the covariance matrix have small rank for a general class of mixed graphs that includes directed acyclic and undirected graphs as special cases.
(via Semantic Scholar)

Source: Web Of Science

Added: August 6, 2018

2009 journal article

A Gröbner basis for the secant ideal of the second hypersimplex

*Journal of Commutative Algebra*, *1*(2), 327–338.

Source: Crossref

Added: June 30, 2019

2009 book

Emerging Applications of Algebraic Geometry

In *The IMA Volumes in Mathematics and its Applications*.

Ed(s): M. Putinar ^{*} & ^{*}

Source: Crossref

Added: June 30, 2019

2009 article

Gaussian conditional independence relations have no finite complete characterization

Sullivant, S. (2009, August). *JOURNAL OF PURE AND APPLIED ALGEBRA*, Vol. 213, pp. 1502–1506.

Source: Web Of Science

Added: August 6, 2018

2009 book

Lectures on Algebraic Statistics

Source: Crossref

Added: June 30, 2019

2009 journal article

Markov models for accumulating mutations

*BIOMETRIKA*, *96*(3), 645–661.

author keywords: Bayesian network; Cancer; Genetic progression; HIV; Partially ordered set; Poset

TL;DR:
A waiting time model for the accumulation of genetic changes using a partially ordered set of mutations and by the rate of fixation of each mutation is introduced and analyzed, shedding light on the mutational pathways underlying the evolutionary process.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science; OpenAlex)

Source: Web Of Science

Added: August 6, 2018

2009 journal article

Prolongations and Computational Algebra

*CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES*, *61*(4), 930–949.

Source: Web Of Science

Added: August 6, 2018

2008 journal article

Algebraic geometry of Gaussian Bayesian networks

*Advances in Applied Mathematics*, *40*(4), 482–513.

author keywords: Bayesian network; graphical model; algebraic statistics; multivariate Gaussian; Grobbner basis

TL;DR:
It is shown that the ideal of any Bayesian network is homogeneous with respect to a multigrading induced by a collection of upstream random variables, which has a number of important consequences for hidden variable models.
(via Semantic Scholar)

Source: Crossref

Added: June 30, 2019

2008 journal article

Combinatorial symbolic powers

*Journal of Algebra*, *319*(1), 115–142.

author keywords: symbolic power; Grobner basis; perfect graph; edge ideal; determinantal ideal

UN Sustainable Development Goal Categories

16. Peace, Justice and Strong Institutions
(OpenAlex)

Source: Crossref

Added: June 30, 2019

2008 journal article

Toric geometry of cuts and splits

*The Michigan Mathematical Journal*, *57*(0), 689–709.

Source: Crossref

Added: June 30, 2019

2007 journal article

A finiteness theorem for Markov bases of hierarchical models

*Journal of Combinatorial Theory, Series A*, *114*(2), 311–321.

author keywords: contingency tables; Markov bases; hierarchical models; graver complexity

TL;DR:
It is shown that the complexity of the Markov bases of multidimensional tables stabilizes eventually if a single table dimension is allowed to vary, and an explicit formula for this bound in terms of Graver bases is given.
(via Semantic Scholar)

Source: Crossref

Added: June 30, 2019

2007 journal article

Algebraic statistical models.

*Statistica Sinica*, *17*(4), 1273–1297.

Source: NC State University Libraries

Added: July 28, 2019

2007 journal article

Toric fiber products

*Journal of Algebra*, *316*(2), 560–577.

author keywords: Grobner basis; algebraic statistics; hierarchical model; phylogenetic invariants

Source: Crossref

Added: June 30, 2019

2006 journal article

Algebraic factor analysis: tetrads, pentads and beyond

*Probability Theory and Related Fields*, *138*(3-4), 463–493.

Source: Crossref

Added: June 30, 2019

2006 journal article

Combinatorial secant varieties.

*Quarterly Journal of Pure and Applied Mathematics*, *2*, 285–309.

