Related papers: Supermodular Rank: Set Function Decomposition and …
A natural and important generalization of submodularity -- $k$-submodularity -- applies to set functions with $k$ arguments and appears in a broad range of applications, such as infrastructure design, machine learning, and healthcare. In…
Which ads should we display in sponsored search in order to maximize our revenue? How should we dynamically rank information sources to maximize the value of the ranking? These applications exhibit strong diminishing returns: Redundancy…
We consider the problem of maximizing submodular functions; while this problem is known to be NP-hard, several numerically efficient local search techniques with approximation guarantees are available. In this paper, we propose a novel…
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…
This paper investigates connections between discrete and continuous approaches for decomposable submodular function minimization. We provide improved running time estimates for the state-of-the-art continuous algorithms for the problem…
Combinatorial optimization can be described as the problem of finding a feasible subset that maximizes a objective function. The paper discusses combinatorial optimization problems, where for each dimension the set of feasible subsets is…
We analyze different re-ranking algorithms for diversification and show that majority of them are based on maximizing submodular/modular functions from the class of parameterized concave/linear over modular functions. We study the…
A supervised learning algorithm searches over a set of functions $A \to B$ parametrised by a space $P$ to find the best approximation to some ideal function $f\colon A \to B$. It does this by taking examples $(a,f(a)) \in A\times B$, and…
A set label disagreement function is defined over the number of variables that deviates from the dominant label. The dominant label is the value assumed by the largest number of variables within a set of binary variables. The submodularity…
In this paper, we study the classic submodular maximization problem subject to a group equality constraint under both non-adaptive and adaptive settings. It has been shown that the utility function of many machine learning applications,…
A matroid has been one of the most important combinatorial structures since it was introduced by Whitney as an abstraction of linear independence. As an important property of a matroid, it can be characterized by several different (but…
Elementary facts and observations on the cone of supermodular set functions are recalled. The manuscript deals with such operations with set functions which preserve supermodularity and the emphasis is put on those such operations which…
In this manuscript, we offer a gentle review of submodularity and supermodularity and their properties. We offer a plethora of submodular definitions; a full description of a number of example submodular functions and their generalizations;…
In this paper, we describe a low-rank matrix completion method based on matrix decomposition. An incomplete matrix is decomposed into submatrices which are filled with a proposed trimming step and then are recombined to form a low-rank…
We consider the problem of minimizing a linear function over an affine section of the cone of positive semidefinite matrices, with the additional constraint that the feasible matrix has prescribed rank. When the rank constraint is active,…
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…
In submodular covering problems, we are given a monotone, nonnegative submodular function $f: 2^N \rightarrow\mathbb{R}_+$ and wish to find the min-cost set $S\subseteq N$ such that $f(S)=f(N)$. This captures SetCover when $f$ is a coverage…
The simplex algorithm for linear programming is based on the fact that any local optimum with respect to the polyhedral neighborhood is also a global optimum. We show that a similar result carries over to submodular maximization. In…
Maximizing a submodular function has a wide range of applications in machine learning and data mining. One such application is data summarization whose goal is to select a small set of representative and diverse data items from a large…
Rank modulation has been recently proposed as a scheme for storing information in flash memories. While rank modulation has advantages in improving write speed and endurance, the current encoding approach is based on the "push to the top"…