About me
I am an assistant professor in Krannert School of Management at
Purdue University.
Previously I was
a research fellow in the Simons Institute for the Theory of Computing
at UC Berkeley,
participating in the program on
Counting Complexity & Phase Transitions in Spring 2016.
In 2015, I was a postdoctoral fellow with the Statistics Department, the Wharton School, University of Pennsylvania,
working with Prof.
Elchanan
Mossel on highdimensional statistical inference and network science.
I received BE (09) from Tsinghua University, MS (11) from UTAustin, and PhD (14) from UIUC, all in ECE.
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.
During the summer of 2012, I was an intern in the Technicolor Paris Research Lab,
mentored by
Dr. Laurent Massoulié
and Dr. Marc Lelarge.
I was an organizer of CSL Student Conference 2014.
arXiv preprints
Google scholar page
Research interests
My research focus is on the intersection of computation and statistics.
I seek to understand the deep interplay between statistical optimality and
computational complexity in
highdimensional statistical inference problems.
As part of this, I have been working on sharp performance analysis of semidefinite
programming relaxations
and belief propagation for community detection.
 Network science
 Highdimensional statistical inference
 Optimization
 Information theory
 Queueing games
 Mean field theory
 Communications and networking
Journal Publications and Preprints
 J. Banks, C. Moore, R. Vershynin, and J. Xu
Informationtheoretic bounds and phase transitions in clustering, sparse PCA, and submatrix localization
arXiv:1607:05222. July 2016.
 Y. Chen, X. Li, and J. Xu
Convexified modularity maximization for degreecorrected stochastic block models
arXiv:1512.08425. Dec. 2015.
[SLIDES]
[CODE]
 B. Hajek, Y. Wu, and J. Xu
Submatrix localization via message passing
arXiv:1510.09219, Oct. 2015.
[SLIDES]
 B. Hajek, Y. Wu, and J. Xu
Recovering a hidden community beyond the spectral limit in
O(E log* V ) time
arXiv:1510.02786, Oct. 2015.
 B. Hajek, Y. Wu, and J. Xu
Information limits for recovering a hidden community
arXiv:1509.07859, Sept. 2015.
 B. Hajek, Y. Wu, and J. Xu
Achieving exact cluster recovery threshold via semidefinite programming: Extensions
arXiv:1502.07738, Accepted to IEEE Transactions on Information Theory, Apr. 2016.
[SLIDES]
 B. Hajek, Y. Wu, and J. Xu
Achieving exact cluster recovery threshold via semidefinite programming
arXiv:1412.6156. Accepted to IEEE Transactions on Information Theory, Jan. 2016.
[SLIDES]
 M. Lelarge, L. Massoulié, and J. Xu
Reconstruction in the labeled stochastic block model
Accepted to IEEE Transactions on Network Science and Engineering, Oct. 2015.
[SLIDES]
 Y. Chen and J. Xu
Statisticalcomputational tradeoffs in planted problems and submatrix localization with a growing number of clusters and submatrices
Accepted to Journal of Machine Learning Research, Sept. 2015.
[SLIDES]
 J. Xu and B. Hajek
The Supermarket game
Stochastic Systems, Vol. 3, No. 2, 405441, 2013.
[SLIDES]
 J. Xu, J. G. Andrews, and S. A. Jafar
MISO broadcast channels with delayed finiterate feedback: predict or observe?
IEEE Transactions on Wireless Communications, Apr. 2012.
 J. Xu, J. Zhang, and J. G. Andrews
On the accuracy of the Wyner model of cellular networks
IEEE Transactions on Wireless Communications, July 2011.
Conference Publications
 F. Krzakala, J. Xu, and L. Zdeborova
Mutual Information in RankOne Matrix Estimation
Information Theory Workshop (ITW), Sept. 2016. arXiv:1603:08447.
