相关论文
2021 - ECML/PKDD
Asymptotic Statistical Analysis of Sparse Group LASSO via Approximate Message Passing

Sparse Group LASSO (SGL) is a regularized model for high-dimensional linear regression problems with grouped covariates. SGL applies $l_1$ and $l_2$ penalties on the individual predictors and group predictors, respectively, to guarantee sparse effects both on the inter-group and within-group levels. In this paper, we apply the approximate message passing (AMP) algorithm to efficiently solve the SGL problem under Gaussian random designs. We further use the recently developed state evolution analysis of AMP to derive an asymptotically exact characterization of SGL solution. This allows us to conduct multiple fine-grained statistical analyses of SGL, through which we investigate the effects of the group information and $\gamma$ (proportion of $\ell_1$ penalty). With the lens of various performance measures, we show that SGL with small $\gamma$ benefits significantly from the group information and can outperform other SGL (including LASSO) or regularized models which does not exploit the group information, in terms of the recovery rate of signal, false discovery rate and mean squared error.

2021 - ArXiv
Multi-Task Neural Processes

Neural processes have recently emerged as a class of powerful neural latent variable models that combine the strengths of neural networks and stochastic processes. As they can encode contextual data in the network’s function space, they offer a new way to model task relatedness in multi-task learning. To study its potential, we develop multi-task neural processes, a new variant of neural processes for multi-task learning. In particular, we propose to explore transferable knowledge from related tasks in the function space to provide inductive bias for improving each individual task. To do so, we derive the function priors in a hierarchical Bayesian inference framework, which enables each task to incorporate the shared knowledge provided by related tasks into its context of the prediction function. Our multi-task neural processes methodologically expand the scope of vanilla neural processes and provide a new way of exploring task relatedness in function spaces for multi-task learning. The proposed multi-task neural processes are capable of learning multiple tasks with limited labeled data and in the presence of domain shift. We perform extensive experimental evaluations on several benchmarks for the multi-task regression and classification tasks. The results demonstrate the effectiveness of multi-task neural processes in transferring useful knowledge among tasks for multi-task learning and superior performance in multi-task classification and brain image segmentation.

2010 - 2010 IEEE Electronics, Robotics and Automotive Mechanics Conference
On the Analysis of a Multi-task Modular Robot System for Field Robotics

This paper describes a reconfigurable modular robot system named Rob MAT which attempts to be used in different applications during tele operation tasks. It permits rapid and cost effective design and fabrication. The approach employs elements from the inventory of three types of heterogeneous modules i.e., power and control module, joint module, and specialized module. The advantage of having interchangeable modules is the ability to build different robot configurations. Depending on the mission, the operator decides what type of robot can provide the best performance within the mission. Forward and inverse kinematics from assembled robot configurations are analyzed.

2019 - IberLEF@SEPLN
LTG-Oslo Hierarchical Multi-task Network: The Importance of Negation for Document-level Sentiment in Spanish

This paper details LTG-Oslo team's participation in the sentiment track of the NEGES 2019 evaluation campaign. We participated in the task with a hierarchical multi-task network, which used shared lower-layers in a deep BiLSTM to predict negation, while the higher layers were dedicated to predicting document-level sentiment. The multi-task component shows promise as a way to incorporate information on negation into deep neural sentiment classifiers, despite the fact that the absolute results on the test set were relatively low for a binary classification task.

2019 - Applied Sciences
Multi-Task Learning Using Task Dependencies for Face Attributes Prediction

Face attributes prediction has an increasing amount of applications in human–computer interaction, face verification and video surveillance. Various studies show that dependencies exist in face attributes. Multi-task learning architecture can build a synergy among the correlated tasks by parameter sharing in the shared layers. However, the dependencies between the tasks have been ignored in the task-specific layers of most multi-task learning architectures. Thus, how to further boost the performance of individual tasks by using task dependencies among face attributes is quite challenging. In this paper, we propose a multi-task learning using task dependencies architecture for face attributes prediction and evaluate the performance with the tasks of smile and gender prediction. The designed attention modules in task-specific layers of our proposed architecture are used for learning task-dependent disentangled representations. The experimental results demonstrate the effectiveness of our proposed network by comparing with the traditional multi-task learning architecture and the state-of-the-art methods on Faces of the world (FotW) and Labeled faces in the wild-a (LFWA) datasets.

