Results 1  10
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233
Regularization paths for generalized linear models via coordinate descent
, 2009
"... We develop fast algorithms for estimation of generalized linear models with convex penalties. The models include linear regression, twoclass logistic regression, and multinomial regression problems while the penalties include ℓ1 (the lasso), ℓ2 (ridge regression) and mixtures of the two (the elastic ..."
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Cited by 535 (13 self)
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We develop fast algorithms for estimation of generalized linear models with convex penalties. The models include linear regression, twoclass logistic regression, and multinomial regression problems while the penalties include ℓ1 (the lasso), ℓ2 (ridge regression) and mixtures of the two (the elastic net). The algorithms use cyclical coordinate descent, computed along a regularization path. The methods can handle large problems and can also deal efficiently with sparse features. In comparative timings we find that the new algorithms are considerably faster than competing methods.
NESTA: A Fast and Accurate FirstOrder Method for Sparse Recovery
, 2009
"... Accurate signal recovery or image reconstruction from indirect and possibly undersampled data is a topic of considerable interest; for example, the literature in the recent field of compressed sensing is already quite immense. Inspired by recent breakthroughs in the development of novel firstorder ..."
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Cited by 167 (2 self)
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Accurate signal recovery or image reconstruction from indirect and possibly undersampled data is a topic of considerable interest; for example, the literature in the recent field of compressed sensing is already quite immense. Inspired by recent breakthroughs in the development of novel firstorder methods in convex optimization, most notably Nesterov’s smoothing technique, this paper introduces a fast and accurate algorithm for solving common recovery problems in signal processing. In the spirit of Nesterov’s work, one of the key ideas of this algorithm is a subtle averaging of sequences of iterates, which has been shown to improve the convergence properties of standard gradientdescent algorithms. This paper demonstrates that this approach is ideally suited for solving largescale compressed sensing reconstruction problems as 1) it is computationally efficient, 2) it is accurate and returns solutions with several correct digits, 3) it is flexible and amenable to many kinds of reconstruction problems, and 4) it is robust in the sense that its excellent performance across a wide range of problems does not depend on the fine tuning of several parameters. Comprehensive numerical experiments on realistic signals exhibiting a large dynamic range show that this algorithm compares favorably with recently proposed stateoftheart methods. We also apply the algorithm to solve other problems for which there are fewer alternatives, such as totalvariation minimization, and
Sparse Representation or Collaborative Representation: Which Helps Face Recognition?
"... As a recently proposed technique, sparse representation based classification (SRC) has been widely used for face recognition (FR). SRC first codes a testing sample as a sparse linear combination of all the training samples, and then classifies the testing sample by evaluating which class leads to th ..."
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Cited by 100 (17 self)
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As a recently proposed technique, sparse representation based classification (SRC) has been widely used for face recognition (FR). SRC first codes a testing sample as a sparse linear combination of all the training samples, and then classifies the testing sample by evaluating which class leads to the minimum representation error. While the importance of sparsity is much emphasized in SRC and many related works, the use of collaborative representation (CR) in SRC is ignored by most literature. However, is it really the l1norm sparsity that improves the FR accuracy? This paper devotes to analyze the working mechanism of SRC, and indicates that it is the CR but not the l1norm sparsity that makes SRC powerful for face classification. Consequently, we propose a very simple yet much more efficient face classification scheme, namely CR based classification with regularized least square (CRC_RLS). The extensive experiments clearly show that CRC_RLS has very competitive classification results, while it has significantly less complexity than SRC.
An Empirical Study of Context in Object Detection
"... This paper presents an empirical evaluation of the role of context in a contemporary, challenging object detection task – the PASCAL VOC 2008. Previous experiments with context have mostly been done on homegrown datasets, often with nonstandard baselines, making it difficult to isolate the contrib ..."
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Cited by 96 (4 self)
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This paper presents an empirical evaluation of the role of context in a contemporary, challenging object detection task – the PASCAL VOC 2008. Previous experiments with context have mostly been done on homegrown datasets, often with nonstandard baselines, making it difficult to isolate the contribution of contextual information. In this work, we present our analysis on a standard dataset, using topperforming local appearance detectors as baseline. We evaluate several different sources of context and ways to utilize it. While we employ many contextual cues that have been used before, we also propose a few novel ones including the use of geographic context and a new approach for using object spatial support. 1.
Trust region Newton method for largescale logistic regression
 In Proceedings of the 24th International Conference on Machine Learning (ICML
, 2007
"... Largescale logistic regression arises in many applications such as document classification and natural language processing. In this paper, we apply a trust region Newton method to maximize the loglikelihood of the logistic regression model. The proposed method uses only approximate Newton steps in ..."
