Algebraic statistics, tables, and networks: The Fienberg advantage.
Elizabeth Gross, Vishesh Karwa, Sonja Petrovi\'c.
To appear in the Springer volume Statistics in the public interest - in memory of Stephen E. Fienberg. arXiv:1910.01692.
Algebraic Statistics in Practice: Applications to Networks,
Marta Casanellas, Sonja Petrović and Caroline Uhler.
Annual Reviews of Statistics and its Applications 2020. 7:9.1–9.24.
arXiv:1906.09537. Published version https://doi.org/10.1146/annurev-statistics-031017-100053
WHAT IS... a Markov basis?
Sonja Petrović. Notices of the American Mathematical Society 2019, 66 (7), 1088—1092.
Read the full article here or on arXiv:1907.07320.
“Old Wine in New Bottles,” and Some More New Wine – Stephen Fienberg’s Influence on Algebraic Statistics,
Sonja Petrović, Aleksandra Slavkovic, and Ruriko Yoshida. Editorial piece for the Journal of Algebraic Statistics' Special Volume in honor of memory of S.E.Fienberg, 2019.
Read the article.
Random Monomial Ideals: a Macaulay2 package
Sonja Petrovic, Despina Stasi, Dane Wilburne.Journal of Software for Algebra and Geometry, 9 (2019), 65–70.
Code available in Macaulay2 as of version 1.11.
Hypergraph encodings of arbitrary toric ideals,
Sonja Petrović, Apostolos Thoma and Marius Vladoiu.
Journal of Combinatorial Theory, Series A 166 (2019) pp. 11-41.
Bouquet algebra of toric ideals,
Sonja Petrović, Apostolos Thoma and Marius Vladoiu.
Journal of Algebra 512 (2018) 493–525
arXiv:1507.02740. (Revised 2017.)
Random Monomial Ideals,
Jesus A. De Loera, Sonja Petrovic, Lily Silverstein, Despina Stasi, Dane Wilburne
Journal of Algebra, 519(1): 440--473, 2019.
arXiv:1701.07130. (Revised April 2018.)
The multiple roots phenomenon in maximum likalihood estimation for factor analysis,
Elizabeth Gross, Sonja Petrovic, Donald Richards, Despina Stasi.
Adv. Stud. Pure Math. 75 (2017).
Statistical models for cores decomposition of an undirected random graph,
Vishesh Karwa, Michael J. Pelsmajer, Sonja Petrović, Despina Stasi, and Dane Wilburne.
Electronic Journal of Statistics 2017, Vol. 11, No. 1, 1949-1982.
arXiv:1410.7357 (v3, Nov 2016); http://dx.doi.org/10.1214/17-EJS1235.
Supplementary material: R code on GitHub.
Coauthorship and citation networks for statisticians: Comment,
Vishesh Karwa and Sonja Petrovic. Invited comment on the paper `Coauthorship and citation networks for statisticians' by Jin and Ji.
Annals of Applied Statistics, 10 (2016), no. 4, 1827--1834. doi:10.1214/16-AOAS978.
On the Geometry and Extremal Properties of the Edge-Degeneracy Model,
Nicolas Kim, Dane Wilburne, Sonja Petrovic, Alessandro Rinaldo.
MNG 2016: The Third SDM Workshop on Mining Networks and Graphs: A Big Data Analytic Challenge.
A survey of discrete methods in (algebraic) statistics for networks, Contemporary Mathematics, vol. 685, 260-281, American Mathematical Society, 2017.
Blow-up algebras, determinantal ideals, and Dedekind-Mertens-like formulas, with Alberto Corso, Uwe Nagel, and Cornelia Yuen. (2016)
Forum Mathematicum, 29(4), pp. 799-830. DOI: 10.1515/forum-2016-0007.
Random Sampling in Computational Algebra: Helly Numbers and Violator Spaces, Jesus A. De Loera, Sonja Petrovic, and Despina Stasi.
Journal of Symbolic Computation, 77 (2016) pp.1-15. 10.1016/j.jsc.2016.01.001. Link to article.
Goodness of fit for log-linear network models: Dynamic Markov bases using hypergraphs, with Elizabeth Gross and Despina Stasi.
Annals of the Institute of Statistical Mathematics (2017) 69: 673. DOI: 10.1007/s10463-016-0560-2
Beta models for random hypergraphs with a given degree sequence, Despina Stasi, Kayvan Sadeghi, Alessandro Rinaldo, Sonja Petrovic, and Stephen Fienberg. Proceedings of 21st International Conference on Computational Statistics (2014).