2020 - MWE-LEX
MTLB-STRUCT @PARSEME 2020: Capturing Unseen Multiword Expressions Using Multi-task Learning and Pre-trained Masked Language Models

This paper describes a semi-supervised system that jointly learns verbal multiword expressions (VMWEs) and dependency parse trees as an auxiliary task. The model benefits from pre-trained multilingual BERT. BERT hidden layers are shared among the two tasks and we introduce an additional linear layer to retrieve VMWE tags. The dependency parse tree prediction is modelled by a linear layer and a bilinear one plus a tree CRF on top of BERT. The system has participated in the open track of the PARSEME shared task 2020 and ranked first in terms of F1-score in identifying unseen VMWEs as well as VMWEs in general, averaged across all 14 languages.

2014 - ECML/PKDD
Gaussian Process Multi-task Learning Using Joint Feature Selection

Multi-task learning involves solving multiple related learning problems by sharing some common structure for improved generalization performance. A promising idea to multi-task learning is joint feature selection where a sparsity pattern is shared across task specific feature representations. In this paper, we propose a novel Gaussian Process (GP) approach to multi-task learning based on joint feature selection. The novelty of the proposed approach is that it captures the task similarity by sharing a sparsity pattern over the kernel hyper-parameters associated with each task. This is achieved by considering a hierarchical model which imposes a multi-Laplacian prior over the kernel hyper-parameters. This leads to a flexible GP model which can handle a wide range of multi-task learning problems and can identify features relevant across all the tasks. The hyper-parameter estimation results in an optimization problem which is solved using a block co-ordinate descent algorithm. Experimental results on synthetic and real world multi-task learning data sets demonstrate that the flexibility of the proposed model is useful in getting better generalization performance.

2018 - Frontiers in Neuroinformatics
Resting-State Brain Functional Hyper-Network Construction Based on Elastic Net and Group Lasso Methods

Brain network analysis has been widely applied in neuroimaging studies. A hyper-network construction method was previously proposed to characterize the high-order relationships among multiple brain regions, where every edge is connected to more than two brain regions and can be represented by a hyper-graph. A brain functional hyper-network is constructed by a sparse linear regression model using resting-state functional magnetic resonance imaging (fMRI) time series, which in previous studies has been solved by the lasso method. Despite its successful application in many studies, the lasso method has some limitations, including an inability to explain the grouping effect. That is, using the lasso method may cause relevant brain regions be missed in selecting related regions. Ideally, a hyper-edge construction method should be able to select interacting brain regions as accurately as possible. To solve this problem, we took into account the grouping effect among brain regions and proposed two methods to improve the construction of the hyper-network: the elastic net and the group lasso. The three methods were applied to the construction of functional hyper-networks in depressed patients and normal controls. The results showed structural differences among the hyper-networks constructed by the three methods. The hyper-network structure obtained by the lasso was similar to that obtained by the elastic net method but very different from that obtained by the group lasso. The classification results indicated that the elastic net method achieved better classification results than the lasso method with the two proposed methods of hyper-network construction. The elastic net method can effectively solve the grouping effect and achieve better classification performance.

