arXiv subjects

Eric P. Xing

Publications and source records attributed to Eric P. Xing.

At least 217 records · Page 12Linked to original sources

arXiv2012

Efficient Algorithm for Extremely Large Multi-task Regression with Massive Structured Sparsity

We develop a highly scalable optimization method called "hierarchical group-thresholding" for solving a multi-task regression model with complex structured sparsity constraints on both input and output spaces. Despite the recent emergence of several efficient optimization algorithms for tackling complex sparsity-inducing regularizers, true scalability in practical high-dimensional problems where a huge amount (e.g., millions) of sparsity patterns need to be enforced remains an open challenge, because all existing algorithms must deal with ALL such patterns exhaustively in every iteration, which is computationally prohibitive. Our proposed algorithm addresses the scalability problem by screening out multiple groups of coefficients simultaneously and systematically. We employ a hierarchical tree representation of group constraints to accelerate the process of removing irrelevant constraints by taking advantage of the inclusion relationships between group sparsities, thereby avoiding dealing with all constraints in every optimization step, and necessitating optimization operation only on a small number of outstanding coefficients. In our experiments, we demonstrate the efficiency of our method on simulation datasets, and in an application of detecting genetic variants associated with gene expression traits.

stat.ML↗

arXiv2012

Graph partition strategies for generalized mean field inference

An autonomous variational inference algorithm for arbitrary graphical models requires the ability to optimize variational approximations over the space of model parameters as well as over the choice of tractable families used for the variational approximation. In this paper, we present a novel combination of graph partitioning algorithms with a generalized mean field (GMF) inference algorithm. This combination optimizes over disjoint clustering of variables and performs inference using those clusters. We provide a formal analysis of the relationship between the graph cut and the GMF approximation, and explore several graph partition strategies empirically. Our empirical results provide rather clear support for a weighted version of MinCut as a useful clustering algorithm for GMF inference, which is consistent with the implications from the formal analysis.

cs.LG↗

arXiv2012

Mining Associated Text and Images with Dual-Wing Harmoniums

We propose a multi-wing harmonium model for mining multimedia data that extends and improves on earlier models based on two-layer random fields, which capture bidirectional dependencies between hidden topic aspects and observed inputs. This model can be viewed as an undirected counterpart of the two-layer directed models such as LDA for similar tasks, but bears significant difference in inference/learning cost tradeoffs, latent topic representations, and topic mixing mechanisms. In particular, our model facilitates efficient inference and robust topic mixing, and potentially provides high flexibilities in modeling the latent topic spaces. A contrastive divergence and a variational algorithm are derived for learning. We specialized our model to a dual-wing harmonium for captioned images, incorporating a multivariate Poisson for word-counts and a multivariate Gaussian for color histogram. We present empirical results on the applications of this model to classification, retrieval and image annotation on news video collections, and we report an extensive comparison with various extant models.

cs.LG↗

arXiv2012

Smoothing proximal gradient method for general structured sparse regression

We study the problem of estimating high-dimensional regression models regularized by a structured sparsity-inducing penalty that encodes prior structural information on either the input or output variables. We consider two widely adopted types of penalties of this kind as motivating examples: (1) the general overlapping-group-lasso penalty, generalized from the group-lasso penalty; and (2) the graph-guided-fused-lasso penalty, generalized from the fused-lasso penalty. For both types of penalties, due to their nonseparability and nonsmoothness, developing an efficient optimization method remains a challenging problem. In this paper we propose a general optimization approach, the smoothing proximal gradient (SPG) method, which can solve structured sparse regression problems with any smooth convex loss under a wide spectrum of structured sparsity-inducing penalties. Our approach combines a smoothing technique with an effective proximal gradient method. It achieves a convergence rate significantly faster than the standard first-order methods, subgradient methods, and is much more scalable than the most widely used interior-point methods. The efficiency and scalability of our method are demonstrated on both simulation experiments and real genetic data sets.