Fibers of multi-way contingency tables given conditionals: relation to marginals, cell bounds and Markov bases, with Aleksandra B. Slavkovic and Xiaotian Zhu. Annals of the Institute of Statistical Mathematics, August 2015, Volume 67, Issue 4, pp 621-648. DOI: 10.1007/s10463-014-0471-z.
arXiv:1401.1397. Published online: June 2014.
Toric algebra of hypergraphs, with Despina Stasi,
Journal of Algebraic Combinatorics, February 2014, Volume 39, Issue 1, pp 187-208.
arXiv:1206.1904. DOI link.
A combinatorial degree bound for toric ideals of hypergraphs, with Elizabeth Gross, International Journal of Algebra and Computation, Volume 23, Issue 06, pp. 1503-1520, September 2013. DOI.
arXiv:1206.2512 (previous title: "Markov complexity of hypergraphs").
PHCpack in Macaulay2, with Elizabeth Gross and Jan Verschelde,
Journal of Software for Algebra and Geometry, Volume 5, 2013; certified code also available with Macaulay2 release 1.6.
arXiv:1105.4881 (see the Software page for more information).
GraphicalModels in Macaulay2, with Seth Sullivant. and Luis Garcia-Puente.
Journal of Software for Algebra and Geometry, Volume 5, 2013; certified code also available with Macaulay2 release 1.5.
arXiv:1208.6550. (see the Software page for more information).
Maximum Likelihood Estimation in the Beta model, with Alessandro Rinaldo and Stephen E. Fienberg.
Annals of Statistics 2013, Vol. 41, No. 3, 1085-1110.
arXiv:1105.6145. ( DOI)
Betti numbers of Stanley-Reisner rings determine hierarchical Markov degrees, with Erik Stokes.
Journal of Algebraic Combinatorics, Volume 37, Issue 4 (2013), Page 667-682.
How Does Maximum Likelihood Estima- tion for the p1 Model Scale for Large Sparse Networks?, Rinaldo, A., Petrovíc, S. and Fienberg, S.E. (2012).
NIPS 2012 workshop on Algorithmic and Statistical Approaches for Large Social Network Data Sets.
Equality of Graver and Universal Gröbner bases of colored partition identities, with Tristram Bogart and Raymond Hemmecke.
Experimental Mathematics 2012, Vol. 21 (4), 395-401.
Maximum likelihood degree of variance component models, with Elizabeth Gross and Mathias Drton.
Electronic Journal of Statistics 2012, Vol. 6, No. 0, 993-1016.
Algebraic Statistics, with Aleksandra Slavkovic.
In M. Lovric, editor, International Encyclopedia of Statistical Science, Part 1, 29-32, Springer. (2011) (DOI: 10.1007/978-3-642-04898-2_112)
Identifiability of two-tree mixtures under group-based models, with Elizabeth Allman, John Rhodes, and Seth Sullivant.
IEEE/ACM Transactions in Computational Biology and Bioinformatics, 8 no. 3 (2011) 710-722.
arXiv:0909.1854; Supplementary material.
Algebraic statistics for a directed random graph model with reciprocation, with Alessandro Rinaldo and Stephen E. Fienberg.
In: Algebraic Methods in Statistics and Probability II, M. Viana and H. Wynn (editors). CONM, vol 516. AMS.
Algebraic statistics for p_1 random graph models: Markov bases and their uses, with Alessandro Rinaldo and Stephen E. Fienberg.
Book chapter in S. Sinharay and N. J. Dorans, editors, Papers in Honor of Paul W. Holland. ETS. (2010) Springer
Properties of cut ideals of ring graphs, with Uwe Nagel.
J. Commut. Algebra 1 (2009), no. 3, 547--565.
Universal Gröbner bases of varieties of minimal degree.
Math. Res. Lett. 15 (2008), no. 6, 1211--1221.
Toric ideals of phylogenetic invariants for the general group-based model on claw trees, with Julia Chifman, in Proceedings of the Second international conference on Algebraic Biology, (eds. H.Anai, K. Horimoto and T. Kutsia),
Springer LNCS 454 (2007), 307--321.
A nonlinear Sturm-Picone comparison theorem for dynamic equations on time scales, with Boris Belinskiy and John Graef.
Int. J. Difference Equ. 2 (2007), no. 1, 25--35. (pdf)