arXiv subjects

Jieping Ye

Publications and source records attributed to Jieping Ye.

At least 217 records · Page 12Linked to original sources

arXiv2016

A Unified Model for Differential Expression Analysis of RNA-seq Data via L1-Penalized Linear Regression

The RNA-sequencing (RNA-seq) is becoming increasingly popular for quantifying gene expression levels. Since the RNA-seq measurements are relative in nature, between-sample normalization of counts is an essential step in differential expression (DE) analysis. The normalization of existing DE detection algorithms is ad hoc and performed once for all prior to DE detection, which may be suboptimal since ideally normalization should be based on non-DE genes only and thus coupled with DE detection. We propose a unified statistical model for joint normalization and DE detection of log-transformed RNA-seq data. Sample-specific normalization factors are modeled as unknown parameters in the gene-wise linear models and jointly estimated with the regression coefficients. By imposing sparsity-inducing L1 penalty (or mixed L1/L2-norm for multiple treatment conditions) on the regression coefficients, we formulate the problem as a penalized least-squares regression problem and apply the augmented lagrangian method to solve it. Simulation studies show that the proposed model and algorithms outperform existing methods in terms of detection power and false-positive rate when more than half of the genes are differentially expressed and/or when the up- and down-regulated genes among DE genes are unbalanced in amount.

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arXiv2016

Large-scale Collaborative Imaging Genetics Studies of Risk Genetic Factors for Alzheimer's Disease Across Multiple Institutions

Genome-wide association studies (GWAS) offer new opportunities to identify genetic risk factors for Alzheimer's disease (AD). Recently, collaborative efforts across different institutions emerged that enhance the power of many existing techniques on individual institution data. However, a major barrier to collaborative studies of GWAS is that many institutions need to preserve individual data privacy. To address this challenge, we propose a novel distributed framework, termed Local Query Model (LQM) to detect risk SNPs for AD across multiple research institutions. To accelerate the learning process, we propose a Distributed Enhanced Dual Polytope Projection (D-EDPP) screening rule to identify irrelevant features and remove them from the optimization. To the best of our knowledge, this is the first successful run of the computationally intensive model selection procedure to learn a consistent model across different institutions without compromising their privacy while ranking the SNPs that may collectively affect AD. Empirical studies are conducted on 809 subjects with 5.9 million SNP features which are distributed across three individual institutions. D-EDPP achieved a 66-fold speed-up by effectively identifying irrelevant features.

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arXiv2016

Seeing the Forest from the Trees in Two Looks: Matrix Sketching by Cascaded Bilateral Sampling

Matrix sketching is aimed at finding close approximations of a matrix by factors of much smaller dimensions, which has important applications in optimization and machine learning. Given a matrix A of size m by n, state-of-the-art randomized algorithms take O(m * n) time and space to obtain its low-rank decomposition. Although quite useful, the need to store or manipulate the entire matrix makes it a computational bottleneck for truly large and dense inputs. Can we sketch an m-by-n matrix in O(m + n) cost by accessing only a small fraction of its rows and columns, without knowing anything about the remaining data? In this paper, we propose the cascaded bilateral sampling (CABS) framework to solve this problem. We start from demonstrating how the approximation quality of bilateral matrix sketching depends on the encoding powers of sampling. In particular, the sampled rows and columns should correspond to the code-vectors in the ground truth decompositions. Motivated by this analysis, we propose to first generate a pilot-sketch using simple random sampling, and then pursue more advanced, "follow-up" sampling on the pilot-sketch factors seeking maximal encoding powers. In this cascading process, the rise of approximation quality is shown to be lower-bounded by the improvement of encoding powers in the follow-up sampling step, thus theoretically guarantees the algorithmic boosting property. Computationally, our framework only takes linear time and space, and at the same time its performance rivals the quality of state-of-the-art algorithms consuming a quadratic amount of resources. Empirical evaluations on benchmark data fully demonstrate the potential of our methods in large scale matrix sketching and related areas.

