CryptGraph: Privacy Preserving Graph Analytics on Encrypted Graph

Many graph mining and analysis services have been deployed on the cloud, which can alleviate users from the burden of implementing and maintaining graph algorithms. However, putting graph analytics on the cloud can invade users' privacy. To solve this problem, we propose CryptGraph, which runs graph analytics on encrypted graph to preserve the privacy of both users' graph data and the analytic results. In CryptGraph, users encrypt their graphs before uploading them to the cloud. The cloud runs graph analysis on the encrypted graphs and obtains results which are also in encrypted form that the cloud cannot decipher. During the process of computing, the encrypted graphs are never decrypted on the cloud side. The encrypted results are sent back to users and users perform the decryption to obtain the plaintext results. In this process, users' graphs and the analytics results are both encrypted and the cloud knows neither of them. Thereby, users' privacy can be strongly protected. Meanwhile, with the help of homomorphic encryption, the results analyzed from the encrypted graphs are guaranteed to be correct. In this paper, we present how to encrypt a graph using homomorphic encryption and how to query the structure of an encrypted graph by computing polynomials. To solve the problem that certain operations are not executable on encrypted graphs, we propose hard computation outsourcing to seek help from users. Using two graph algorithms as examples, we show how to apply our methods to perform analytics on encrypted graphs. Experiments on two datasets demonstrate the correctness and feasibility of our methods

Tree-guided group lasso for multi-response regression with structured sparsity, with an application to eQTL mapping

We consider the problem of estimating a sparse multi-response regression function, with an application to expression quantitative trait locus (eQTL) mapping, where the goal is to discover genetic variations that influence gene-expression levels. In particular, we investigate a shrinkage technique capable of capturing a given hierarchical structure over the responses, such as a hierarchical clustering tree with leaf nodes for responses and internal nodes for clusters of related responses at multiple granularity, and we seek to leverage this structure to recover covariates relevant to each hierarchically-defined cluster of responses. We propose a tree-guided group lasso, or tree lasso, for estimating such structured sparsity under multi-response regression by employing a novel penalty function constructed from the tree. We describe a systematic weighting scheme for the overlapping groups in the tree-penalty such that each regression coefficient is penalized in a balanced manner despite the inhomogeneous multiplicity of group memberships of the regression coefficients due to overlaps among groups. For efficient optimization, we employ a smoothing proximal gradient method that was originally developed for a general class of structured-sparsity-inducing penalties. Using simulated and yeast data sets, we demonstrate that our method shows a superior performance in terms of both prediction errors and recovery of true sparsity patterns, compared to other methods for learning a multivariate-response regression.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS549 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Ultra-high Dimensional Multiple Output Learning With Simultaneous Orthogonal Matching Pursuit: A Sure Screening Approach

We propose a novel application of the Simultaneous Orthogonal Matching Pursuit (S-OMP) procedure for sparsistant variable selection in ultra-high dimensional multi-task regression problems. Screening of variables, as introduced in \cite{fan08sis}, is an efficient and highly scalable way to remove many irrelevant variables from the set of all variables, while retaining all the relevant variables. S-OMP can be applied to problems with hundreds of thousands of variables and once the number of variables is reduced to a manageable size, a more computationally demanding procedure can be used to identify the relevant variables for each of the regression outputs. To our knowledge, this is the first attempt to utilize relatedness of multiple outputs to perform fast screening of relevant variables. As our main theoretical contribution, we prove that, asymptotically, S-OMP is guaranteed to reduce an ultra-high number of variables to below the sample size without losing true relevant variables. We also provide formal evidence that a modified Bayesian information criterion (BIC) can be used to efficiently determine the number of iterations in S-OMP. We further provide empirical evidence on the benefit of variable selection using multiple regression outputs jointly, as opposed to performing variable selection for each output separately. The finite sample performance of S-OMP is demonstrated on extensive simulation studies, and on a genetic association mapping problem. $Keywords$ Adaptive Lasso; Greedy forward regression; Orthogonal matching pursuit; Multi-output regression; Multi-task learning; Simultaneous orthogonal matching pursuit; Sure screening; Variable selectio

Integrating Document Clustering and Topic Modeling

Document clustering and topic modeling are two closely related tasks which can mutually benefit each other. Topic modeling can project documents into a topic space which facilitates effective document clustering. Cluster labels discovered by document clustering can be incorporated into topic models to extract local topics specific to each cluster and global topics shared by all clusters. In this paper, we propose a multi-grain clustering topic model (MGCTM) which integrates document clustering and topic modeling into a unified framework and jointly performs the two tasks to achieve the overall best performance. Our model tightly couples two components: a mixture component used for discovering latent groups in document collection and a topic model component used for mining multi-grain topics including local topics specific to each cluster and global topics shared across clusters.We employ variational inference to approximate the posterior of hidden variables and learn model parameters. Experiments on two datasets demonstrate the effectiveness of our model.Comment: Appears in Proceedings of the Twenty-Ninth Conference on Uncertainty in Artificial Intelligence (UAI2013