 B. Hajek, Y. Wu, and J. Xu
Information limits for recovering a hidden community
International Symposium on Information Theory (ISIT), July 2016. arXiv:1509.07859.
 B. Hajek, Y. Wu, and J. Xu
Semidefinite programs for exact recovery of a hidden community
Conference on Learning Theory (COLT), June 2016. arXiv: 1602.06410.
 E. Mossel and J.Xu
Density evolution in the degreecorrelated stochastic block model
Conference on Learning Theory (COLT), June 2016. arXiv:1509.03281.
[SLIDES]
 E. Mossel and J. Xu
Local algorithms for block models with side information
7th Innovations in Theoretical Computer Science (ITCS), Jan. 2016. arXiv:1508.02344.
 S. Oh, K. K. Thekumparampil, and J. Xu
Collaboratively learning preferences from ordinal data
Neural Information Processing Systems (NIPS), Dec. 2015.
 B. Hajek, Y. Wu, and J. Xu
Achieving exact cluster recovery threshold via semidefinite programming under the stochastic block model
Asilomar Conference on Signals, Systems, and Computers, Nov. 2015, invited.
[SLIDES]
 B. Hajek, Y. Wu, and J. Xu
Exact recovery threshold in the binary censored block model
Information Theory Workshop (ITW), Oct. 2015, invited.
[SLIDES]
 E. Mossel and J. Xu
On the optimality of local belief propagation under the degreecorrelated stochastic block model
Information Theory Workshop (ITW), Oct. 2015, invited.
[SLIDES]
 B. Hajek, Y. Wu, and J. Xu
Computational lower bounds for community detection on random graphs
Conference on Learning Theory (COLT), July 2015.
[SLIDES]
 B. Hajek, Y. Wu, and J. Xu
Achieving exact cluster recovery threshold via semidefinite programming
International Symposium on Information Theory (ISIT), June 2015, semiplenary talk.
[SLIDES]
 R. Wu, J. Xu, R. Srikant, L. Massoulié, M. Lelarge, and B. Hajek
Clustering and inference from pairwise comparisons
ACM SIGMETRICS, June 2015 (short paper).
 B. Hajek, S. Oh, and J. Xu
Minimaxoptimal inference from partial rankings
Neural Information Processing Systems (NIPS), Dec. 2014.
 M. Lelarge, L. Massoulié, and J. Xu
Edge label inference in generalized stochastic block model: from spectral theory to impossibility results
Conference on Learning Theory (COLT), June 2014.
 J. Xu, R. Wu, K. Zhu, B. Hajek, R. Srikant, and L. Ying
Jointly clustering rows and columns of binary matrices: algorithms and tradeoffs
ACM SIGMETRICS, June 2014.
[SLIDES]
 Y. Chen and J. Xu
Statisticalcomputational phase transitions in planted models: the highdimensional setting
International Conference on Machine Learning (ICML), June 2014.
 M. Lelarge, L. Massoulié, and J. Xu
Reconstruction in the labeled stochastic block model
Information Theory Workshop (ITW), Sept. 2013.
[SLIDES]
 J. Xu and B. Hajek
The supermarket game
International Symposium on Information Theory (ISIT), July 2012.
[SLIDES]
Thesis
 Jiaming Xu
Statistical inference in networks: fundamental limits and efficient algorithms
Doctoral Dissertation, University of Illinois, Dec. 2014.
My research interests are in the broad area of stochastic systems with emphasis on large scale distributed networks and highdimensional data analysis.
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 signaltonoise ratio λ>1/e, while a linear message passing algorithm finds the single community in loglog(n) iterations
if and only if λ>1.
Papers:
B. Hajek, Y. Wu, and J. Xu
Submatrix localization via message passing
arXiv:1510.09219, Oct. 2015.
[SLIDES]
B. Hajek, Y. Wu, and J. Xu
Recovering a hidden community beyond the spectral limit in
O(E log* V ) time
arXiv:1510.02786, Oct. 2015.

