Participant in the workshop: Women in Commutative Algebra II (WICA II) at CIRM Trento (Italy) on October 16-20, 2023. Organized by Sara Faridi, Elisa Gorla, Martina Juhnke-Kubitzke, Haydee Lindo, and Alexandra Seceleanu.
Participant in the workshop on Computations and Data in Algebraic Statistics, Casa Matemática Oaxaca (CMO) of the Banff International Research Station for Mathematical Innovation and Discovery (BIRS), Oaxaca, Mexico, May 14-19, 2023.
Sampling and learning from random polynomials: two stories, special session on Topological and Combinatorial Methods in Commutative Algebra, Joint Mathematics Meetings, Boston MA, January 4-7, 2023.A commutative algebraist's interest in randomness has many facets, of which this talk highlights two: 1) how to use basic statistics and machine learning for improving Buchberger's algorithm and 2) how to generate samples of ideals in a `controlled' way. The two topics, based on joint work with various collaborators and students, form a two-step process in learning on algebraic structures.For the learning angle, we study performance of linear regression models in predicting a performance metric for Buchberger's algorithm, and train a simple recursive neural network that outperforms these linear models. Our work serves as a proof of concept, demonstrating that learning certain invariants in algebraic computations is a feasible problem from the point of view of machine learning.For the sampling angle, we present random monomial ideals, using which we prove theorems about the probability distributions, expectations and thresholds for events involving monomial ideals with given Hilbert function, Krull dimension, first graded Betti numbers, and present several experimentally-backed conjectures about regularity, projective dimension, strong genericity, and Cohen-Macaulayness of random monomial ideals. The models for monomial ideals can be used as a basis for generating other types of algebraic objects, and proving existence of desired properties.
Longitudinal Network Models, Log-Linear Multigraph Models, and Implications to Estimation and Testing Model Fit. Workshop on Graph Limits, Non-Parametric Models, and Estimation. Simons Institute, Berkeley, 26-30 September 2022.
Sampling and learning in computational algebra: two stories. Algebra-Geometry-Combinatorics seminar, San Francisco State University, 28 September 2022.This talk is motivated by probabilistic models of random monomial ideals that mirror and extend those from random graphs and simplicial complexes literatures. Our results provide precise probabilistic statements about various algebraic invariants of (coordinate rings of) monomial ideals: the probability distributions, expectations and thresholds for events involving monomial ideals with given Hilbert function, Krull dimension, first graded Betti numbers.We will tackle the following related questions: What is a systematic way, in a probabilistic-model sense, to generate binomial ideals randomly? What can be (machine) learned from such data sets? How do we 'test out the waters' to see if a problem is 'learnable'? How do we generate, share, and make available large training data sets for machine learning in computational algebra? These topics are based on joint work with various collaborators and students and form a two-step process in learning on algebraic structures.
Learning in commutative algebra & models for random algebraic structures, Workshop on applications of machine learning ("DANGER"), organized by Alexander Kasprzyk, Yang-Hui He, Tom Oliver. Online. 25-26 August 2021.
What is a Markov basis? a talk in the series "My Favorite Theorem" organized by the SIAM student chapter at IIT. Online. March 2021.
Randomness in Commutative Algebra: Part I -- Random Monomial Ideals
SIAM Seminar on Applied Geometry and Algebra, Online. January 12, 2021.
*What a year!!
Algebraic Statistics for Networks - The Fienberg advantage and linear ERGMs
Seminar talk in Statistical Data Science, École polytechnique fédérale de Lausanne, Switzerland, June 12, 2020
* I was on maternity leave for the majority of 2019.
Goodness of fit of (mixtures of) log-linear models, Minisymposium on Algebraic Statistics at the 2019 SIAM Conference on Applied Algebraic Geometry in Bern, Switzerland (July 9-13, 2019).
I taught a short course on The role of algebraic statistics in estimation and modeling of random graphs and networks in the Summer school on algebraic statistics, taking place September 24-28, 2018, The Arctic University of Norway in Tromso. The lectures were on the board but here are some slides with references.
I taught a short course on The role of algebraic statistics in estimation and modeling of random graphs and networks in the 2018 CIMPA Research School - Latinamerica: "Commutative Algebra with Applications to Statistics and Coding Theory", taking place June 25 - July 6, 2018, Zacatecas, MEXICO.
Finite-sample goodness-of-fit tests for stochastic block models and extensions to latent-variable log-linear models . Invited session on "Algebraic Methods in Statistics" for the 2018 Annual Meeting of the IMS, Institute of Mathematical Statistics. Vilnius, Lithuania, July 2 – 6, 2018.
An invitation to algebraic statistics: a brief overview. AMS special session on algebraic statistics at the spring Eastern Section meeting, April 21-22, 2018, Boston.
Randomized algorithms for computing with polynomials, IIT Center for Interdisciplinary Scientific Computation matchmaking seminar. April 4th, 2018.
*I was on maternity leave during half of 2017, which resulted in cancellation of 3 invited talks (at FoCM - Foundations of Computational Mathematics, MCA - Mathematical Congress of the Americas, and AMS - American Mathematical Society sectional meeting).
Discrete methods for statistical network analysis, Special session on Probabilistic Methods in Combinatorics at the Spring 2017 AMS Central Sectional Meeting at the Indiana University in Bloomington, IN. April 1-2, 2017.
Exact tests for mixtures of log-linear models: stochastic block models for random graphs, Algebraic statistics workshop, Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics), April 16-22, 2017.
The role of algebraic statistics in estimation and modeling of random graphs and networks. Invited talk at the first COSTNET conference [COST Conference on Statistical Network Science], Ribno, Slovenia, September 2016.
The role of algebraic statistics in estimation and modeling of random graphs and networks. Invited talk at the Invited paper session on Recent advances on algebraic methods in statistics. The 4th Institute of Mathematical Statistics Asia Pacific Rim Meeting, The Chinese University of Hong Kong, June 27-30, 2016.
Fitting 3 variants of the p1 random graph model (varying reciprocity). Plenary talk at the "Applications of Algebraic Methods to Statistics" conference at the Research Institute of Mathematical Science (RIMS) of Kyoto University, 20 - 24 June, 2016.
Network data: (Ir)relevant insights, Bay Area IIT Alumni Association gathering, San Francisco, April 2016.
Algebra on hypergraphs, AMS Special Session on Algebraic and Geometric Methods in Applied Discrete Mathematics (a Mathematics Research Communities Session) at the 2015 Joint Mathematics Meetings, San Antonio, January 2015.