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Robust multitask feature learning
 Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
, 2012
"... Multitask sparse feature learning aims to improve the generalization performance by exploiting the shared features among tasks. It has been successfully applied to many applications including computer vision and biomedical informatics. Most of the existing multitask sparse feature learning algorit ..."
Abstract

Cited by 13 (2 self)
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Multitask sparse feature learning aims to improve the generalization performance by exploiting the shared features among tasks. It has been successfully applied to many applications including computer vision and biomedical informatics. Most of the existing multitask sparse feature learning algorithms are formulated as a convex sparse regularization problem, which is usually suboptimal, due to its looseness for approximating an ℓ0type regularizer. In this paper, we propose a nonconvex formulation for multitask sparse feature learning based on a novel regularizer. To solve the nonconvex optimization problem, we propose a MultiStage MultiTask Feature Learning (MSMTFL) algorithm. Moreover, we present a detailed theoretical analysis showing that MSMTFL achieves a better parameter estimation error bound than the convex formulation. Empirical studies on both synthetic and realworld data sets demonstrate the effectiveness of MSMTFL in comparison with the state of the art multitask sparse feature learning algorithms. 1
N(0,Σ). Then
"... The appendix contains a collection of known results as well as the technical proofs. 6.1 Tail bounds for Chisquared variables Throughout the paper we will often use one of the following tail bounds for central χ 2 random variables. These are well known and proofs can be found in the original papers ..."
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The appendix contains a collection of known results as well as the technical proofs. 6.1 Tail bounds for Chisquared variables Throughout the paper we will often use one of the following tail bounds for central χ 2 random variables. These are well known and proofs can be found in the original papers. Lemma 6 ([25]). Let X ∼ χ2 d. For all x ≥ 0,
Uniform inference Model selection Doublyrobust estimator
, 2015
"... Heterogeneous treatment effects ..."
Average Case Analysis of HighDimensional BlockSparse Recovery and Regression for Arbitrary Designs
, 2015
"... This paper studies conditions for highdimensional inference when the set of observations is given by a linear combination of a small number of groups of columns of a design matrix, termed the “blocksparse” case. In this regard, it first specifies conditions on the design matrix under which most of ..."
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This paper studies conditions for highdimensional inference when the set of observations is given by a linear combination of a small number of groups of columns of a design matrix, termed the “blocksparse” case. In this regard, it first specifies conditions on the design matrix under which most of its block submatrices are well conditioned. It then leverages this result for averagecase analysis of highdimensional blocksparse recovery and regression. In contrast to earlier works: (i) this paper provides conditions on arbitrary designs that can be explicitly computed in polynomial time, (ii) the provided conditions translate into nearoptimal scaling of the number of observations with the number of active blocks of the design matrix, and (iii) the conditions suggest that the spectral norm, rather than the column/block coherences, of the design matrix fundamentally limits the performance of computational methods in highdimensional settings.
Average Case Analysis of HighDimensional BlockSparse Recovery and Regression for Arbitrary Designs
"... Abstract This paper studies conditions for highdimensional inference when the set of observations is given by a linear combination of a small number of groups of columns of a design matrix, termed the "blocksparse" case. In this regard, it first specifies conditions on the design matrix ..."
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Abstract This paper studies conditions for highdimensional inference when the set of observations is given by a linear combination of a small number of groups of columns of a design matrix, termed the "blocksparse" case. In this regard, it first specifies conditions on the design matrix under which most of its block submatrices are well conditioned. It then leverages this result for averagecase analysis of highdimensional blocksparse recovery and regression. In contrast to earlier works: (i) this paper provides conditions on arbitrary designs that can be explicitly computed in polynomial time, (ii) the provided conditions translate into nearoptimal scaling of the number of observations with the number of active blocks of the design matrix, and (iii) the conditions suggest that the spectral norm, rather than the column/block coherences, of the design matrix fundamentally limits the performance of computational methods in highdimensional settings.
Multivariate Regression with Calibration
, 2013
"... We propose a new method named calibrated multivariate regression (CMR) for fitting high dimensional multivariate regression models. Compared to existing methods, CMR calibrates the regularization for each regression task with respect to its noise level so that it is simultaneously tuning insensitiv ..."
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We propose a new method named calibrated multivariate regression (CMR) for fitting high dimensional multivariate regression models. Compared to existing methods, CMR calibrates the regularization for each regression task with respect to its noise level so that it is simultaneously tuning insensitive and achieves an improved finite sample performance. Computationally, we develop an efficient smoothed proximal gradient algorithm with a worstcase numerical rate of convergence O(1/), where is a prespecified accuracy. Theoretically, we prove that CMR achieves the optimal rate of convergence in parameter estimation. We illustrate the usefulness of CMR by thorough numerical simulations and show that CMR consistently outperforms existing multivariate regression methods. We also apply CMR on a brain activity prediction problem and find that CMR even outperforms the handcrafted models created by human experts. 1
Sharp Threshold for Multivariate MultiResponse Lin ear Regression via Block Regularized Lasso
"... ar ..."
Block Regularized Lasso for Multivariate MultiResponse Linear Regression
"... Abstract The multivariate multiresponse (MVMR) linear regression problem is investigated, in which design matrices are Gaussian with co ..."
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Abstract The multivariate multiresponse (MVMR) linear regression problem is investigated, in which design matrices are Gaussian with co