2014 - Journal of Applied Statistics
Sparse group variable selection based on quantile hierarchical Lasso

The group Lasso is a penalized regression method, used in regression problems where the covariates are partitioned into groups to promote sparsity at the group level [27]. Quantile group Lasso, a natural extension of quantile Lasso [25], is a good alternative when the data has group information and has many outliers and/or heavy tails. How to discover important features that are correlated with interest of outcomes and immune to outliers has been paid much attention. In many applications, however, we may also want to keep the flexibility of selecting variables within a group. In this paper, we develop a sparse group variable selection based on quantile methods which select important covariates at both the group level and within the group level, which penalizes the empirical check loss function by the sum of square root group-wise L1-norm penalties. The oracle properties are established where the number of parameters diverges. We also apply our new method to varying coefficient model with categorial effect modifiers. Simulations and real data example show that the newly proposed method has robust and superior performance.

2017 - PLoS ONE
Sparse EEG/MEG source estimation via a group lasso

Non-invasive recordings of human brain activity through electroencephalography (EEG) or magnetoencelphalography (MEG) are of value for both basic science and clinical applications in sensory, cognitive, and affective neuroscience. Here we introduce a new approach to estimating the intra-cranial sources of EEG/MEG activity measured from extra-cranial sensors. The approach is based on the group lasso, a sparse-prior inverse that has been adapted to take advantage of functionally-defined regions of interest for the definition of physiologically meaningful groups within a functionally-based common space. Detailed simulations using realistic source-geometries and data from a human Visual Evoked Potential experiment demonstrate that the group-lasso method has improved performance over traditional ℓ2 minimum-norm methods. In addition, we show that pooling source estimates across subjects over functionally defined regions of interest results in improvements in the accuracy of source estimates for both the group-lasso and minimum-norm approaches.

2019 - NeurIPS
Fast Sparse Group Lasso

Sparse Group Lasso is a method of linear regression analysis that finds sparse parameters in terms of both feature groups and individual features. Block Coordinate Descent is a standard approach to obtain the parameters of Sparse Group Lasso, and iteratively updates the parameters for each parameter group. However, as an update of only one parameter group depends on all the parameter groups or data points, the computation cost is high when the number of the parameters or data points is large. This paper proposes a fast Block Coordinate Descent for Sparse Group Lasso. It efficiently skips the updates of the groups whose parameters must be zeros by using the parameters in one group. In addition, it preferentially updates parameters in a candidate group set, which contains groups whose parameters must not be zeros. Theoretically, our approach guarantees the same results as the original Block Coordinate Descent. Experiments show that our algorithm enhances the efficiency of the original algorithm without any loss of accuracy.

2012 - IEEE Transactions on Audio, Speech, and Language Processing
Novel Variations of Group Sparse Regularization Techniques With Applications to Noise Robust Automatic Speech Recognition

This paper presents novel variations of group sparse regularization techniques. We expand upon the Sparse Group LASSO formulation to incorporate different learning techniques for better sparsity enforcement within a group and demonstrate the effectiveness of the algorithms for spectral denoising with applications to robust Automatic Speech Recognition (ASR). In particular, we show that with a strategic selection of groupings greater robustness to noisy speech recognition can be achieved when compared to state-of-the-art techniques like the Fast Iterative Shrinkage Thresholding Algorithm (FISTA) implementation of the Sparse Group LASSO. Moreover, we demonstrate that group sparse regularization techniques can offer significant gains over efficient techniques like the Elastic Net. We also show that the proposed algorithms are effective in exploiting collinear dictionaries to deal with the inherent highly coherent nature of speech spectral segments. Experiments on the Aurora 2.0 continuous digit database and the Aurora 3.0 realistic noisy database demonstrate the performance improvement with the proposed methods, including showing that their execution time is comparable to FISTA, making our algorithms practical for application to a wide range of regularization problems.

