I am an associate professor in the Fuqua School of Business at
Duke University.
I received BE (09) from Tsinghua University, MS (11) from UT-Austin, and PhD (14) from UIUC, all in Electrical and Computer Engineering.
I was fortunate to have Prof. Bruce Hajek as my PhD adviser.
My thesis "Statistical inference in networks: fundamental limits and efficient algorithms" is available here.
My research and teaching interests are on the interface of operation research, artificial intelligence, and data analytics.
My work spans data analysis, algorithms design, and performance evaluation in large-scale networks and
stochastic systems with applications drawn from business, engineering, and natural sciences.
I am developing a fundamental understanding and powerful methodologies for inferring information from data to enable downstream data-driven decision-making at scale. I am also designing new models and algorithms for improving decision-making efficiency under uncertainties and various resource constraints and addressing emerging privacy and security issues.
J. Gaudio, C. Sandon, J. Xu, and D. Yang
Finding Planted Cycles in a Random Graph
Accepted to Random Structures & Algorithms, April 2026
arXiv:2511.04058, March 2025
E. Mossel and J. Xu
On the optimality of local belief propagation under the degree-correlated stochastic block model
Information Theory Workshop (ITW), Oct. 2015, invited.
[SLIDES]
My research interests are in the broad area of stochastic systems with emphasis on large scale distributed networks and high-dimensional data analysis.
Given a pair of graphs, the problem of graph matching or network alignment refers to finding a
bijection between the vertex sets so that the edge sets are maximally aligned.
This is a ubiquitous problem arising in a variety of applications, including network
de-anonymization, pattern recognition, and computational biology.
Finding the best matching between two graphs can be cast as a quadratic assignment problem,
which is NP-hard to solve or to approximate in the worst case.
I have been working on the average-case analysis of graph matchings
where the two graphs are randomly generated.
Graph matching via degree profiles
Despite the worst-case intractability of graph matching, we develop a nearly linear-time algorithm which perfectly recovers the true vertex correspondence with high probability, provided that the average degree is at least polylog(n) and the two graphs differ by at most 1/polylog(n) fraction of edges. The methodology is based on appropriately chosen distance statistics of the degree profiles (empirical distribution of the degrees of neighbors).
Spectral graph matching and regularized quadratic relaxations
We develop a new spectral method,
which computes eigendecomposition of the two graph adjacency matrices and returns a matching based on the pairwise alignments between all eigenvectors of the first graph with all eigenvectors of the second.
This spectral method can be equivalently viewed as solving a regularized quadratic programming relaxation of the quadratic assignment problem.
We show that this method can return the exact matching with high probability, provided that the average degree is at least polylog(n) and the two graphs differ by at most a 1/polylog(n) fraction of edges. Our analysis exploits local laws for the resolvents of sparse Wigner matrices.
Seeded graph matching via large neighborhood statistics
We consider a seeded graph matching problem, where an initial seed set of correctly matched vertex
pairs is revealed as side information. We show that it is possible to achieve the information theoretic limit
of graph sparsity in polynomial-time with n^{eps} seeds. Our algorithm matches vertices
if their large neighborhoods have a significant overlap in the number of seeds.
In many modern systems, e.g. recommender systems, similar objects form hidden clusters and we are interested in recovering the clusters based on observation of pairwise interactions among objects. The data of pairwise interactions can be viewed as a graph consisting of nodes representing objects and edge connections encoding pairwise interactions, and the cluster recovery problem is called community detection, a.k.a. graph clustering.
I have been working on developing optimal, fast, and robust community detection algorithms, and characterizing the fundamental limits for community detection.
Community detection via message passing
Finding small communities in networks is a notoriously hard problem. We show that a single community can be
found in nearly linear time via the belief propagation algorithm in log*(n) iterations if and only if the suitably defined signal-to-noise ratio λ>1/e, while a linear message passing algorithm finds the single community in loglog(n) iterations
if and only if λ>1.
The solid curves show the recovery threshold for a single community of size ρn for three values of ρ.
The two dashed curves correspond to the recovery threshold for two equal-sized clusters
We show that a semidefinite programming (SDP) relaxation of the maximum likelihood estimator can
achieve the sharp threshold for exactly recovering the community structure if and only if the community size is above a certain threshold depending on the network size.
Papers:
B. Hajek, Y. Wu, and J. Xu
Semidefinite programs for exact recovery of a hidden community
Conference on Learning Theory (COLT), June 2016.
[SLIDES]
The facebook friendship network formed by students at Caltech. Nodes are colored according to the clustering result of convexified modularity maximization.
The 8 clusters found roughly correspond to the 8 dorms at Caltech.
