Related papers: Sparsification of Decomposable Submodular Function…
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…
Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…
Low-rank approximations are essential in modern data science. The interpolative decomposition provides one such approximation. Its distinguishing feature is that it reuses columns from the original matrix. This enables it to preserve matrix…
A widely used method for solving SOS (Sum Of Squares) decomposition problem is to reduce it to the problem of semi-definite programs (SDPs) which can be efficiently solved in theory. In practice, although many SDP solvers can work out some…
Matching pursuits are a class of greedy algorithms commonly used in signal processing, for solving the sparse approximation problem. They rely on an atom selection step that requires the calculation of numerous projections, which can be…
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…
Submodular functions can be exactly minimized in polynomial time, and the special case that graph cuts solve with max flow \cite{KZ:PAMI04} has had significant impact in computer vision \cite{BVZ:PAMI01,Kwatra:SIGGRAPH03,Rother:GrabCut04}.…
Inspired by the analysis of variance (ANOVA) decomposition of functions we propose a Gaussian-Uniform mixture model on the high-dimensional torus which relies on the assumption that the function we wish to approximate can be well explained…
A wide variety of problems in machine learning, including exemplar clustering, document summarization, and sensor placement, can be cast as constrained submodular maximization problems. A lot of recent effort has been devoted to developing…
We study the problem of minimizing or maximizing the average value $ f(S)/|S| $ of a submodular or supermodular set function $ f: 2^V \to \mathbb{R} $ over non-empty subsets $ S \subseteq V $. This generalizes classical problems such as…
In big data image/video analytics, we encounter the problem of learning an overcomplete dictionary for sparse representation from a large training dataset, which can not be processed at once because of storage and computational constraints.…
Simply put, a sparse polynomial is one whose zero coefficients are not explicitly stored. Such objects are ubiquitous in exact computing, and so naturally we would like to have efficient algorithms to handle them. However, with this compact…
Dictionary learning algorithms have been successfully used for both reconstructive and discriminative tasks, where an input signal is represented with a sparse linear combination of dictionary atoms. While these methods are mostly developed…
Sparse coding is a crucial subroutine in algorithms for various signal processing, deep learning, and other machine learning applications. The central goal is to learn an overcomplete dictionary that can sparsely represent a given input…
Submodularity is an important property of set functions and has been extensively studied in the literature. It models set functions that exhibit a diminishing returns property, where the marginal value of adding an element to a set…
Pareto optimization via evolutionary multi-objective algorithms has been shown to efficiently solve constrained monotone submodular functions. Traditionally when solving multiple problems, the algorithm is run for each problem separately.…
This paper addresses the problem of sequential submodular maximization: selecting and ranking items in a sequence to optimize some composite submodular function. In contrast to most of the previous works, which assume access to the utility…
The scalability of submodular optimization methods is critical for their usability in practice. In this paper, we study the reducibility of submodular functions, a property that enables us to reduce the solution space of submodular…
We propose a functional view of matrix decomposition problems on graphs such as geometric matrix completion and graph regularized dimensionality reduction. Our unifying framework is based on the key idea that using a reduced basis to…
Binary optimization, a representative subclass of discrete optimization, plays an important role in mathematical optimization and has various applications in computer vision and machine learning. Usually, binary optimization problems are…