Sparsity has become an important tool in many mathematical sciences such as statistics, machine learning, and signal processing. While sparsity is a good model for data in many applications, data often has additional structure that goes beyond the notion of “standard” sparsity. In many cases, we can represent this additional information in a structured sparsity model. Recent research has shown ...

In many learning tasks with structural properties, structural sparsity methods help induce sparse models, usually leading to better interpretability and higher generalization performance. One popular approach is to use group sparsity regularization that enforces sparsity on the clustered groups of features, while another popular approach is to adopt graph sparsity regularization that considers ...

This study deals with the 3D recovering of magnetic susceptibility model by incorporating the sparsity-based constraints in the inversion algorithm. For this purpose, the area under prospect was divided into a large number of rectangular prisms in a mesh with unknown susceptibilities. Tikhonov cost functions with two sparsity functions were used to recover the smooth parts as well as the sharp ...

Sufficient number of linear and noisy measurements for exact and approximate sparsity pattern/support set recovery in the high dimensional setting is derived. Although this problem as been addressed in the recent literature, there is still considerable gaps between those results and the exact limits of the perfect support set recovery. To reduce this gap, in this paper, the sufficient con...

Performance on a statistical language processing task relies upon accurate information being found in a corpus. However, it is known (and this paper will confirm) that many perfectly valid word sequences do not appear in training corpora. The percentage of n-grams in a test document which are seen in a training corpus is defined as n-gram coverage, and work in the speech processing community [7...

Twitter has brought much attention recently as a hot research topic in the domain of sentiment analysis. Training sentiment classifiers from tweets data often faces the data sparsity problem partly due to the large variety of short and irregular forms introduced to tweets because of the 140-character limit. In this work we propose using two different sets of features to alleviate the data spars...

In this paper, we address the issue for learning better translation consensus in machine translation (MT) research, and explore the search of translation consensus from similar, rather than the same, source sentences or their spans. Unlike previous work on this topic, we formulate the problem as structured labeling over a much smaller graph, and we propose a novel structured label propagation f...

The facility location problem is widely used for summarizing large datasets and has additional applications in sensor placement, image retrieval, and clustering. One difficulty of this problem is that submodular optimization algorithms require the calculation of pairwise benefits for all items in the dataset. This is infeasible for large problems, so recent work proposed to only calculate neare...

Subspace clustering is the process of assigning subspace memberships to a set of unlabeled data points assumed to have been drawn from the union of an unknown number of low-dimensional subspaces, possibly interlaced with outliers or other data corruptions. By exploiting the fact that each inlier point has a sparse representation with respect to a dictionary formed by all the other points, an `1...