Source: NC State University Libraries

Added: July 10, 2019

2006 journal article

Compressed polytopes and statistical disclosure limitation

*Tohoku Mathematical Journal*, *58*(3), 433–445.

author keywords: compressed polytope; disclosure limitation; algebraic statistics; integer programming; cut polytope

TL;DR:
It is shown that every compressed lattice polytope is affinely isomorphic to a 0/1-polytope and consequences for studying linear programming relaxations in statistical disclosure limitation are discussed.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

10. Reduced Inequalities
(OpenAlex)

Source: Crossref

Added: June 30, 2019

2006 journal article

Polyhedral conditions for the nonexistence of the MLE for hierarchical log-linear models

*Journal of Symbolic Computation*, *41*(2), 222–233.

author keywords: maximum likelihood estimate (MLE); marginal cone; tree width; collapsing

TL;DR:
This work provides a polyhedral description of the conditions for the existence of the maximum likelihood estimate (MLE) for a hierarchical log-linear model and gives an algorithm for determining if the MLE exists.
(via Semantic Scholar)

Source: Crossref

Added: June 30, 2019

2006 journal article

Sequential importance sampling for multiway tables

*The Annals of Statistics*, *34*(1), 523–545.

author keywords: conditional inference; contingency table; exact test; Monte Carlo sequential importance sampling; toric ideal

TL;DR:
An algorithm for the sequential sampling of entries in multiway contingency tables with given constraints is described and the numerical results demonstrate that the theory is applicable and that the algorithm performs well.
(via Semantic Scholar)

Source: Crossref

Added: June 30, 2019

2006 journal article

The space of compatible full conditionals is a unimodular toric variety

*Journal of Symbolic Computation*, *41*(2), 196–209.

author keywords: odds ratios; toric ideal; unimodular

TL;DR:
This work identifies the defining polynomials of these ideals with closed walks on a bipartite graph and provides a natural generalization of the requirement that compatible conditionals have identical odds ratios and holds regardless of the patterns of zeros in the conditional arrays.
(via Semantic Scholar)

Source: Crossref

Added: June 30, 2019

2005 journal article

Small Contingency Tables with Large Gaps

*SIAM Journal on Discrete Mathematics*, *18*(4), 787–793.

author keywords: disclosure limitation; integer programming; Grobner basis; contingency table

TL;DR:
Examples of contingency tables on n binary random variables where the gap between the linear programming lower/upper bound and the true integer lower/ upper bounds on cell entries is exponentially large provide evidence that linear programming may not be an effective heuristic for detecting disclosures when releasing margins of multiway tables.
(via Semantic Scholar)

Source: Crossref

Added: June 30, 2019

2005 journal article

Toric Ideals of Phylogenetic Invariants

*Journal of Computational Biology*, *12*(2), 204–228.

MeSH headings : Animals; Computational Biology / statistics & numerical data; Data Interpretation, Statistical; Humans; Models, Genetic; Phylogeny

TL;DR:
Generators and Gröbner bases are determined for the Jukes-Cantor and Kimura models on a binary tree and for several widely used models for biological sequences that have transition matrices that can be diagonalized by means of the Fourier transform of an Abelian group.
(via Semantic Scholar)

Source: Crossref

Added: June 30, 2019

2004 journal article

A Divide-and-Conquer Algorithm for Generating Markov Bases of Multi-way Tables

*Computational Statistics*, *19*(3), 347–366.

author keywords: contingency tables; decomposable graphical models; disclosure limitation; exact distributions; Grobner bases; Markov bases

TL;DR:
A divide-and-conquer technique for generating a Markov basis that connects all tables of counts having a fixed set of marginal totals based on decomposing the independence graph induced by these marginals is described.
(via Semantic Scholar)

Source: Crossref

Added: June 30, 2019

2004 journal article

Ideals of adjacent minors

*Journal of Algebra*, *277*(2), 615–642.

Source: Crossref

Added: June 30, 2019

2003 journal article

Markov Bases of Binary Graph Models

*Annals of Combinatorics*, *7*(4), 441–466.

Source: Crossref

Added: June 30, 2019

2002 journal article

Gröbner Bases and Polyhedral Geometry of Reducible and Cyclic Models

*Journal of Combinatorial Theory, Series A*, *100*(2), 277–301.

Source: Crossref

Added: June 30, 2019

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