2015 - 2015 IEEE Workshop on Automatic Speech Recognition and Understanding (ASRU)
Multi-task joint-learning of deep neural networks for robust speech recognition

Although deep neural networks (DNNs) have achieved great success in automatic speech recognition (ASR), significant performance degradation still exists in noisy environments. In this paper, a novel multi-task joint-learning framework is proposed to address the noise robustness for speech recognition. The architecture integrates two different DNNs, including the regressive denoising DNN and the discriminative recognition DNN, into a complete multi-task structure and all the parameters can be optimized in a real joint-learning mode just from the beginning in model training. In addition, the basic multi-task structure is further explored and reorganized into a more general framework which can get substantial gains. Furthermore, noise adaptive training can also be easily incorporated within this architecture to achieve further performance improvement. Experiments on the Aurora4 task showed that the proposed approach can achieve a WER below 10% without using adaptation or sequence training, a very large and significant (more than 20% relative) improvement over a strong DNN-HMM baseline.

2016 - AAAI
Multi-Stage Multi-Task Learning with Reduced Rank

Multi-task learning (MTL) seeks to improve the generalization performance by sharing information among multiple tasks. Many existing MTL approaches aim to learn the low-rank structure on the weight matrix, which stores the model parameters of all tasks, to achieve task sharing, and as a consequence the trace norm regularization is widely used in the MTL literature. A major limitation of these approaches based on trace norm regularization is that all the singular values of the weight matrix are penalized simultaneously, leading to impaired estimation on recovering the larger singular values in the weight matrix. To address the issue, we propose a Reduced rAnk MUlti-Stage multi-tAsk learning (RAMUSA) method based on the recently proposed capped norms. Different from existing trace-norm-based MTL approaches which minimize the sum of all the singular values, the RAMUSA method uses a capped trace norm regularizer to minimize only the singular values smaller than some threshold. Due to the non-convexity of the capped trace norm, we develop a simple but well guaranteed multi-stage algorithm to learn the weight matrix iteratively. We theoretically prove that the estimation error at each stage in the proposed algorithm shrinks and finally achieves a lower upper-bound as the number of stages becomes large enough. Empirical studies on synthetic and real-world datasets demonstrate the effectiveness of the RAMUSA method in comparison with the state-of-the-art methods.

2015 - Biometrics
Multivariate sparse group lasso for the multivariate multiple linear regression with an arbitrary group structure

We propose a multivariate sparse group lasso variable selection and estimation method for data with high-dimensional predictors as well as high-dimensional response variables. The method is carried out through a penalized multivariate multiple linear regression model with an arbitrary group structure for the regression coefficient matrix. It suits many biology studies well in detecting associations between multiple traits and multiple predictors, with each trait and each predictor embedded in some biological functional groups such as genes, pathways or brain regions. The method is able to effectively remove unimportant groups as well as unimportant individual coefficients within important groups, particularly for large p small n problems, and is flexible in handling various complex group structures such as overlapping or nested or multilevel hierarchical structures. The method is evaluated through extensive simulations with comparisons to the conventional lasso and group lasso methods, and is applied to an eQTL association study.

2012 - KDD : proceedings. International Conference on Knowledge Discovery & Data Mining
Modeling disease progression via fused sparse group lasso

Alzheimer's Disease (AD) is the most common neurodegenerative disorder associated with aging. Understanding how the disease progresses and identifying related pathological biomarkers for the progression is of primary importance in Alzheimer's disease research. In this paper, we develop novel multi-task learning techniques to predict the disease progression measured by cognitive scores and select biomarkers predictive of the progression. In multi-task learning, the prediction of cognitive scores at each time point is considered as a task, and multiple prediction tasks at different time points are performed simultaneously to capture the temporal smoothness of the prediction models across different time points. Specifically, we propose a novel convex fused sparse group Lasso (cFSGL) formulation that allows the simultaneous selection of a common set of biomarkers for multiple time points and specific sets of biomarkers for different time points using the sparse group Lasso penalty and in the meantime incorporates the temporal smoothness using the fused Lasso penalty. The proposed formulation is challenging to solve due to the use of several non-smooth penalties. We show that the proximal operator associated with the proposed formulation exhibits a certain decomposition property and can be computed efficiently; thus cFSGL can be solved efficiently using the accelerated gradient method. To further improve the model, we propose two non-convex formulations to reduce the shrinkage bias inherent in the convex formulation. We employ the difference of convex programming technique to solve the non-convex formulations. Our extensive experiments using data from the Alzheimer's Disease Neuroimaging Initiative demonstrate the effectiveness of the proposed progression models in comparison with existing methods for disease progression. We also perform longitudinal stability selection to identify and analyze the temporal patterns of biomarkers in disease progression.