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arXiv2015

Linear Convergence of Variance-Reduced Stochastic Gradient without Strong Convexity

Stochastic gradient algorithms estimate the gradient based on only one or a few samples and enjoy low computational cost per iteration. They have been widely used in large-scale optimization problems. However, stochastic gradient algorithms are usually slow to converge and achieve sub-linear convergence rates, due to the inherent variance in the gradient computation. To accelerate the convergence, some variance-reduced stochastic gradient algorithms, e.g., proximal stochastic variance-reduced gradient (Prox-SVRG) algorithm, have recently been proposed to solve strongly convex problems. Under the strongly convex condition, these variance-reduced stochastic gradient algorithms achieve a linear convergence rate. However, many machine learning problems are convex but not strongly convex. In this paper, we introduce Prox-SVRG and its projected variant called Variance-Reduced Projected Stochastic Gradient (VRPSG) to solve a class of non-strongly convex optimization problems widely used in machine learning. As the main technical contribution of this paper, we show that both VRPSG and Prox-SVRG achieve a linear convergence rate without strong convexity. A key ingredient in our proof is a Semi-Strongly Convex (SSC) inequality which is the first to be rigorously proved for a class of non-strongly convex problems in both constrained and regularized settings. Moreover, the SSC inequality is independent of algorithms and may be applied to analyze other stochastic gradient algorithms besides VRPSG and Prox-SVRG, which may be of independent interest. To the best of our knowledge, this is the first work that establishes the linear convergence rate for the variance-reduced stochastic gradient algorithms on solving both constrained and regularized problems without strong convexity.

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arXiv2015

Safe Screening for Multi-Task Feature Learning with Multiple Data Matrices

Multi-task feature learning (MTFL) is a powerful technique in boosting the predictive performance by learning multiple related classification/regression/clustering tasks simultaneously. However, solving the MTFL problem remains challenging when the feature dimension is extremely large. In this paper, we propose a novel screening rule---that is based on the dual projection onto convex sets (DPC)---to quickly identify the inactive features---that have zero coefficients in the solution vectors across all tasks. One of the appealing features of DPC is that: it is safe in the sense that the detected inactive features are guaranteed to have zero coefficients in the solution vectors across all tasks. Thus, by removing the inactive features from the training phase, we may have substantial savings in the computational cost and memory usage without sacrificing accuracy. To the best of our knowledge, it is the first screening rule that is applicable to sparse models with multiple data matrices. A key challenge in deriving DPC is to solve a nonconvex problem. We show that we can solve for the global optimum efficiently via a properly chosen parametrization of the constraint set. Moreover, DPC has very low computational cost and can be integrated with any existing solvers. We have evaluated the proposed DPC rule on both synthetic and real data sets. The experiments indicate that DPC is very effective in identifying the inactive features---especially for high dimensional data---which leads to a speedup up to several orders of magnitude.

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arXiv2015

Persistent Homology in Sparse Regression and its Application to Brain Morphometry

Sparse systems are usually parameterized by a tuning parameter that determines the sparsity of the system. How to choose the right tuning parameter is a fundamental and difficult problem in learning the sparse system. In this paper, by treating the the tuning parameter as an additional dimension, persistent homological structures over the parameter space is introduced and explored. The structures are then further exploited in speeding up the computation using the proposed soft-thresholding technique. The topological structures are further used as multivariate features in the tensor-based morphometry (TBM) in characterizing white matter alterations in children who have experienced severe early life stress and maltreatment. These analyses reveal that stress-exposed children exhibit more diffuse anatomical organization across the whole white matter region.

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arXiv2014

Stochastic Coordinate Coding and Its Application for Drosophila Gene Expression Pattern Annotation

\textit{Drosophila melanogaster} has been established as a model organism for investigating the fundamental principles of developmental gene interactions. The gene expression patterns of \textit{Drosophila melanogaster} can be documented as digital images, which are annotated with anatomical ontology terms to facilitate pattern discovery and comparison. The automated annotation of gene expression pattern images has received increasing attention due to the recent expansion of the image database. The effectiveness of gene expression pattern annotation relies on the quality of feature representation. Previous studies have demonstrated that sparse coding is effective for extracting features from gene expression images. However, solving sparse coding remains a computationally challenging problem, especially when dealing with large-scale data sets and learning large size dictionaries. In this paper, we propose a novel algorithm to solve the sparse coding problem, called Stochastic Coordinate Coding (SCC). The proposed algorithm alternatively updates the sparse codes via just a few steps of coordinate descent and updates the dictionary via second order stochastic gradient descent. The computational cost is further reduced by focusing on the non-zero components of the sparse codes and the corresponding columns of the dictionary only in the updating procedure. Thus, the proposed algorithm significantly improves the efficiency and the scalability, making sparse coding applicable for large-scale data sets and large dictionary sizes. Our experiments on Drosophila gene expression data sets demonstrate the efficiency and the effectiveness of the proposed algorithm.

