相关论文: A submodular-supermodular procedure with applicati…

Submodular Functions are a special class of set functions, which generalize several information-theoretic quantities such as entropy and mutual information [1]. Submodular functions have subgradients and subdifferentials [2] and admit…

We extend the work of Narasimhan and Bilmes [30] for minimizing set functions representable as a difference between submodular functions. Similar to [30], our new algorithms are guaranteed to monotonically reduce the objective function at…

Submodular functions are discrete functions that model laws of diminishing returns and enjoy numerous algorithmic applications. They have been used in many areas, including combinatorial optimization, machine learning, and economics. In…

Submodularity is a discrete domain functional property that can be interpreted as mimicking the role of the well-known convexity/concavity properties in the continuous domain. Submodular functions exhibit strong structure that lead to…

We extend the work of Narasimhan and Bilmes [30] for minimizing set functions representable as a dierence between submodular functions. Similar to [30], our new algorithms are guaranteed to monotonically reduce the objective function at…

A number of discrete and continuous optimization problems in machine learning are related to convex minimization problems under submodular constraints. In this paper, we deal with a submodular function with a directed graph structure, and…

In model selection problems for machine learning, the desire for a well-performing model with meaningful structure is typically expressed through a regularized optimization problem. In many scenarios, however, the meaningful structure is…

In this paper, we propose the first exact algorithm for minimizing the difference of two submodular functions (D.S.), i.e., the discrete version of the D.C. programming problem. The developed algorithm is a branch-and-bound-based algorithm…

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…

Sparse methods for supervised learning aim at finding good linear predictors from as few variables as possible, i.e., with small cardinality of their supports. This combinatorial selection problem is often turned into a convex optimization…

Submodular set-functions have many applications in combinatorial optimization, as they can be minimized and approximately maximized in polynomial time. A key element in many of the algorithms and analyses is the possibility of extending the…

In this paper, we investigate a class of submodular problems which in general are very hard. These include minimizing a submodular cost function under combinatorial constraints, which include cuts, matchings, paths, etc., optimizing a…

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…

Most supervised learning models are trained for full automation. However, their predictions are sometimes worse than those by human experts on some specific instances. Motivated by this empirical observation, our goal is to design…

Submodular functions describe a variety of discrete problems in machine learning, signal processing, and computer vision. However, minimizing submodular functions poses a number of algorithmic challenges. Recent work introduced an…

We consider a class of submodular maximization problems in which decision-makers have limited access to the objective function. We explore scenarios where the decision-maker can observe only pairwise information, i.e., can evaluate the…

We investigate three related and important problems connected to machine learning: approximating a submodular function everywhere, learning a submodular function (in a PAC-like setting [53]), and constrained minimization of submodular…

In many naturally occurring optimization problems one needs to ensure that the definition of the optimization problem lends itself to solutions that are tractable to compute. In cases where exact solutions cannot be computed tractably, it…

Submodular width is a central structural measure governing the complexity of conjunctive query evaluation. In this paper we recast submodular width in geometric terms. We how that submodular width can be approximated, up to a factor $3/2$,…

We consider the differentiation of the value function for parametric optimization problems. Such problems are ubiquitous in Machine Learning applications such as structured support vector machines, matrix factorization and min-min or…