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Works (65)
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.
TL;DR:
This work gives the first general formula for the coefficients of input-output equations (certain equations that can be used to determine identifiability) that allows for input and output to be in distinct compartments.
(via Semantic Scholar)
arxiv.org (repository)
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.
author keywords: Identifiability; Structural identifiability; LCR circuit; Resultant; Algebraic geometry; Algebraic statistics
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.
author keywords: algebraic matroids; Gaussian graphical models; matrix completion; maximum likelihood estimation; maximum likelihood threshold; rigidity theory; score matching estimator; weak maximum likelihood threshold
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.
author keywords: Gaussian random variables; Conditional independence; Gaussian graphical models; Matrix Schubert varieties; Kazhdan-Lusztig varieties
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.
TL;DR:
The set of known phylogenetic invariants for the general strand symmetric model of the three leaf claw tree entirely defines the ideal, and it is shown that the known equations generate a prime ideal of the correct dimension using elimination theory.
(via Semantic Scholar)
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.
author keywords: Toric fiber product; Toric ideal; Segre product; Markov basis; Primary decomposition; Algebraic statistics; Conditional independence ideal; Normality of ideals
Source: Web Of Science
Added: August 6, 2018
2014 journal article
POSITIVE MARGINS AND PRIMARY DECOMPOSITION
JOURNAL OF COMMUTATIVE ALGEBRA, 6(2), 173–208.
author keywords: Algebraic statistics; Markov basis; connectivity of fibers; binomial primary decomposition
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.
TL;DR:
The Macaulay2 package GraphicalModels contains algorithms for the algebraic study of graphical models associated to undirected, directed and mixed graphs, and associated collections of conditional independence statements, and can be used to study fundamental problems about graphical models.
(via Semantic Scholar)
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.
author keywords: Grobner basis; Algebraic statistics; Semigroup ring; Well-partial order; Symmetric group; Markov basis
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.
author keywords: Covariance matrix; Gaussian distribution; graphical model; multivariate normal distribution; parameter identification; structural equation model
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.
TL;DR:
It is shown that there can be no finite list of conditional independence relations which can be used to deduce all conditional independence implications among Gaussian random variables.
(via Semantic Scholar)
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.
TL;DR:
This work uses the geometric notion of prolongations to derive a new family of secant equations for the binary symmetric model in phylogenetics and develops methods for computing prolongations that are combinatorial in nature.
(via Semantic Scholar)
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.
TL;DR:
The topological invariant of a graph given by the maximum degree of a Markov basis element for the corresponding graph model for binary contingency tables is described and the algebraic degree of the model when the underlying graph is a forest.
(via Semantic Scholar)
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.
TL;DR:
The polyhedral structure and combinatorics of polytopes that arise from hierarchical models in statistics are studied, and it is shown how to construct Grobner bases of toric ideals associated to a subset of such models.
(via Semantic Scholar)
Source: Crossref
Added: June 30, 2019
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