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arXiv2014

Lasso Screening Rules via Dual Polytope Projection

Lasso is a widely used regression technique to find sparse representations. When the dimension of the feature space and the number of samples are extremely large, solving the Lasso problem remains challenging. To improve the efficiency of solving large-scale Lasso problems, El Ghaoui and his colleagues have proposed the SAFE rules which are able to quickly identify the inactive predictors, i.e., predictors that have $0$ components in the solution vector. Then, the inactive predictors or features can be removed from the optimization problem to reduce its scale. By transforming the standard Lasso to its dual form, it can be shown that the inactive predictors include the set of inactive constraints on the optimal dual solution. In this paper, we propose an efficient and effective screening rule via Dual Polytope Projections (DPP), which is mainly based on the uniqueness and nonexpansiveness of the optimal dual solution due to the fact that the feasible set in the dual space is a convex and closed polytope. Moreover, we show that our screening rule can be extended to identify inactive groups in group Lasso. To the best of our knowledge, there is currently no "exact" screening rule for group Lasso. We have evaluated our screening rule using synthetic and real data sets. Results show that our rule is more effective in identifying inactive predictors than existing state-of-the-art screening rules for Lasso.

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arXiv2014

Two-Layer Feature Reduction for Sparse-Group Lasso via Decomposition of Convex Sets

Sparse-Group Lasso (SGL) has been shown to be a powerful regression technique for simultaneously discovering group and within-group sparse patterns by using a combination of the $\ell_1$ and $\ell_2$ norms. However, in large-scale applications, the complexity of the regularizers entails great computational challenges. In this paper, we propose a novel Two-Layer Feature REduction method (TLFre) for SGL via a decomposition of its dual feasible set. The two-layer reduction is able to quickly identify the inactive groups and the inactive features, respectively, which are guaranteed to be absent from the sparse representation and can be removed from the optimization. Existing feature reduction methods are only applicable for sparse models with one sparsity-inducing regularizer. To our best knowledge, TLFre is the first one that is capable of dealing with multiple sparsity-inducing regularizers. Moreover, TLFre has a very low computational cost and can be integrated with any existing solvers. We also develop a screening method---called DPC (DecomPosition of Convex set)---for the nonnegative Lasso problem. Experiments on both synthetic and real data sets show that TLFre and DPC improve the efficiency of SGL and nonnegative Lasso by several orders of magnitude.

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arXiv2014

Safe Screening With Variational Inequalities and Its Application to LASSO

Sparse learning techniques have been routinely used for feature selection as the resulting model usually has a small number of non-zero entries. Safe screening, which eliminates the features that are guaranteed to have zero coefficients for a certain value of the regularization parameter, is a technique for improving the computational efficiency. Safe screening is gaining increasing attention since 1) solving sparse learning formulations usually has a high computational cost especially when the number of features is large and 2) one needs to try several regularization parameters to select a suitable model. In this paper, we propose an approach called "Sasvi" (Safe screening with variational inequalities). Sasvi makes use of the variational inequality that provides the sufficient and necessary optimality condition for the dual problem. Several existing approaches for Lasso screening can be casted as relaxed versions of the proposed Sasvi, thus Sasvi provides a stronger safe screening rule. We further study the monotone properties of Sasvi for Lasso, based on which a sure removal regularization parameter can be identified for each feature. Experimental results on both synthetic and real data sets are reported to demonstrate the effectiveness of the proposed Sasvi for Lasso screening.

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arXiv2014

Geodesic Distance Function Learning via Heat Flow on Vector Fields

Learning a distance function or metric on a given data manifold is of great importance in machine learning and pattern recognition. Many of the previous works first embed the manifold to Euclidean space and then learn the distance function. However, such a scheme might not faithfully preserve the distance function if the original manifold is not Euclidean. Note that the distance function on a manifold can always be well-defined. In this paper, we propose to learn the distance function directly on the manifold without embedding. We first provide a theoretical characterization of the distance function by its gradient field. Based on our theoretical analysis, we propose to first learn the gradient field of the distance function and then learn the distance function itself. Specifically, we set the gradient field of a local distance function as an initial vector field. Then we transport it to the whole manifold via heat flow on vector fields. Finally, the geodesic distance function can be obtained by requiring its gradient field to be close to the normalized vector field. Experimental results on both synthetic and real data demonstrate the effectiveness of our proposed algorithm.