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arXiv2012

Feature Selection via Block-Regularized Regression

Identifying co-varying causal elements in very high dimensional feature space with internal structures, e.g., a space with as many as millions of linearly ordered features, as one typically encounters in problems such as whole genome association (WGA) mapping, remains an open problem in statistical learning. We propose a block-regularized regression model for sparse variable selection in a high-dimensional space where the covariates are linearly ordered, and are possibly subject to local statistical linkages (e.g., block structures) due to spacial or temporal proximity of the features. Our goal is to identify a small subset of relevant covariates that are not merely from random positions in the ordering, but grouped as contiguous blocks from large number of ordered covariates. Following a typical linear regression framework between the features and the response, our proposed model employs a sparsity-enforcing Laplacian prior for the regression coefficients, augmented by a 1st-order Markovian process along the feature sequence that "activates" the regression coefficients in a coupled fashion. We describe a sampling-based learning algorithm and demonstrate the performance of our method on simulated and biological data for marker identification under WGA.

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arXiv2012

Structured Input-Output Lasso, with Application to eQTL Mapping, and a Thresholding Algorithm for Fast Estimation

We consider the problem of learning a high-dimensional multi-task regression model, under sparsity constraints induced by presence of grouping structures on the input covariates and on the output predictors. This problem is primarily motivated by expression quantitative trait locus (eQTL) mapping, of which the goal is to discover genetic variations in the genome (inputs) that influence the expression levels of multiple co-expressed genes (outputs), either epistatically, or pleiotropically, or both. A structured input-output lasso (SIOL) model based on an intricate l1/l2-norm penalty over the regression coefficient matrix is employed to enable discovery of complex sparse input/output relationships; and a highly efficient new optimization algorithm called hierarchical group thresholding (HiGT) is developed to solve the resultant non-differentiable, non-separable, and ultra high-dimensional optimization problem. We show on both simulation and on a yeast eQTL dataset that our model leads to significantly better recovery of the structured sparse relationships between the inputs and the outputs, and our algorithm significantly outperforms other optimization techniques under the same model. Additionally, we propose a novel approach for efficiently and effectively detecting input interactions by exploiting the prior knowledge available from biological experiments.

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arXiv2012

Timeline: A Dynamic Hierarchical Dirichlet Process Model for Recovering Birth/Death and Evolution of Topics in Text Stream

Topic models have proven to be a useful tool for discovering latent structures in document collections. However, most document collections often come as temporal streams and thus several aspects of the latent structure such as the number of topics, the topics' distribution and popularity are time-evolving. Several models exist that model the evolution of some but not all of the above aspects. In this paper we introduce infinite dynamic topic models, iDTM, that can accommodate the evolution of all the aforementioned aspects. Our model assumes that documents are organized into epochs, where the documents within each epoch are exchangeable but the order between the documents is maintained across epochs. iDTM allows for unbounded number of topics: topics can die or be born at any epoch, and the representation of each topic can evolve according to a Markovian dynamics. We use iDTM to analyze the birth and evolution of topics in the NIPS community and evaluated the efficacy of our model on both simulated and real datasets with favorable outcome.

cs.IR↗

arXiv2012

Smoothing Proximal Gradient Method for General Structured Sparse Learning

We study the problem of learning high dimensional regression models regularized by a structured-sparsity-inducing penalty that encodes prior structural information on either input or output sides. We consider two widely adopted types of such penalties as our motivating examples: 1) overlapping group lasso penalty, based on the l1/l2 mixed-norm penalty, and 2) graph-guided fusion penalty. For both types of penalties, due to their non-separability, developing an efficient optimization method has remained a challenging problem. In this paper, we propose a general optimization approach, called smoothing proximal gradient method, which can solve the structured sparse regression problems with a smooth convex loss and a wide spectrum of structured-sparsity-inducing penalties. Our approach is based on a general smoothing technique of Nesterov. It achieves a convergence rate faster than the standard first-order method, subgradient method, and is much more scalable than the most widely used interior-point method. Numerical results are reported to demonstrate the efficiency and scalability of the proposed method.