In real-world networks, the degree distributions are often highly inhomogeneous across nodes, sometimes exhibiting a heavy tail behavior with some nodes having very
high degrees (so-called hubs), and some nodes having very small degrees. We introduce a new approach based on a convexification of modularity maximization followed by weighted k-median clustering, and show that our approach improves upon the state-of-the-art both theoretically and empirically.
(1) The impossible regime, where all algorithms fail; (2) the hard
regime, where the computationally intractable Maximum Likelihood Estimator (MLE) succeeds;
(3) the easy regime, where a convex relaxation of MLE succeeds; (4) the simple regime,
where a simple counting/thresholding procedure succeeds.
We study the fundamental limits of community detection under the stochastic block model. In its simplest form, it consists of n nodes with r K of them partitioned into r clusters of equal size K and the remaining n-r K nodes not in any cluster; each pair of two nodes is connected independently by an edge with probability p if they are in the same cluster and q otherwise. Given a graph generated as above, the goal is to exactly recover the clusters with high probability as n goes to the infinity. In the case with more than one cluster, we show that the space of the model parameters can be partitioned into four disjoint regions in decreasing order of statistical and computational complexities.
Recommender systems sort through massive amounts of data to identify potential user preferences. They have been applied in a variety of applications, including personalized advertisement, online learning, and targeted marketing.
I have been working on developing and analyzing optimal and fast algorithms for predicting users' inherent preferences
from noisy and partial rating or ranking data.
Rating predictions: algorithms and limits
When explicit user ratings are available, there are three popular approaches: (1) nearest neighbor (NN); (2) spectral method (3) convex method. We performed a theoretical analysis of these three methods assuming both users and items exhibit cluster structure. We find that the simple NN method outperforms the other two more sophisticated ones for small cluster sizes if there are abundant observations.
When only partial rankings are available, little is known about how to learn the individual preferences efficiently, and what is the sample complexity to reach a prescribed estimation accuracy. Our main results revealed important insight on this issue: (1) we propose a clustering and ranking algorithm, which is shown to be order-optimal in sample complexity; (2) we show the estimation error depends on the spectral gap of a comparison graph and the random assignment of items to users is order-optimal among all schemes.
Imagine being a customer in a supermarket where there is a large number of check-out counters, and the queue at each counter is only seen locally. With the goal of minimizing the sum of the waiting cost and the searching cost, how many counters would you prefer to check?
The above example reflects the spirit of my work on investigating the impact of customers'
strategic behavior in queueing systems. The problem described in the example is known as the
distributed load balancing problem, and it appears in a diverse set of applications such as network
routing, dynamic wireless spectrum access, and cloud computing services.
We propose a supermarket game model and study it in the large system regime using mean
field theory. By assuming Poisson arrival with rate λ and exponential service with unit rate, we show that there always exists a Nash equilibrium for λ < 1 and the Nash equilibrium is unique for λ <=1/sqrt(2).
Allerton Conference on Communication, Control, and Computing, UIUC, Sept. 2025
Workshop on Statistical Network Analysis and Beyond, Tokyo, Japan, June 2025
Workshop on Detection, Estimation, and Reconstruction in Networks, Simons Laufer Mathematical Sciences Institute, April 2025
[Video Presentation]
Stochastic Networks Conference, Stockholm, Sweden, July 2024
Workshop on Statistical Network Analysis and Beyond, Nassau, Bahamas, June 2024
Tutorial lecture, ACM Sigmetrics, Venice, Italy, June 2024
Workshop on Learning in Networks: Discovering Hidden Structure, Northwestern University, April 2024
LU-NU-UMN Joint Probability Seminar, January 2022
Northwestern University, Industrial Engineering and Management Sciences, Oct. 2021
Harvard University, Statistics and School of Engineering and Applied Sciences, June 2021
INRIA, Paris, France, April 2021
Stochastic Networks, Applied Probability, and Performance (SNAPP) Seminar, Mar. 2021
IMS Annual Meeting on Probability and Statistics, July 2018
Workshop in Operations Research and Data Science, Duke University, Dec. 2017
School of Operations Research and Information Engineering, Cornell University, Nov. 2017
Allerton Conference on Communication, Control, and Computing, Monticello, Oct. 2017
Joint Statistical Meeting, Baltimore, Aug. 2017
Simons Institute at UC Berkeley, June 2017
Workshop on Statistical Physics, Learning, Inference and Networks, Les Houches, France, Feb. 2017
Fudan International Conference on Data Science, Dec. 2016
INFORMS Annual Meeting, Nashville, Nov. 2016
Sante Fe Institute, Santa Fe, June 2016
Asilomar Conference on Signals, Systems, and Computers, Nov. 2015
