Detection and Recovery of hidden structure in high-dimensional data

This line of research focuses on the detection and recovery of hidden structures in high-dimensional data, especially those presented in the form of random graphs or statistical networks.

Graph matching (a.k.a. network alignment)

The problem of graph matching or network alignment consists in matching the vertices of two unlabeled, edge-correlated graphs so that their edges are maximally aligned. We developed methods for graph matching and detection of correlation between graphs, one of which is implemented here.

Mixture models

Mixture models are used to represent data from heterogeneous populations. This research aims to develop algorithmic and analytic tools for both mixtures in the Euclidean space and mixtures of permutations.

Ranking from pairwise comparisons

Ranking from pairwise comparisons, as the name suggests, is the task of aggregating a set of comparisons between pairs of items to produce a ranking of the items. We particularly worked on a class of permutation-based models.

Other problems with latent permutations and shape constraints

Some of my other research also concerns statistical estimation with latent combinatorial structure and/or shape constraints.