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Cited by 90 (21 self)
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Largescale logistic regression arises in many applications such as document classification and natural language processing. In this paper, we apply a trust region Newton method to maximize the loglikelihood of the logistic regression model. The proposed method uses only approximate Newton steps in the beginning, but achieves fast convergence in the end. Experiments show that it is faster than the commonly used quasi Newton approach for logistic regression. We also compare it with existing linear SVM implementations. 1
Regularization and feature selection in leastsquares temporal difference learning
, 2009
"... We consider the task of reinforcement learning with linear value function approximation. Temporal difference algorithms, and in particular the LeastSquares Temporal Difference (LSTD) algorithm, provide a method for learning the parameters of the value function, but when the number of features is la ..."
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Cited by 72 (1 self)
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We consider the task of reinforcement learning with linear value function approximation. Temporal difference algorithms, and in particular the LeastSquares Temporal Difference (LSTD) algorithm, provide a method for learning the parameters of the value function, but when the number of features is large this algorithm can overfit to the data and is computationally expensive. In this paper, we propose a regularization framework for the LSTD algorithm that overcomes these difficulties. In particular, we focus on the case of l1 regularization, which is robust to irrelevant features and also serves as a method for feature selection. Although the l1 regularized LSTD solution cannot be expressed as a convex optimization problem, we present an algorithm similar to the Least Angle Regression (LARS) algorithm that can efficiently compute the optimal solution. Finally, we demonstrate the performance of the algorithm experimentally.
Highly undersampled magnetic resonance image reconstruction via homotopic ℓ0minimization
 IEEE Trans. Med. Imaging
, 2009
"... any reduction in scan time offers a number of potential benefits ranging from hightemporalrate observation of physiological processes to improvements in patient comfort. Following recent developments in Compressive Sensing (CS) theory, several authors have demonstrated that certain classes of MR i ..."
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Cited by 68 (1 self)
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any reduction in scan time offers a number of potential benefits ranging from hightemporalrate observation of physiological processes to improvements in patient comfort. Following recent developments in Compressive Sensing (CS) theory, several authors have demonstrated that certain classes of MR images which possess sparse representations in some transform domain can be accurately reconstructed from very highly undersampled Kspace data by solving a convex ℓ1minimization problem. Although ℓ1based techniques are extremely powerful, they inherently require a degree of oversampling above the theoretical minimum sampling rate to guarantee that exact reconstruction can be achieved. In this paper, we propose a generalization of the Compressive Sensing paradigm based on homotopic approximation of the ℓ0 quasinorm and show how MR image reconstruction can be pushed even further below the Nyquist limit and significantly closer to the theoretical bound. Following a brief review of standard Compressive Sensing methods and the developed theoretical extensions, several example MRI reconstructions from highly undersampled Kspace data are presented.
Sparse Channel Estimation for Multicarrier Underwater Acoustic Communication: From Subspace Methods to Compressed Sensing
"... Abstract—In this paper, we present various channel estimators that exploit the channel sparsity in a multicarrier underwater acoustic system, including subspace algorithms from the array precessing literature, namely rootMUSIC and ESPRIT, and recent compressed sensing algorithms in form of Orthogon ..."
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Cited by 66 (30 self)
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Abstract—In this paper, we present various channel estimators that exploit the channel sparsity in a multicarrier underwater acoustic system, including subspace algorithms from the array precessing literature, namely rootMUSIC and ESPRIT, and recent compressed sensing algorithms in form of Orthogonal Matching Pursuit (OMP) and Basis Pursuit (BP). Numerical simulation and experimental data of an OFDM blockbyblock receiver are used to evaluate the proposed algorithms in comparison to the conventional leastsquares (LS) channel estimator. We observe that subspace methods can tolerate small to moderate Doppler effects, and outperform the LS approach when the channel is indeed sparse. On the other hand, compressed sensing algorithms uniformly outperform the LS and subspace methods. Coupled with a channel equalizer mitigating intercarrier interference, the compressed sensing algorithms can handle channels with significant Doppler spread.
ESTIMATING TIMEVARYING NETWORKS
, 2010
"... 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 es ..."
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Cited by 53 (12 self)
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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 timevarying networks from time series of entity attributes. In this paper we present two new machine learning methods for estimating timevarying networks, which both build on a temporally smoothed l1regularized logistic regression formalism that can be cast as a standard convexoptimization problem and solved efficiently using generic solvers scalable to large networks. We report promising results on recovering simulated timevarying 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.