 Community detection via SDP relaxations

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 equalsized 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
In preparation. Dec. 2015.
B. Hajek, Y. Wu, and J. Xu
Achieving exact cluster recovery threshold via semidefinite programming: Extensions arXiv:1502.07738. Accepted to IEEE Transactions on Information Theory. Apr. 2016.
[SLIDES]
B. Hajek, Y. Wu, and J. Xu
Achieving exact cluster recovery threshold via semidefinite programming
arXiv:1412.6156. Accepted to IEEE Transactions on Information Theory, Jan. 2016.
[SLIDES]

 Community detection with degree corrections

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 realworld networks, the degree distributions are often highly inhomogeneous across nodes, sometimes exhibiting a heavy tail behavior with some nodes having very
high degrees (socalled hubs), and some nodes having very small degrees. We introduce a new approach based on a convexification of modularity maximization followed by weighted kmedian clustering, and show that our approach improves upon the stateoftheart both theoretically and empirically.
Paper:
Y. Chen, X. Li, and J. Xu
Convexified modularity maximization for degreecorrected stochastic block models
arXiv:1512.08425. Dec. 2015.

 Fundamental limits for community detection

(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 nr 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.
Papers:
Y. Chen and J. Xu
Statisticalcomputational tradeoffs in planted problems and submatrix localization with a growing number of clusters and submatrices
Accepted in Journal of Machine Learning Research, Sept. 2015.
[SLIDES]
B. Hajek, Y. Wu, and J. Xu
Computational lower bounds for community detection on
random graphs
Conference on Learning Theory (COLT), July 2015.
[SLIDES]
B. Hajek, Y. Wu, and J. Xu
Information limits for recovering a hidden community
arXiv:1509.07859, Sept. 2015.

Learning user preferences
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.
Papers:
J. Xu, R. Wu, K. Zhu, B. Hajek, R. Srikant, and L. Ying
Jointly clustering rows and columns of binary matrices:
algorithms and tradeoffs
ACM SIGMETRICS, June 2014.
[SLIDES]
M. Lelarge, L. Massoulié, and J. Xu
Edge label inference in generalized stochastic block model: from spectral theory to impossibility results
Conference on Learning Theory (COLT), June 2014.

 Inferring preferences from partial rankings


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 orderoptimal 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 orderoptimal among all schemes.
Papers:
B. Hajek, S. Oh, and J. Xu
Minimaxoptimal inference from partial rankings
Neural Information Processing Systems (NIPS), Dec. 2014.
R. Wu, J. Xu, R. Srikant, L. Massoulié, M. Lelarge, and B. Hajek
Clustering and inference from pairwise comparisons
ACM SIGMETRICS, June 2015 (short paper).
S. Oh, K. K. Thekumparampil, and J. Xu
Collaboratively learning preferences from ordinal data
Neural Information Processing Systems (NIPS), Dec. 2015.

The supermarket game
Imagine being a customer in a supermarket where there is a large number of checkout 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).
Paper:
J. Xu and B. Hajek
The Supermarket game
Stochastic Systems, Vol. 3, No. 2, 405441, 2013.
[SLIDES]

Instructor

MGMT 690: PhD seminar in Analytics: Topics in Highdimensional Data Analysis, Purdue, Fall 2016.

MGMT 306: Management Science, Purdue, Fall 2016.

ECE313: Probability with Engineering Applications, UIUC, Summer 2014.
Teaching Assistant

EE 381K Analysis & Design of Communication Networks, UT Austin, Spring 2011.

EE 381K Digital Logic Design, UT Austin, Spring 2010.

EE 322C Data Structures UT Austin, Spring 2010, Fall 2009
Invited Seminars and Talks

Finding a hidden community in networks: where is the
hard regime?
Simons Institute at UC Berkeley, Apr. 2016

Achieving exact cluster recovery threshold via semidefinite programming
Asilomar Conference on Signals, Systems, and Computers, Nov. 2015

Recovering a hidden community in networks
Electrical Engineering, Korea Advanced Institute of Science and Technology, Oct. 2015
On the optimality of local belief propagation under the degreecorrelated stochastic block model
Information Theory Workshop (ITW), Oct. 2015
Exact recovery threshold in the binary censored block model
Information Theory Workshop (ITW), Oct. 2015
Information and computation limits for recovering a hidden community in Networks
HajekFest: A Workshop on Networks, Games, and Algorithms, UIUC, Oct. 2015
Achieving exact cluster recovery threshold via semidefinite programming
International Symposium on Information Theory (ISIT), June 2015, SemiPlenary Talk
Community detection in networks: understanding the fundamental limits of polynomialtime algorithms
IDeAS Seminar, PACM, Princeton, Apr. 2015
Community detection in networks: fundamental limits and efficient algorithms
Information Theory and Applications Workshop (ITA), Feb. 2015, Graduation Day Talks
Statistical inference in networks: fundamental limits and efficient algorithms
Electrical Engineering Seminar Series, Harvard, Jan. 2015

Fundamental limits for community detection
Research Group Seminar, Department of Statistics, University of California, Berkeley, Oct. 2014

Fundamental limits for community detection
Information Theory Forum, Stanford University, Sept. 2014

Fundamental limits for community detection
Department of Statistics, The Wharton School, University of Pennsylvania, Aug. 2014
Jointly clustering rows and columns of binary matrices: algorithms and tradeoffs
ACM SIGMETRICS, June 2014

Statistical and computational phase transitions in planted models
Artificial Intelligence & Information Systems Seminar, Computer Science, UIUC, Mar. 2014

Statistical and computational phase transitions in planted models
CSL Communications Seminar, UIUC, Nov. 2013

Reconstruction in the sparse labeled stochastic block model
Information Theory Workshop (ITW), Sept. 2013

The supermarket game
Technicolor Paris Research Lab, June 2012
