Related papers: Mixed-Integer Programming for a Class of Robust Su…
Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper,…
We present a robust adaptive beamforming algorithm based on the worst-case criterion and the constrained constant modulus approach, which exploits the constant modulus property of the desired signal. Similarly to the existing worst-case…
Subspace segmentation or subspace learning is a challenging and complicated task in machine learning. This paper builds a primary frame and solid theoretical bases for the minimal subspace segmentation (MSS) of finite samples. Existence and…
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…
This paper extends algorithms that remove the fixed point bias of decentralized gradient descent to solve the more general problem of distributed optimization over subspace constraints. Leveraging the integral quadratic constraint…
Mixed integer sets have a strong modeling capacity to describe practical systems. Nevertheless, incorporating a mixed integer set often renders an optimization formulation drastically more challenging to compute. In this paper, we study how…
The problem of Cloud resource provisioning for component-based applications consists in the allocation of virtual machines (VMs) offers from various Cloud Providers to a set of applications such that the constraints induced by the…
Robust optimization typically follows a worst-case perspective, where a single scenario may determine the objective value of a given solution. Accordingly, it is a challenging task to reduce the size of an uncertainty set without changing…
We consider the problem of jointly inferring the M-best diverse labelings for a binary (high-order) submodular energy of a graphical model. Recently, it was shown that this problem can be solved to a global optimum, for many practically…
Optimization over the Stiefel manifold is a fundamental computational problem in many scientific and engineering applications. Despite considerable research effort, high-dimensional optimization problems over the Stiefel manifold remain…
The sheer scale of modern datasets has resulted in a dire need for summarization techniques that identify representative elements in a dataset. Fortunately, the vast majority of data summarization tasks satisfy an intuitive diminishing…
The Reduced Basis Method (RBM) is a rigorous model reduction approach for solving parametrized partial differential equations. It identifies a low-dimensional subspace for approximation of the parametric solution manifold that is embedded…
In many networks, it is of great interest to identify "communities", unusually densely knit groups of individuals. Such communities often shed light on the function of the networks or underlying properties of the individuals. Recently,…
Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization and cardinality regularized optimization as special cases. This paper proposes…
We introduce the \emph{submodular objectives chasing problem}, which generalizes many natural and previously-studied problems: a sequence of constrained submodular maximization problems is revealed over time, with both the objective and…
Maximizing a monotone submodular function is a fundamental task in machine learning. In this paper, we study the deletion robust version of the problem under the classic matroids constraint. Here the goal is to extract a small size summary…
We explore a multiple-stage variant of the min-max robust selection problem with budgeted uncertainty that includes queries. First, one queries a subset of items and gets the exact values of their uncertain parameters. Given this…
The subspace selection problem seeks a subspace that maximizes an objective function under some constraint. This problem includes several important machine learning problems such as the principal component analysis and sparse dictionary…
Submodular functions have many applications. Matchings have many applications. The bitext word alignment problem can be modeled as the problem of maximizing a nonnegative, monotone, submodular function constrained to matchings in a complete…
We study the problem of selecting a subset of vectors from a large set, to obtain the best signal representation over a family of functions. Although greedy methods have been widely used for tackling this problem and many of those have been…