Preprints (submitted)

The Weak Lefschetz property and unimodality of Hilbert functions of random monomial algebras

Uwe Nagel and Sonja Petrov

Get the algorithm and code for examples on our GitHub page

New directions in algebraic statistics: Three challenges from 2023

Yulia Alexandr, Miles Bakenhus, Mark Curiel, Sameer K. Deshpande, Elizabeth Gross,  Yuqi Gu, Max Hill, Joseph Johnson, Bryson Kagy, Vishesh Karwa, Jiayi Li, Hanbaek Lyu, Sonja Petrović, and Jose Israel Rodriguez

Irreducible Markov Chains on spaces of graphs with fixed degree-color sequences

Félix Almendra-Hernández, Jesús A. De Loera, and Sonja Petrović.  

The Spark Randomizer: a learned randomized framework for computing Gröbner basis

Shahrzad Jamshidi and Sonja Petrović.  

Predicting the cardinality of a reduced Gröbner basis

Shahrzad Jamshidi, Eric Kang, and Sonja Petrović.  

Papers with code.

View the Macaulay2 data generating code and Jupyter notebooks for learning on our code page

Goodness of fit for log-linear ERGMs

Elizabeth Gross, Sonja Petrović, and Despina Stasi. 

published / accepted / in press

Sampling lattice points in a polytope: a Bayesian biased algorithm with random updates

Miles Bakenhus and Sonja Petrović. 
Algebraic Statisitcs, to appear

Get the algorithm and code for examples on our GitHub page

Markov bases: a 25 year update

Félix Almendra-Hernández, Jesús A. De Loera, and Sonja Petrović.  

Journal of the American Statistical Association, January 2024. DOI link 

Get the algorithm and code for examples on our GitHub page

Monte Carlo goodness-of-fit tests for degree corrected and related stochastic blockmodels,

Vishesh Karwa, Debdeep Pati, Sonja Petrović, Liam Solus, Nikita Alexeev, Mateja Raič, Dane Wilburne, Robert Williams, Bowei Yan.

Journal of the Royal Statistical Society Series B: Statistical Methodology, Volume 86, Issue 1, February 2024, Pages 90–121. DOI link 

Learning a performance metric of Buchberger's algorithm

Jelena Mojsilović, Dylan Peifer, and Sonja Petrović

Involve, a Journal of Mathematics 16-2 (2023), 227--248.
    DOI 10.2140/involve.2023.16.227 

Papers with code.
Download the data set via DOI:10.5281/zenodo.6599502

Longitudinal network models and permutation-uniform Markov chains,  

William K. Schwartz, Sonja Petrović, and Hemanshu Kaul

Scandinavian Journal of Statistics, 2022. 

Marginal independence models,   

Tobias Boege, Sonja Petrović, and Bernd Sturmfels. 

In Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation (ISSAC ’22), July 4–7, 2022, Villeneuve-d’Ascq, France. ACM, New York, NY, USA.

I believe in FAIRnesshere is our MathRepo link

Threaded Gr\"obner Bases: a Macaulay2 package, 

Sonja Petrović and Shahrzad Jamshidi Zelenberg.

Journal of Software for Algebra and Geometry, Vol. 11 (2021), 123–127.
Package ThreadedGB.m2 released with Macaulay2, starting with version 1.19. 

DERGMs: Degeneracy-restricted exponential random graph models,

Vishesh Karwa, Sonja Petrović and Denis Bajić.

Network Science, Volume 10, Issue 1, March 2022 , pp. 82 - 110.
Appeared online 31.3.2022. 

Supplementary material: on GitHub.

*project completion delayed by a few years due to a combination of leaves by the lead authors.

Algebraic statistics, tables, and networks: The Fienberg advantage.

Elizabeth Gross, Vishesh Karwa, Sonja Petrovi\'c.

In: Carriquiry, A.L., Tanur, J.M., Eddy, W.F. (eds) Statistics in the Public Interest. (2022) Springer Series in the Data Sciences. Springer, Cham.
arXiv:1910.01692. Published version

Algebraic Statistics in Practice: Applications to Networks,

Marta Casanellas, Sonja Petrović and Caroline Uhler.

Annual Reviews of Statistics and its Applications 2020. 7 (1), 227-250.
arXiv:1906.09537. Published version

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 Petrović, 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.
arXiv: 1711.04354.

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 Petrović, 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 likelihood estimation for factor analysis,

Elizabeth Gross, Sonja Petrović, 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);
Supplementary material: R code on GitHub.

Coauthorship and citation networks for statisticians: Comment,

Vishesh Karwa and Sonja Petrović. 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 Petrović, 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, 

Sonja Petrović.

Contemporary Mathematics, vol. 685, 260-281, American Mathematical Society, 2017.

Blow-up algebras, determinantal ideals, and Dedekind-Mertens-like formulas, 

Alberto Corso, Uwe Nagel, Sonja Petrović, 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 Petrović, 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,

Elizabeth Gross, Sonja Petrović, and Despina Stasi.

Annals of the Institute of Statistical Mathematics (2017) 69: 673. DOI: 10.1007/s10463-016-0560-2
arXiv:1401.4896 .
Supplementary material.

Beta models for random hypergraphs with a given degree sequence, 

Despina Stasi, Kayvan Sadeghi, Alessandro Rinaldo, Sonja Petrović, 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, 

Aleksandra B. Slavkovic, Sonja Petrović, 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, 

Sonja Petrović and 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, 

Elizabeth Gross and Sonja Petrović.

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, 

Elizabeth Gross, Sonja Petrović, 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, 

Luis Garcia-Puente, Sonja Petrović, and Seth Sullivant

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

Alessandro Rinaldo, Sonja Petrović, 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, 

Sonja Petrović and Erik Stokes.

Journal of Algebraic Combinatorics, Volume 37, Issue 4 (2013), Page 667-682.
arXiv:0910.1610 (DOI)

How Does Maximum Likelihood Estimation for the p1 Model Scale for Large Sparse Networks?

Rinaldo, A., Petrović, S. and Fienberg, S.E. (2012).

NIPS 2012 workshop on Algorithmic and Statistical Approaches for Large Social Network Data Sets.
Based on arXiv:1010.0745 

Equality of Graver and Universal Gröbner bases of colored partition identities, 

Tristram Bogart, Raymond Hemmecke, and Sonja Petrović

Experimental Mathematics 2012, Vol. 21 (4), 395-401.

Maximum likelihood degree of variance component models, 

Elizabeth Gross, Mathias Drton, and Sonja Petrović.

Electronic Journal of Statistics 2012, Vol. 6, No. 0, 993-1016.

Algebraic Statistics, 

Sonja Petrović and 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, 

Elizabeth Allman, John Rhodes, Sonja Petrović, 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, 

Sonja Petrović, 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, 

Stephen E. Fienberg, Sonja Petrović, and Alessandro Rinaldo.

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, 

Uwe Nagel and Sonja Petrović.

J. Commut. Algebra 1 (2009), no. 3, 547--565.

Universal Gröbner bases of varieties of minimal degree.

Sonja Petrović. Math. Res. Lett. 15 (2008), no. 6, 1211--1221.


Toric ideals of phylogenetic invariants for the general group-based model on claw trees, 

Julia Chifman and Sonja Petrović

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, 

Boris Belinskiy, John Graef, and Sonja Petrović. 

Int. J. Difference Equ. 2 (2007), no. 1, 25--35. (pdf)

My ORCID ID is 0000-0002-4784-4169