17 citations · 48 across the 14 of their papers we have counts for
17 papers
Predicting the cardinality and maximum degree of a reduced Gröbner basis
Shahrzad Jamshidi, Eric Kang, Sonja Petrović
We construct neural network regression models to predict key metrics of complexity for Gröbner bases of binomial ideals. This work illustrates why predictions with neural networks…
Hypergraph encodings of arbitrary toric ideals
Sonja Petrović, Apostolos Thoma, Marius Vladoiu
Relying on the combinatorial classification of toric ideals using their bouquet structure, we focus on toric ideals of hypergraphs and study how they relate to general toric ideals…
Random Monomial Ideals
Jesus A. De Loera, Sonja Petrovic, Lily Silverstein +2
Inspired by the study of random graphs and simplicial complexes, and motivated by the need to understand average behavior of ideals, we propose and study probabilistic models of ra…
DERGMs: Degeneracy-restricted exponential random graph models
Vishesh Karwa, Sonja Petrović, Denis Bajić
Exponential random graph models, or ERGMs, are a flexible and general class of models for modeling dependent data. While the early literature has shown them to be powerful in captu…
Coauthorship and citation networks for statisticians: Comment
Vishesh Karwa, Sonja Petrović
This is a comment on the paper arXiv:1410.2840 by Ji and Jin, to appear in the AOAS.
On the Geometry and Extremal Properties of the Edge-Degeneracy Model
Nicolas Kim, Dane Wilburne, Sonja Petrović +1
The edge-degeneracy model is an exponential random graph model that uses the graph degeneracy, a measure of the graph's connection density, and number of edges in a graph as its su…
A survey of discrete methods in (algebraic) statistics for networks
Sonja Petrović
Sampling algorithms, hypergraph degree sequences, and polytopes play a crucial role in statistical analysis of network data. This article offers a brief overview of open problems i…
Random Sampling in Computational Algebra: Helly Numbers and Violator Spaces
Jesús A. De Loera, Sonja Petrović, Despina Stasi
This paper transfers a randomized algorithm, originally used in geometric optimization, to computational problems in commutative algebra. We show that Clarkson's sampling algorithm…
models for random hypergraphs with a given degree sequence
Despina Stasi, Kayvan Sadeghi, Alessandro Rinaldo +2
We introduce the beta model for random hypergraphs in order to represent the occurrence of multi-way interactions among agents in a social network. This model builds upon and gener…
Goodness-of-fit for log-linear network models: Dynamic Markov bases using hypergraphs
Elizabeth Gross, Sonja Petrović, Despina Stasi
Social networks and other large sparse data sets pose significant challenges for statistical inference, as many standard statistical methods for testing model fit are not applicabl…
Fibers of multi-way contingency tables given conditionals: relation to marginals, cell bounds and Markov bases
Aleksandra B. Slavković, Xiaotian Zhu, Sonja Petrović
A reference set, or a fiber, of a contingency table is the space of all realizations of the table under a given set of constraints such as marginal totals. Understanding the geomet…
Combinatorial degree bound for toric ideals of hypergraphs
Elizabeth Gross, Sonja Petrović
Associated to any hypergraph is a toric ideal encoding the algebraic relations among its edges. We study these ideals and the combinatorics of their minimal generators, and derive…
Toric algebra of hypergraphs
Sonja Petrović, Despina Stasi
The edges of any hypergraph parametrize a monomial algebra called the edge subring of the hypergraph. We study presentation ideals of these edge subrings, and describe their genera…
PHCpack in Macaulay2
Elizabeth Gross, Sonja Petrović, Jan Verschelde
The Macaulay2 package PHCpack.m2 provides an interface to PHCpack, a general-purpose polynomial system solver that uses homotopy continuation. The main method is a numerical blackb…
On the Existence of the MLE for a Directed Random Graph Network Model with Reciprocation
A. Rinaldo, S. Petrović, S. E. Fienberg
Holland and Leinhardt (1981) proposed a directed random graph model, the p1 model, to describe dyadic interactions in a social network. In previous work (Petrovic et al., 2010), we…
Betti numbers of Stanley-Reisner rings determine hierarchical Markov degrees
Sonja Petrović, Erik Stokes
There are two seemingly unrelated ideals associated with a simplicial complex Δ. One is the Stanley-Reisner ideal I_Δ, the monomial ideal generated by minimal non-faces of Δ, well-…
Toric ideals of phylogenetic invariants for the general group-based model on claw trees
Julia Chifman, Sonja Petrović
We address the problem of studying the toric ideals of phylogenetic invariants for a general group-based model on an arbitrary claw tree. We focus on the group and ch…