## Summary

My research focuses on the interplay between commutative algebra and statistics, where the interaction goes two ways. First, I build statistical models for discrete relational data that capture more complex behavior than traditional models, study them through the algebrogeometric lens, prove their interpretability in practice, and develop scalable model/data fit testing methodologies using a blend of combinatorial, algebraic, probabilistic, and Bayesian algorithms. In the other direction, I study randomized algorithm approaches to computational algebra problems whose expected runtimes are much lower then the well-known worst-case complexity bounds, develop probabilistic models to study average and extreme behavior of algebraic objects, and use machine learning to predict and improve behavior of algebraic computations.

## Algebraic statistics for network models

- Non-asymptotic goodness-of-fit tests based on Markov bases;
- Existence and complexity of MLE;
- Dynamic combinatorially-inspired data-oriented algorithms for model fitting;
- Application to (large) sparse network data.

DARPA FA9550-12-1-0392 (2012-2013), AFOSR FA9550-14-1-0141 (2014-2017).

## Statistical models in psychology

- Computational challenges in occupational health psychology:

using statistics to model dynamic worker well-being.

2018 CISC seed grant with Mahima Saxena, IIT Psychology, and Lulu Kang, IIT Applied Math.

## Randomness and learning for non-linear algebra

- Stochastic non-linear algebra;
- Solving systems of multivariate equations;
- Fast randomized algorithms for large structured systems;
- Randomized structures in algebra with applicaitons.

NSF DMS-1522662 (2015-2019).

Here are my Google Scholar and ResearchGate profiles, though the latter seems outdated.

I actively mentor and involve students in my research. If you are interested, check out these research summary slides from April 2017.