2022 - Mathematical Programming Computation
Noname manuscript No. (will be inserted by the editor) Efficient Block-coordinate Descent Algorithms for the Group Lasso

We present two algorithms to solve the Group Lasso problem (Yuan and Lin in, J R Stat Soc Ser B (Stat Methodol) 68(1):49–67, 2006). First, we propose a general version of the Block Coordinate Descent (BCD) algorithm for the Group Lasso that employs an efficient approach for optimizing each subproblem exactly. We show that it exhibits excellent performance when the groups are of moderate size. For groups of large size, we propose an extension of ISTA/FISTA SIAM (Beck and Teboulle in, SIAM J Imag Sci 2(1):183–202, 2009) based on variable step-lengths that can be viewed as a simplified version of BCD. By combining the two approaches we obtain an implementation that is very competitive and often outperforms other state-of-the-art approaches for this problem. We show how these methods fit into the globally convergent general block coordinate gradient descent framework in Tseng and Yun (Math Program 117(1):387–423, 2009). We also show that the proposed approach is more efficient in practice than the one implemented in Tseng and Yun (Math Program 117(1):387–423, 2009). In addition, we apply our algorithms to the Multiple Measurement Vector (MMV) recovery problem, which can be viewed as a special case of the Group Lasso problem, and compare their performance to other methods in this particular instance.

2020 - NeurIPS
Gradient Surgery for Multi-Task Learning

While deep learning and deep reinforcement learning (RL) systems have demonstrated impressive results in domains such as image classification, game playing, and robotic control, data efficiency remains a major challenge. Multi-task learning has emerged as a promising approach for sharing structure across multiple tasks to enable more efficient learning. However, the multi-task setting presents a number of optimization challenges, making it difficult to realize large efficiency gains compared to learning tasks independently. The reasons why multi-task learning is so challenging compared to single-task learning are not fully understood. In this work, we identify a set of three conditions of the multi-task optimization landscape that cause detrimental gradient interference, and develop a simple yet general approach for avoiding such interference between task gradients. We propose a form of gradient surgery that projects a task's gradient onto the normal plane of the gradient of any other task that has a conflicting gradient. On a series of challenging multi-task supervised and multi-task RL problems, this approach leads to substantial gains in efficiency and performance. Further, it is model-agnostic and can be combined with previously-proposed multi-task architectures for enhanced performance.

2022 - Comput. Stat. Data Anal.
Computational Statistics and Data Analysis a Note on Adaptive Group Lasso

Group lasso is a natural extension of lasso and selects variables in a grouped manner. However, group lasso suffers from estimation inefficiency and selection inconsistency. To remedy these problems, we propose the adaptive group lasso method. We show theoretically that the new method is able to identify the true model consistently, and the resulting estimator can be as efficient as oracle. Numerical studies confirmed our theoretical findings.

2015 - 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
Instance-Aware Semantic Segmentation via Multi-task Network Cascades

Semantic segmentation research has recently witnessed rapid progress, but many leading methods are unable to identify object instances. In this paper, we present Multitask Network Cascades for instance-aware semantic segmentation. Our model consists of three networks, respectively differentiating instances, estimating masks, and categorizing objects. These networks form a cascaded structure, and are designed to share their convolutional features. We develop an algorithm for the nontrivial end-to-end training of this causal, cascaded structure. Our solution is a clean, single-step training framework and can be generalized to cascades that have more stages. We demonstrate state-of-the-art instance-aware semantic segmentation accuracy on PASCAL VOC. Meanwhile, our method takes only 360ms testing an image using VGG-16, which is two orders of magnitude faster than previous systems for this challenging problem. As a by product, our method also achieves compelling object detection results which surpass the competitive Fast/Faster R-CNN systems. The method described in this paper is the foundation of our submissions to the MS COCO 2015 segmentation competition, where we won the 1st place.

