Related papers: A Note on Isolating Cut Lemma for Submodular Funct…
Submodular functions are relevant to machine learning for at least two reasons: (1) some problems may be expressed directly as the optimization of submodular functions and (2) the lovasz extension of submodular functions provides a useful…
Recently, it has become evident that submodularity naturally captures widely occurring concepts in machine learning, signal processing and computer vision. Consequently, there is need for efficient optimization procedures for submodular…
DR-submodular functions encompass a broad class of functions which are generally non-convex and non-concave. We study the problem of minimizing any DR-submodular function, with continuous and general integer variables, under box constraints…
The minimum $s$-$t$ cut problem in graphs is one of the most fundamental problems in combinatorial optimization, and graph cuts underlie algorithms throughout discrete mathematics, theoretical computer science, operations research, and data…
In a nutshell, submodular functions encode an intuitive notion of diminishing returns. As a result, submodularity appears in many important machine learning tasks such as feature selection and data summarization. Although there has been a…
Pioneered by Benczur and Karger for cuts in graphs [STOC'96], sparsification is a fundamental topic with wide-ranging applications that has been studied, e.g., for graphs and hypergraphs, in a combinatorial and a spectral setting, and with…
Many combinatorial problems arising in machine learning can be reduced to the problem of minimizing a submodular function. Submodular functions are a natural discrete analog of convex functions, and can be minimized in strongly polynomial…
We study an extension of the classical graph cut problem, wherein we replace the modular (sum of edge weights) cost function by a submodular set function defined over graph edges. Special cases of this problem have appeared in different…
We study algorithms for the Submodular Multiway Partition problem (SubMP). An instance of SubMP consists of a finite ground set $V$, a subset of $k$ elements $S = \{s_1,s_2,...,s_k\}$ called terminals, and a non-negative submodular set…
We introduce a new convex optimization problem, termed quadratic decomposable submodular function minimization. The problem is closely related to decomposable submodular function minimization and arises in many learning on graphs and…
Submodular function minimization (SFM) is a fundamental and efficiently solvable problem class in combinatorial optimization with a multitude of applications in various fields. Surprisingly, there is only very little known about constraint…
Clustering with submodular functions has been of interest over the last few years. Symmetric submodular functions are of particular interest as minimizing them is significantly more efficient and they include many commonly used functions in…
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…
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…
In connection with the needs of solving optimization problems, the development of conditional minimization methods with convenient numerical implementation continues to attract the attention of mathematicians. In this monograph we propose…
Combinatorial algorithms for minimization of functions of many variables, which take their values in finite totally ordered sets, are developed. For that the decomposition of the functions by Boolean polynomials is used. The modified SFM…
This paper considers the minimization problem of relaxed submodular functions. For a positive integer $k$, a set function is called $k$-distant submodular if the submodular inequality holds for every pair whose symmetric difference is at…
We consider active, semi-supervised learning in an offline transductive setting. We show that a previously proposed error bound for active learning on undirected weighted graphs can be generalized by replacing graph cut with an arbitrary…
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…
We introduce several generalizations of classical computer science problems obtained by replacing simpler objective functions with general submodular functions. The new problems include submodular load balancing, which generalizes load…