Related papers: Convex Biclustering
Distributionally Robust Optimization (DRO), as a popular method to train robust models against distribution shift between training and test sets, has received tremendous attention in recent years. In this paper, we propose and analyze…
Cluster analysis relates to the task of assigning objects into groups which ideally present some desirable characteristics. When a cluster structure is confined to a subset of the feature space, traditional clustering techniques face…
We introduce a convex approach for mixed linear regression over $d$ features. This approach is a second-order cone program, based on L1 minimization, which assigns an estimate regression coefficient in $\mathbb{R}^{d}$ for each data point.…
Clustering analysis is one of the most widely used statistical tools in many emerging areas such as microarray data analysis. For microarray and other high-dimensional data, the presence of many noise variables may mask underlying…
We study constrained clustering, where constraints guide the clustering process. In existing works, two categories of constraints have been widely explored, namely pairwise and cardinality constraints. Pairwise constraints enforce the…
Clustering is a widely used technique in data mining applications for discovering patterns in underlying data. Most traditional clustering algorithms are limited to handling datasets that contain either numeric or categorical attributes.…
Non-convex optimization plays a key role in a growing number of machine learning applications. This motivates the identification of specialized structure that enables sharper theoretical analysis. One such identified structure is…
Nonconvex optimization problems arise in many areas of computational science and engineering and are (approximately) solved by a variety of algorithms. Existing algorithms usually only have local convergence or subsequence convergence of…
We study a general class of convex submodular optimization problems with indicator variables. Many applications such as the problem of inferring Markov random fields (MRFs) with a sparsity or robustness prior can be naturally modeled in…
Gradient boosting is a state-of-the-art prediction technique that sequentially produces a model in the form of linear combinations of simple predictors---typically decision trees---by solving an infinite-dimensional convex optimization…
Statistical inference of the dependence between objects often relies on covariance matrices. Unless the number of features (e.g. data points) is much larger than the number of objects, covariance matrix cleaning is necessary to reduce…
The implementation of computational sensing strategies often faces calibration problems typically solved by means of multiple, accurately chosen training signals, an approach that can be resource-consuming and cumbersome. Conversely, blind…
We propose a new shape-based modeling technique for applications in imaging problems. Given a collection of shape priors (a shape dictionary), we define our problem as choosing the right dictionary elements and geometrically composing them…
We study a class of convex-concave min-max problems in which the coupled component of the objective is linear in at least one of the two decision vectors. We identify such problem structure as interpolating between the bilinearly and…
Robust Optimization is becoming increasingly important in machine learning applications. This paper studies the problem of robust submodular minimization subject to combinatorial constraints. Constrained Submodular Minimization arises in…
We propose a low-rank transformation-learning framework to robustify subspace clustering. Many high-dimensional data, such as face images and motion sequences, lie in a union of low-dimensional subspaces. The subspace clustering problem has…
We consider convex-concave saddle-point problems where the objective functions may be split in many components, and extend recent stochastic variance reduction methods (such as SVRG or SAGA) to provide the first large-scale linearly…
Previous work has suggested that the structural restrictions of graphs from classes of bounded expansion--locally dense pockets in a globally sparse graph--naturally coincide with common properties of real-world networks such as clustering…
The robust truss topology optimization against the uncertain static external load can be formulated as mixed-integer semidefinite programming. Although a global optimal solution can be computed with a branch-and-bound method, it is very…
Many problems in operations research require that constraints be specified in the model. Determining the right constraints is a hard and laborsome task. We propose an approach to automate this process using artificial intelligence and…