Tree-Guided Group Lasso for Multi-Task Regression with Structured Sparsity

Eric P. Xing
|
Seyoung Kim
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E. Xing
|
Seyoung Kim

Abstract:We consider the problem of learning a sparse multi-task regression, where the structure in the outputs can be represented as a tree with leaf nodes as outputs and internal nodes as clusters of the outputs at multiple granularity. Our goal is to recover the common set of relevant inputs for each output cluster. Assuming that the tree structure is available as prior knowledge, we formulate this problem as a new multi-task regularized regression called tree-guided group lasso. Our structured regularization is based on a group-lasso penalty, where groups are defined with respect to the tree structure. We describe a systematic weighting scheme for the groups in the penalty such that each output variable is penalized in a balanced manner even if the groups overlap. We present an efficient optimization method that can handle a large-scale problem. Using simulated and yeast datasets, 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 multi-task learning.

参考文献

[1]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[2]  J. Mesirov,et al.  Molecular classification of cancer: class discovery and class prediction by gene expression monitoring. , 1999, Science.

[3]  R. Tibshirani,et al.  Supervised harvesting of expression trees , 2001, Genome Biology.

[4]  R. Tibshirani,et al.  Gene expression patterns of breast carcinomas distinguish tumor subclasses with clinical implications , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[5]  D. Pe’er,et al.  Module networks: identifying regulatory modules and their condition-specific regulators from gene expression data , 2003, Nature Genetics.

[6]  A. Ng.  Feature selection, L1 vs. L2 regularization, and rotational invariance , 2004, Twenty-first international conference on Machine learning - ICML '04.

[7]  S. Horvath,et al.  Statistical Applications in Genetics and Molecular Biology , 2011 .

[8]  Joshua T. Burdick,et al.  Mapping determinants of human gene expression by regional and genome-wide association , 2005, Nature.

[9]  S. Hunt,et al.  Genome-Wide Associations of Gene Expression Variation in Humans , 2005, PLoS genetics.

[10]  H. Zou,et al.  Regularization and variable selection via the elastic net , 2005 .

[11]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[12]  D. Pe’er,et al.  Identifying regulatory mechanisms using individual variation reveals key role for chromatin modification , 2006, Proceedings of the National Academy of Sciences.

[13]  Martin J. Wainwright,et al.  High-Dimensional Graphical Model Selection Using ℓ1-Regularized Logistic Regression , 2006, NIPS.

[14]  M. Yuan,et al.  Model selection and estimation in regression with grouped variables , 2006 .

[15]  K. Gunsalus,et al.  Network modeling links breast cancer susceptibility and centrosome dysfunction. , 2007, Nature genetics.

[16]  Massimiliano Pontil,et al.  Convex multi-task feature learning , 2008, Machine Learning.

[17]  P. Zhao,et al.  Grouped and Hierarchical Model Selection through Composite Absolute Penalties , 2007 .

[18]  R. Tibshirani,et al.  PATHWISE COORDINATE OPTIMIZATION , 2007, 0708.1485.

[19]  Martin J. Wainwright,et al.  High-dimensional support union recovery in multivariate regression , 2008, NIPS.

[20]  Francis R. Bach,et al.  Consistency of the group Lasso and multiple kernel learning , 2007, J. Mach. Learn. Res..

[21]  Rachel B. Brem,et al.  Integrating large-scale functional genomic data to dissect the complexity of yeast regulatory networks , 2008, Nature Genetics.