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arXiv2014

Orthogonal Rank-One Matrix Pursuit for Low Rank Matrix Completion

In this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend orthogonal matching pursuit method from the vector case to the matrix case. We further propose an economic version of our algorithm by introducing a novel weight updating rule to reduce the time and storage complexity. Both versions are computationally inexpensive for each matrix pursuit iteration, and find satisfactory results in a few iterations. Another advantage of our proposed algorithm is that it has only one tunable parameter, which is the rank. It is easy to understand and to use by the user. This becomes especially important in large-scale learning problems. In addition, we rigorously show that both versions achieve a linear convergence rate, which is significantly better than the previous known results. We also empirically compare the proposed algorithms with several state-of-the-art matrix completion algorithms on many real-world datasets, including the large-scale recommendation dataset Netflix as well as the MovieLens datasets. Numerical results show that our proposed algorithm is more efficient than competing algorithms while achieving similar or better prediction performance.

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arXiv2014

Forward-Backward Greedy Algorithms for General Convex Smooth Functions over A Cardinality Constraint

We consider forward-backward greedy algorithms for solving sparse feature selection problems with general convex smooth functions. A state-of-the-art greedy method, the Forward-Backward greedy algorithm (FoBa-obj) requires to solve a large number of optimization problems, thus it is not scalable for large-size problems. The FoBa-gdt algorithm, which uses the gradient information for feature selection at each forward iteration, significantly improves the efficiency of FoBa-obj. In this paper, we systematically analyze the theoretical properties of both forward-backward greedy algorithms. Our main contributions are: 1) We derive better theoretical bounds than existing analyses regarding FoBa-obj for general smooth convex functions; 2) We show that FoBa-gdt achieves the same theoretical performance as FoBa-obj under the same condition: restricted strong convexity condition. Our new bounds are consistent with the bounds of a special case (least squares) and fills a previously existing theoretical gap for general convex smooth functions; 3) We show that the restricted strong convexity condition is satisfied if the number of independent samples is more than $\bar{k}\log d$ where $\bar{k}$ is the sparsity number and $d$ is the dimension of the variable; 4) We apply FoBa-gdt (with the conditional random field objective) to the sensor selection problem for human indoor activity recognition and our results show that FoBa-gdt outperforms other methods (including the ones based on forward greedy selection and L1-regularization).

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arXiv2014

Generalization Bounds for Representative Domain Adaptation

In this paper, we propose a novel framework to analyze the theoretical properties of the learning process for a representative type of domain adaptation, which combines data from multiple sources and one target (or briefly called representative domain adaptation). In particular, we use the integral probability metric to measure the difference between the distributions of two domains and meanwhile compare it with the H-divergence and the discrepancy distance. We develop the Hoeffding-type, the Bennett-type and the McDiarmid-type deviation inequalities for multiple domains respectively, and then present the symmetrization inequality for representative domain adaptation. Next, we use the derived inequalities to obtain the Hoeffding-type and the Bennett-type generalization bounds respectively, both of which are based on the uniform entropy number. Moreover, we present the generalization bounds based on the Rademacher complexity. Finally, we analyze the asymptotic convergence and the rate of convergence of the learning process for representative domain adaptation. We discuss the factors that affect the asymptotic behavior of the learning process and the numerical experiments support our theoretical findings as well. Meanwhile, we give a comparison with the existing results of domain adaptation and the classical results under the same-distribution assumption.

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arXiv2013

Fused Multiple Graphical Lasso

In this paper, we consider the problem of estimating multiple graphical models simultaneously using the fused lasso penalty, which encourages adjacent graphs to share similar structures. A motivating example is the analysis of brain networks of Alzheimer's disease using neuroimaging data. Specifically, we may wish to estimate a brain network for the normal controls (NC), a brain network for the patients with mild cognitive impairment (MCI), and a brain network for Alzheimer's patients (AD). We expect the two brain networks for NC and MCI to share common structures but not to be identical to each other; similarly for the two brain networks for MCI and AD. The proposed formulation can be solved using a second-order method. Our key technical contribution is to establish the necessary and sufficient condition for the graphs to be decomposable. Based on this key property, a simple screening rule is presented, which decomposes the large graphs into small subgraphs and allows an efficient estimation of multiple independent (small) subgraphs, dramatically reducing the computational cost. We perform experiments on both synthetic and real data; our results demonstrate the effectiveness and efficiency of the proposed approach.

