Pan Xu

Pan Xu
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Pan Xu

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Pub Categories

Statistics - Machine Learning (2)
Computer Science - Data Structures and Algorithms (2)
Mathematics - Probability (1)
Computer Science - Databases (1)
Mathematics - Combinatorics (1)
Computer Science - Discrete Mathematics (1)
Computer Science - Learning (1)
Computer Science - Computer Science and Game Theory (1)

Publications Authored By Pan Xu

We study the estimation of the latent variable Gaussian graphical model (LVGGM), where the precision matrix is the superposition of a sparse matrix and a low-rank matrix. In order to speed up the estimation of the sparse plus low-rank components, we propose a sparsity constrained maximum likelihood estimator based on matrix factorization, and an efficient alternating gradient descent algorithm with hard thresholding to solve it. Our algorithm is orders of magnitude faster than the convex relaxation based methods for LVGGM. Read More

We propose communication-efficient distributed estimation and inference methods for the transelliptical graphical model, a semiparametric extension of the elliptical distribution in the high dimensional regime. In detail, the proposed method distributes the $d$-dimensional data of size $N$ generated from a transelliptical graphical model into $m$ worker machines, and estimates the latent precision matrix on each worker machine based on the data of size $n=N/m$. It then debiases the local estimators on the worker machines and send them back to the master machine. Read More

Online matching has received significant attention over the last 15 years due to its close connection to Internet advertising. As the seminal work of Karp, Vazirani, and Vazirani has an optimal (1 - 1/e) competitive ratio in the standard adversarial online model, much effort has gone into developing useful online models that incorporate some stochasticity in the arrival process. One such popular model is the known I. Read More

We consider mining dense substructures (maximal cliques) from an uncertain graph, which is a probability distribution on a set of deterministic graphs. For parameter 0 < {\alpha} < 1, we present a precise definition of an {\alpha}-maximal clique in an uncertain graph. We present matching upper and lower bounds on the number of {\alpha}-maximal cliques possible within an uncertain graph. Read More