Jiaming Xu

Jiaming Xu

Assistant Professor
Krannert School of Management
Purdue University

E-mail: xu972@purdue.edu

Address: 431 Krannert Building
403 W. State Street
West Lafayette, IN 47907-2056

CV (updated Aug. 2016)

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 high-dimensional statistical inference and network science.

I received BE (09) from Tsinghua University, MS (11) from UT-Austin, 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 high-dimensional 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
  • High-dimensional statistical inference
  • Optimization
  • Information theory
  • Queueing games
  • Mean field theory
  • Communications and networking

Journal Publications and Preprints

Conference Publications

My research interests are in the broad area of stochastic systems with emphasis on large scale distributed networks and high-dimensional data analysis.

Community detection in networks

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.

  • 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 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.

  • 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.
  • 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 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.

  • Y. Chen, X. Li, and J. Xu
    Convexified modularity maximization for degree-corrected 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 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.

  • Y. Chen and J. Xu
    Statistical-computational 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.

  • J. Xu, R. Wu, K. Zhu, B. Hajek, R. Srikant, and L. Ying
    Jointly clustering rows and columns of binary matrices:
    algorithms and trade-offs

  • 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 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.

  • B. Hajek, S. Oh, and J. Xu
    Minimax-optimal 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 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).

  • J. Xu and B. Hajek
    The Supermarket game
    Stochastic Systems, Vol. 3, No. 2, 405-441, 2013. [SLIDES]

  • Instructor

    • MGMT 690: PhD seminar in Analytics: Topics in High-dimensional 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