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arXiv2013

Scaling SVM and Least Absolute Deviations via Exact Data Reduction

The support vector machine (SVM) is a widely used method for classification. Although many efforts have been devoted to develop efficient solvers, it remains challenging to apply SVM to large-scale problems. A nice property of SVM is that the non-support vectors have no effect on the resulting classifier. Motivated by this observation, we present fast and efficient screening rules to discard non-support vectors by analyzing the dual problem of SVM via variational inequalities (DVI). As a result, the number of data instances to be entered into the optimization can be substantially reduced. Some appealing features of our screening method are: (1) DVI is safe in the sense that the vectors discarded by DVI are guaranteed to be non-support vectors; (2) the data set needs to be scanned only once to run the screening, whose computational cost is negligible compared to that of solving the SVM problem; (3) DVI is independent of the solvers and can be integrated with any existing efficient solvers. We also show that the DVI technique can be extended to detect non-support vectors in the least absolute deviations regression (LAD). To the best of our knowledge, there are currently no screening methods for LAD. We have evaluated DVI on both synthetic and real data sets. Experiments indicate that DVI significantly outperforms the existing state-of-the-art screening rules for SVM, and is very effective in discarding non-support vectors for LAD. The speedup gained by DVI rules can be up to two orders of magnitude.

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arXiv2013

Dictionary LASSO: Guaranteed Sparse Recovery under Linear Transformation

We consider the following signal recovery problem: given a measurement matrix $Φ\in \mathbb{R}^{n\times p}$ and a noisy observation vector $c\in \mathbb{R}^{n}$ constructed from $c = Φθ^* + ε$ where $ε\in \mathbb{R}^{n}$ is the noise vector whose entries follow i.i.d. centered sub-Gaussian distribution, how to recover the signal $θ^*$ if $Dθ^*$ is sparse {\rca under a linear transformation} $D\in\mathbb{R}^{m\times p}$? One natural method using convex optimization is to solve the following problem: $$\min_θ {1\over 2}\|Φθ- c\|^2 + λ\|Dθ\|_1.$$ This paper provides an upper bound of the estimate error and shows the consistency property of this method by assuming that the design matrix $Φ$ is a Gaussian random matrix. Specifically, we show 1) in the noiseless case, if the condition number of $D$ is bounded and the measurement number $n\geq Ω(s\log(p))$ where $s$ is the sparsity number, then the true solution can be recovered with high probability; and 2) in the noisy case, if the condition number of $D$ is bounded and the measurement increases faster than $s\log(p)$, that is, $s\log(p)=o(n)$, the estimate error converges to zero with probability 1 when $p$ and $s$ go to infinity. Our results are consistent with those for the special case $D=\bold{I}_{p\times p}$ (equivalently LASSO) and improve the existing analysis. The condition number of $D$ plays a critical role in our analysis. We consider the condition numbers in two cases including the fused LASSO and the random graph: the condition number in the fused LASSO case is bounded by a constant, while the condition number in the random graph case is bounded with high probability if $m\over p$ (i.e., $#text{edge}\over #text{vertex}$) is larger than a certain constant. Numerical simulations are consistent with our theoretical results.

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arXiv2013

A Safe Screening Rule for Sparse Logistic Regression

The l1-regularized logistic regression (or sparse logistic regression) is a widely used method for simultaneous classification and feature selection. Although many recent efforts have been devoted to its efficient implementation, its application to high dimensional data still poses significant challenges. In this paper, we present a fast and effective sparse logistic regression screening rule (Slores) to identify the 0 components in the solution vector, which may lead to a substantial reduction in the number of features to be entered to the optimization. An appealing feature of Slores is that the data set needs to be scanned only once to run the screening and its computational cost is negligible compared to that of solving the sparse logistic regression problem. Moreover, Slores is independent of solvers for sparse logistic regression, thus Slores can be integrated with any existing solver to improve the efficiency. We have evaluated Slores using high-dimensional data sets from different applications. Extensive experimental results demonstrate that Slores outperforms the existing state-of-the-art screening rules and the efficiency of solving sparse logistic regression is improved by one magnitude in general.

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