cs.LG↗

arXiv2012

Sparse Topical Coding

We present sparse topical coding (STC), a non-probabilistic formulation of topic models for discovering latent representations of large collections of data. Unlike probabilistic topic models, STC relaxes the normalization constraint of admixture proportions and the constraint of defining a normalized likelihood function. Such relaxations make STC amenable to: 1) directly control the sparsity of inferred representations by using sparsity-inducing regularizers; 2) be seamlessly integrated with a convex error function (e.g., SVM hinge loss) for supervised learning; and 3) be efficiently learned with a simply structured coordinate descent algorithm. Our results demonstrate the advantages of STC and supervised MedSTC on identifying topical meanings of words and improving classification accuracy and time efficiency.

cs.LG↗

arXiv2011

TopicViz: Semantic Navigation of Document Collections

When people explore and manage information, they think in terms of topics and themes. However, the software that supports information exploration sees text at only the surface level. In this paper we show how topic modeling -- a technique for identifying latent themes across large collections of documents -- can support semantic exploration. We present TopicViz, an interactive environment for information exploration. TopicViz combines traditional search and citation-graph functionality with a range of novel interactive visualizations, centered around a force-directed layout that links documents to the latent themes discovered by the topic model. We describe several use scenarios in which TopicViz supports rapid sensemaking on large document collections.

cs.HC↗

arXiv2010

Estimating Networks With Jumps

We study the problem of estimating a temporally varying coefficient and varying structure (VCVS) graphical model underlying nonstationary time series data, such as social states of interacting individuals or microarray expression profiles of gene networks, as opposed to i.i.d. data from an invariant model widely considered in current literature of structural estimation. In particular, we consider the scenario in which the model evolves in a piece-wise constant fashion. We propose a procedure that minimizes the so-called TESLA loss (i.e., temporally smoothed L1 regularized regression), which allows jointly estimating the partition boundaries of the VCVS model and the coefficient of the sparse precision matrix on each block of the partition. A highly scalable proximal gradient method is proposed to solve the resultant convex optimization problem; and the conditions for sparsistent estimation and the convergence rate of both the partition boundaries and the network structure are established for the first time for such estimators.

stat.ML↗

arXiv2010

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 selection

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arXiv2010

A state-space mixed membership blockmodel for dynamic network tomography

In a dynamic social or biological environment, the interactions between the actors can undergo large and systematic changes. In this paper we propose a model-based approach to analyze what we will refer to as the dynamic tomography of such time-evolving networks. Our approach offers an intuitive but powerful tool to infer the semantic underpinnings of each actor, such as its social roles or biological functions, underlying the observed network topologies. Our model builds on earlier work on a mixed membership stochastic blockmodel for static networks, and the state-space model for tracking object trajectory. It overcomes a major limitation of many current network inference techniques, which assume that each actor plays a unique and invariant role that accounts for all its interactions with other actors; instead, our method models the role of each actor as a time-evolving mixed membership vector that allows actors to behave differently over time and carry out different roles/functions when interacting with different peers, which is closer to reality. We present an efficient algorithm for approximate inference and learning using our model; and we applied our model to analyze a social network between monks (i.e., the Sampson's network), a dynamic email communication network between the Enron employees, and a rewiring gene interaction network of fruit fly collected during its full life cycle. In all cases, our model reveals interesting patterns of the dynamic roles of the actors.

stat.ML↗

arXiv2010

Estimating time-varying networks

Stochastic networks are a plausible representation of the relational information among entities in dynamic systems such as living cells or social communities. While there is a rich literature in estimating a static or temporally invariant network from observation data, little has been done toward estimating time-varying networks from time series of entity attributes. In this paper we present two new machine learning methods for estimating time-varying networks, which both build on a temporally smoothed $l_1$-regularized logistic regression formalism that can be cast as a standard convex-optimization problem and solved efficiently using generic solvers scalable to large networks. We report promising results on recovering simulated time-varying networks. For real data sets, we reverse engineer the latent sequence of temporally rewiring political networks between Senators from the US Senate voting records and the latent evolving regulatory networks underlying 588 genes across the life cycle of Drosophila melanogaster from the microarray time course.

