Blockwise coordinate descent procedures for the multi-task lasso, with applications to neural semantic basis discovery

By Han Liu, Mark Palatucci, Jian Zhang. 2009

237 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability, Representation & Self-Supervised Learning

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Citations in the corpus

An Overview of Multi-task Learning (2018, methodology): “Concrete instances of the (cid:2) p , q regularization include the (cid:2) 2,1 regularization proposed in [8,9] and the (cid:2) ∞ ,1 regularization proposed in [10].”
A Survey on Multi-Task Learning (2017, background): “[31] propose to use the `∞,1 norm to select features with the objective function formulated as”
Coordinate descent algorithms (2015, background): “Liu, Paratucco, and Zhang [26] describe a block CD approach for linear least squares plus a regularization function consisting of a sum of `∞ norms of subvectors of x.”
Optimization with Sparsity-Inducing Penalties (2011, background): “groups of variables penalizing features across all classes [92, 70].”
Distributed Multi-Task Learning (2015, neutral): “,m |βt j| [21, 22].”
Visual classification with multi-task joint sparse representation (2010, methodology): “In this paper, motivated by the success of multitask sparse linear regression models [10][15][25], we investigate into the problem of multi-task joint sparse representation along with its applications in visual recognition.”
Probabilistic Multi-Task Feature Selection (2010, methodology): “The objective functions of most existing multi-task feature selection methods [24, 17, 28, 1, 2, 15, 20, 16, 18] can be expressed in the following form:”
Accelerated Mini-batch Randomized Block Coordinate Descent Method (2014, result): “Recent work has corroborated the empirical advantage of RBCD methods over the proximal gradient method [4, 19, 8].”
Graph-Structured Multi-task Regression and an Efficient Optimization Method for General Fused Lasso (2010, methodology): “Since neural activities in the brain are locally correlated, it is necessary to take into ac count this local correlation in different brain regions rather than assuming that all regions share a s imilar response as in [11].”
Structured sparsity through convex optimization (2011, background): “…encountered takes the form of a graph deﬁned on the set of input variables, which is such that connected variables are more likely to be simultaneously relevant or irrelevant; this type of prior is common in genomics where regulation, co-expression or interaction networks between genes (or…”
$\ell_{p}-\ell_{q}$ Penalty for Sparse Linear and Sparse Multiple Kernel Multitask Learning (2011, background): “Obozinski et al. [36] use p = 1a ndq = 2, while Liu et al. [31], [ 32 ], Quattoni et al. [39], [40], and Chen et al. [11] have considered the use of p = 1a ndq =∞ . In all these works, the authors have focused on convex situations since � p,q is known to be convex whenever p, q ≥ 1 and nonconvex for”
SLEP: Sparse Learning with Efficient Projections (2011, background): “l1/lq-Norm Regularization Recent studies in areas such as machine learning and statist ics have also witnessed growing interests in extending the l1-regularization to thel1/lq-regularization [2, 3, 6, 10, 28, 29, 30, 31, 33, 40, 43, 49, 50, 53, 72, 73].”
Safe Screening for Multi-Task Feature Learning with Multiple Data Matrices (2015, methodology): “MTFL has found great success in many real-world applications including but not limited to: breast cancer classification (Zhang et al., 2010), disease progression prediction (Zhou et al., 2012), gene data analysis (Kim and Xing, 2009), and neural semantic basis discovery (Liu et al., 2009a).”
Parallel Multi-task Learning (2015, methodology): “We classify regularized multi-task algorithms into two main categories: learning with feature covariance [5], [7], [6], [8], [9], [10], [11], [19], [20], [21], [22] and learning with task relations [2], [3], [4], [13], [15], [14], [17], [18], [16].”
Union Support Recovery in Multi-task Learning (2010, unknown): “…learning has received much attention in the machine learning and statistics community (see for example Zhang, 2006; Negahban and Wainwright, 2009; Obozinski et al., 2010; Lounici et al., 2009; Liu et al., 2009; Lounici et al., 2010; Argyriou et al., 2008; Kim et al., 2009, and references therein).”