The Spark Randomizer: a learned randomized framework for computing Gröbner basis
Shahrzad Jamshidi and Sonja Petrović.
Markov bases: a 25 year update
Félix Almendra-Hernández, Jesús A. De Loera, and Sonja Petrović.
Goodness of fit for log-linear ERGMs
Elizabeth Gross, Sonja Petrović, and Despina Stasi.
published / accepted / in press
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.
To appear in Journal of the Royal Statistical Society, Series B, 2023+.
Longitudinal network models and permutation-uniform Markov chains,
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. https://doi.org/10.1145/3476446.3536193
DERGMs: Degeneracy-restricted exponential random graph models,
Vishesh Karwa, Sonja Petrović and Denis Bajić.
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 https://doi.org/10.1007/978-3-030-75460-0_3
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 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.
“Old Wine in New Bottles,” and Some More New Wine – Stephen Fienberg’s Influence on Algebraic Statistics,
Sonja Petrović, Aleksandra Slavkovic, and Ruriko Yoshida.
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,
Journal of Combinatorial Theory, Series A 166 (2019) pp. 11-41.
Bouquet algebra of toric ideals,
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,
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.
On the Geometry and Extremal Properties of the Edge-Degeneracy Model,
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,
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,
Goodness of fit for log-linear network models: Dynamic Markov bases using hypergraphs,
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.
Toric algebra of hypergraphs,
Sonja Petrović and Despina Stasi.
A combinatorial degree bound for toric ideals of hypergraphs,
Elizabeth Gross and Sonja Petrović.
PHCpack in Macaulay2,
GraphicalModels in Macaulay2,
Maximum Likelihood Estimation in the Beta model,
Betti numbers of Stanley-Reisner rings determine hierarchical Markov degrees,
Sonja Petrović and Erik Stokes.
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,
Experimental Mathematics 2012, Vol. 21 (4), 395-401.
Maximum likelihood degree of variance component models,
Electronic Journal of Statistics 2012, Vol. 6, No. 0, 993-1016.
Sonja Petrović and Aleksandra Slavkovic.
Identifiability of two-tree mixtures under group-based models,
Algebraic statistics for a directed random graph model with reciprocation,
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)