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arXiv2010

Online Multiple Kernel Learning for Structured Prediction

Despite the recent progress towards efficient multiple kernel learning (MKL), the structured output case remains an open research front. Current approaches involve repeatedly solving a batch learning problem, which makes them inadequate for large scale scenarios. We propose a new family of online proximal algorithms for MKL (as well as for group-lasso and variants thereof), which overcomes that drawback. We show regret, convergence, and generalization bounds for the proposed method. Experiments on handwriting recognition and dependency parsing testify for the successfulness of the approach.

stat.ML↗

arXiv2010

Infinite Hierarchical MMSB Model for Nested Communities/Groups in Social Networks

Actors in realistic social networks play not one but a number of diverse roles depending on whom they interact with, and a large number of such role-specific interactions collectively determine social communities and their organizations. Methods for analyzing social networks should capture these multi-faceted role-specific interactions, and, more interestingly, discover the latent organization or hierarchy of social communities. We propose a hierarchical Mixed Membership Stochastic Blockmodel to model the generation of hierarchies in social communities, selective membership of actors to subsets of these communities, and the resultant networks due to within- and cross-community interactions. Furthermore, to automatically discover these latent structures from social networks, we develop a Gibbs sampling algorithm for our model. We conduct extensive validation of our model using synthetic networks, and demonstrate the utility of our model in real-world datasets such as predator-prey networks and citation networks.

stat.ML↗

arXiv2010

Graph-Structured Multi-task Regression and an Efficient Optimization Method for General Fused Lasso

We consider the problem of learning a structured multi-task regression, where the output consists of multiple responses that are related by a graph and the correlated response variables are dependent on the common inputs in a sparse but synergistic manner. Previous methods such as l1/l2-regularized multi-task regression assume that all of the output variables are equally related to the inputs, although in many real-world problems, outputs are related in a complex manner. In this paper, we propose graph-guided fused lasso (GFlasso) for structured multi-task regression that exploits the graph structure over the output variables. We introduce a novel penalty function based on fusion penalty to encourage highly correlated outputs to share a common set of relevant inputs. In addition, we propose a simple yet efficient proximal-gradient method for optimizing GFlasso that can also be applied to any optimization problems with a convex smooth loss and the general class of fusion penalty defined on arbitrary graph structures. By exploiting the structure of the non-smooth ''fusion penalty'', our method achieves a faster convergence rate than the standard first-order method, sub-gradient method, and is significantly more scalable than the widely adopted second-order cone-programming and quadratic-programming formulations. In addition, we provide an analysis of the consistency property of the GFlasso model. Experimental results not only demonstrate the superiority of GFlasso over the standard lasso but also show the efficiency and scalability of our proximal-gradient method.

stat.ML↗

arXiv2009

MedLDA: A General Framework of Maximum Margin Supervised Topic Models

Supervised topic models utilize document's side information for discovering predictive low dimensional representations of documents. Existing models apply the likelihood-based estimation. In this paper, we present a general framework of max-margin supervised topic models for both continuous and categorical response variables. Our approach, the maximum entropy discrimination latent Dirichlet allocation (MedLDA), utilizes the max-margin principle to train supervised topic models and estimate predictive topic representations that are arguably more suitable for prediction tasks. The general principle of MedLDA can be applied to perform joint max-margin learning and maximum likelihood estimation for arbitrary topic models, directed or undirected, and supervised or unsupervised, when the supervised side information is available. We develop efficient variational methods for posterior inference and parameter estimation, and demonstrate qualitatively and quantitatively the advantages of MedLDA over likelihood-based topic models on movie review and 20 Newsgroups data sets.

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