Research Topics
Random geometric graphs
Random geometric graphs are latent-space network models in which edges depend on geometric relationships between unobserved points. My work studies statistical inference problems involving random geometric graphs, particularly in high-dimensional settings.
- Resolution of the Detection Threshold Conjecture for Random Geometric Graphs in the d > n Regime
- Random Geometric Graphs with Smooth Kernels: Sharp Detection Threshold and a Spectral Conjecture
- Spectral Recovery of a Planted Triangle-Dense Subgraph
- Recovery of Latent Inner Products from an Anisotropic Gaussian Random Geometric Graph
- Impossibility of Latent Inner Product Recovery via Rate Distortion
Matching and alignment
Matching and alignment problems seek hidden correspondences in noisy data. My work studies statistical limits and computational methods for tasks such as graph alignment and geometric matching.
- Geometric Planted Matchings in High Dimensions: The Power of Multiple Views
- Cluster Expansion of the Log-Likelihood Ratio: Optimal Detection of Planted Matchings
- Random Graph Matching at Otter's Threshold via Counting Chandeliers
- Testing Network Correlation Efficiently via Counting Trees
- Exact Matching of Random Graphs with Constant Correlation
- Random Graph Matching with Improved Noise Robustness
- Spectral Graph Matching and Regularized Quadratic Relaxations: Part I, Part II, and conference version
Detection and recovery of hidden structures in high-dimensional data
Below is additional work on detection and recovery of hidden structures in high-dimensional data. One focus is obtaining computational thresholds using the low-degree polynomial methods.
Models for pairwise comparisons
Pairwise comparison data arise in ranking, preference learning, and related statistical problems. My work studies mixture models, permutation-based models, and isotonic structures.
- Sharp Analysis of EM for Learning Mixtures of Pairwise Differences
- Learning Mixtures of Permutations: Groups of Pairwise Comparisons and Combinatorial Method of Moments
- Towards Optimal Estimation of Bivariate Isotonic Matrices with Unknown Permutations
- Worst-Case versus Average-Case Design for Estimation from Partial Pairwise Comparisons
- Minimax Rates and Efficient Algorithms for Noisy Sorting
Estimation with latent permutations and shape constraints
This line of work studies nonparametric estimation with latent permutations or shape constraints.
Other
My other work concerns various topics in probability and operations research.