Group Lasso Problem Research Articles

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.

Determining Unintelligible Words from their Textual Contexts

We propose a method to determine unintelligible words based on the textual context of the word determined. As there can be many different possibilities for the word, a robust, large-scale method is needed.The large scale makes the problem sensitive to spurious similarities of contexts: when the contexts of two, different words are similar. To reduce this effect, we induce structured sparsity on the words by formulating the task as a group Lasso problem. We compare this formulation to a k-nearest neighbor and a support vector machine based approach, and find that group Lasso outperforms both by a large margin. We achieve up to 75% of accuracy when determining the word from among 1000 words both on the Brown corpus and on the British National Corpus.Unintelligible words are often the result of errors in Optical Character Recognition (OCR) algorithms. As the proposed method utilizes information independent from information used in OCR, we expect that a combined approach could be very successful, as OCR and the proposed method complement each other.

Joint Base Station Clustering and Beamformer Design for Partial Coordinated Transmission in Heterogeneous Networks

We consider the interference management problem in a multicell MIMO heterogeneous network. Within each cell there is a large number of distributed micro/pico base stations (BSs) that can be potentially coordinated for joint transmission. To reduce coordination overhead, we consider user-centric BS clustering so that each user is served by only a small number of (potentially overlapping) BSs. Thus, given the channel state information, our objective is to jointly design the BS clustering and the linear beamformers for all BSs in the network. In this paper, we formulate this problem from a {sparse optimization} perspective, and propose an efficient algorithm that is based on iteratively solving a sequence of group LASSO problems. A novel feature of the proposed algorithm is that it performs BS clustering and beamformer design jointly rather than separately as is done in the existing approaches for partial coordinated transmission. Moreover, the cluster size can be controlled by adjusting a single penalty parameter in the nonsmooth regularized utility function. The convergence of the proposed algorithm (to a stationary solution) is guaranteed, and its effectiveness is demonstrated via extensive simulation.