An accelerated gradient method for trace norm minimization

By Shuiwang Ji, Jieping Ye. 2009

591 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Mechanics

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Citations in the corpus

Spectral Regularization Algorithms for Learning Large Incomplete Matrices (2010, methodology): “Note that for all the examples considered in Table 3, the implementations of algorithms NESTEROV (Liu et al., 2009; Ji and Ye, 2009) and MMMF (Rennie and Srebro, 2005) are prohibitively expensive both in terms of computational time and memory requirements, and hence could not be run.”
Deep Meta-Learning: Learning to Learn in the Concept Space (2018, background): “=9,034,502,400, and multi-task learning methods may fail in dealing with too many parameters induced by the large number of tasks (Argyriou et al., 2007; Ji & Ye, 2009).”
Sluice networks: Learning what to share between loosely related tasks (2017, methodology): “Other regularization schemes used in multi-task learning include the (cid:96) 1 /(cid:96) 2 group lasso [1] and the trace norm [17].”
Fast global convergence rates of gradient methods for high-dimensional statistical recovery (2010, methodology): “, [5, 20, 4]) have used variants of Nesterov’s accelerated gradient method [31] to obtain algorithms for high-dimensional statistical problems with a sublinear rate of convergence.”
Multi-target regression via input space expansion: treating targets as inputs (2012, methodology): “A well-studied category of methods, which are particularly useful when dealing with high-dimensional input spaces, assume that models for different tasks share a common low-rank subspace and impose a trace-norm constraint on the parameter matrix (Argyriou et al 2006, 2008; Ji and Ye 2009).”
Accelerated Gradient Methods for Stochastic Optimization and Online Learning (2009, methodology): “These accelerated gradient methods have also been successfully applied in the optimization problems of m ultiple kernel learning [11] and trace norm minimization [12].”
Estimation of (near) low-rank matrices with noise and high-dimensional scaling (2009, methodology): “In all cases, we solved the convex program (6) by using our own implementation in MATLAB of an accelerated gradient descent method which adapts a non-smooth convex optimization procedure (15) to the nuclear-norm (16).”
Multitask Matrix Completion for Learning Protein Interactions Across Diseases (2016, unknown): “There has been a lot of work on other low-rank models for multitask learning (Ando and Zhang, 2005; Ji and Ye, 2009; Chen et al., 2012, 2013).”
Collaborative Multi-domain Sentiment Classification (2015, methodology): “In trace norm regularized multitask learning methods [10], [22], the models from multiple related tasks are assumed to share a low-dimensional subspace.”
Integrating low-rank and group-sparse structures for robust multi-task learning (2011, background): “APM has attracted extensive attentions in the machine learning and data mining communities [20, 19, 15, 8, 18, 21] due to its optimal convergence rate among all first-order techniques and its ability of dealing with large-scale non-smooth optimization problems.”
Multi-Task Learning for Spatio-Temporal Event Forecasting (2015, background): “Diﬀerent regularization/constraint terms capture diﬀerent types of task relatedness [12, 1, 16, 11].”
Trace Norm Regularised Deep Multi-Task Learning (2016, background): “In this section, we will brieﬂy review some studies in this area.”
Efficient Output Kernel Learning for Multiple Tasks (2015, methodology): “etter 61:2 0:8 61:0 1:6 60:5 1:1 60:5 1:8 61:2 0:9 60:3 1:4 61:4 0:7 61:5 1:0 61:4 1:0 Letter: A data set containing handwritten letters from several writers and having 9 binary classiﬁ- cation tasks [31]. Table 2 presents the data set statistics. We compare the following algorithms: MTL [16]: A cla”
Multi-Label Learning with Global and Local Label Correlation (2017, background): “A common approach to encourage this low-rank assumption during inference is by using the nuclear-norm regularizer [6], [21].”
Multi-Task Convolutional Neural Network for Pose-Invariant Face Recognition (2017, background): “The weight vectors of all tasks form a weight matrix, which is regularized by l2,1 norm [3], [38] or trace norm [22] to encourage a low-rank matrix.”
Guaranteed Rank Minimization via Singular Value Projection (2009, methodology): “[20], Toh and Yun [25], while Ji and Ye [13] use Nesterov’s gradient descent methods for opti mizing the trace-norm.”
On the Linear Convergence of the Proximal Gradient Method for Trace Norm Regularization (2013, methodology): “Currently, a popular method for solving (1) is the proximal gradient method (PGM), which exploits the composite nature of the objective function F and certain smoothness properties of the loss function f [8, 19, 11].”