[22]  Yves Grandvalet,et al.  Y.: SimpleMKL , 2008 .

[23]  H. Stefánsson,et al.  Genetics of gene expression and its effect on disease , 2008, Nature.

[24]  S. Horvath,et al.  Variations in DNA elucidate molecular networks that cause disease , 2008, Nature.

[25]  Michael I. Jordan,et al.  High-dimensional union support recovery in multivariate regression , 2008, NIPS 2008.

[26]  Jean-Philippe Vert,et al.  Group lasso with overlap and graph lasso , 2009, ICML '09.

[27]  E. Xing,et al.  Statistical Estimation of Correlated Genome Associations to a Quantitative Trait Network , 2009, PLoS genetics.

[28]  P. Zhao,et al.  The composite absolute penalties family for grouped and hierarchical variable selection , 2009, 0909.0411.

[29]  Marc Teboulle,et al.  A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems , 2009, SIAM J. Imaging Sci..

[30]  Trevor J. Hastie,et al.  Genome-wide association analysis by lasso penalized logistic regression , 2009, Bioinform..

[31]  Ben Taskar,et al.  Joint covariate selection and joint subspace selection for multiple classification problems , 2010, Stat. Comput..

[32]  Huan Liu.  Feature Selection , 2010, Encyclopedia of Machine Learning.

[33]  Shuicheng Yan,et al.  Visual classification with multi-task joint sparse representation , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[34]  Yi Zhang,et al.  Multi-Task Active Learning with Output Constraints , 2010, AAAI.

[35]  R. Tibshirani,et al.  A note on the group lasso and a sparse group lasso , 2010, 1001.0736.

[36]  Rong Jin,et al.  Exclusive Lasso for Multi-task Feature Selection , 2010, AISTATS.

[37]  Francis R. Bach,et al.  Structured Variable Selection with Sparsity-Inducing Norms , 2009, J. Mach. Learn. Res..

[38]  Xi Chen,et al.  Smoothing Proximal Gradient Method for General Structured Sparse Learning , 2011, UAI.

[39]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[40]  Tree-guided group lasso for multi-response regression with structured sparsity, with an application to eQTL mapping , 2009, 0909.1373.

引用
Towards Scalable Analysis of Images and Videos
2014
Metadata-Based Clustered Multi-task Learning for Thread Mining in Web Communities
MLDM
2016
Learning Sparse Convolutional Neural Network via Quantization With Low Rank Regularization
IEEE Access
2019
GWAS in a Box: Statistical and Visual Analytics of Structured Associations via GenAMap
PloS one
2014
Advanced Data Mining and Applications
Lecture Notes in Computer Science
2017
Heterogeneous Contrastive Learning
ArXiv
2021
Generalized Dictionary for Multitask Learning with Boosting
IJCAI
2016
Neural Granger Causality for Nonlinear Time Series
1802.05842
2018
Semantic Kernel Forests from Multiple Taxonomies
NIPS
2012
When Low Rank Representation Based Hyperspectral Imagery Classification Meets Segmented Stacked Denoising Auto-Encoder Based Spatial-Spectral Feature
Remote. Sens.
2018
An Efficient Proximal Gradient Method for General Structured Structured Sparse Learning
2010
An E-cient Proximal Gradient Method for General Structured Sparse Learning
2010
Smoothing Proximal Gradient Method for General Structured Sparse Learning
UAI
2011
A Family of Penalty Functions for Structured Sparsity
NIPS
2010
Regularizers for structured sparsity
Advances in Computational Mathematics
2010
Structured sparsity with convex penalty functions
2012
Smoothing proximal gradient method for general structured sparse regression
The Annals of Applied Statistics
2010
Distributed Multi-Task Learning with Shared Representation
ArXiv
2016
Structured sparsity via optimal interpolation norms
2017
Sparse coding for machine learning, image processing and computer vision
2010