Related papers: IoU is not submodular

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…

Set-functions appear in many areas of computer science and applied mathematics, such as machine learning, computer vision, operations research or electrical networks. Among these set-functions, submodular functions play an important role,…

Sensor fusion is a fundamental process in robotic systems as it extends the perceptual range and increases robustness in real-world operations. Current multi-sensor deep learning based semantic segmentation approaches do not provide…

Submodular functions play a key role in the area of optimization as they allow to model many real-world problems that face diminishing returns. Evolutionary algorithms have been shown to obtain strong theoretical performance guarantees for…

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…

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…

The increasing size and complexity of scientific data could dramatically enhance discovery and prediction for basic scientific applications. Realizing this potential, however, requires novel statistical analysis methods that are both…

We present Boundary IoU (Intersection-over-Union), a new segmentation evaluation measure focused on boundary quality. We perform an extensive analysis across different error types and object sizes and show that Boundary IoU is significantly…

The asynchronous systems $f$ are the models of the asynchronous circuits from digital electrical engineering. They are multi-valued functions that associate to each input $u:\mathbf{R}\to \{0,1\}^{m}$ a set of states $x\in f(u),$ where…

Disjoint union is a partial binary operation returning the union of two sets if they are disjoint and undefined otherwise. A disjoint-union partial algebra of sets is a collection of sets closed under disjoint unions, whenever they are…

In recent years, many semantic segmentation methods have been proposed to predict label of pixels in the scene. In general, we measure area prediction errors or boundary prediction errors for comparing methods. However, there is no…

Current approaches to generic segmentation start by creating a hierarchy of nested image partitions and then specifying a segmentation from it. Our first contribution is to describe several ways, most of them new, for specifying…

We initiate the study of property testing of submodularity on the boolean hypercube. Submodular functions come up in a variety of applications in combinatorial optimization. For a vast range of algorithms, the existence of an oracle to a…

Tensors or {\em multi-way arrays} are functions of three or more indices $(i,j,k,\cdots)$ -- similar to matrices (two-way arrays), which are functions of two indices $(r,c)$ for (row,column). Tensors have a rich history, stretching over…

Information-theoretic quantities like entropy and mutual information have found numerous uses in machine learning. It is well known that there is a strong connection between these entropic quantities and submodularity since entropy over a…

Anti-unification (AU) is a fundamental operation for generalization computation used for inductive inference. It is the dual operation to unification, an operation at the foundation of automated theorem proving. Interest in AU from the AI…

Submodularity in combinatorial optimization has been a topic of many studies and various algorithmic techniques exploiting submodularity of a studied problem have been proposed. It is therefore natural to ask, in cases where the cost…

We study a mixed-integer set $S:=\{(x,t) \in \{0,1\}^n \times \mathbb{R}: f(x) \ge t\}$ arising in the submodular maximization problem, where $f$ is a submodular function defined over $\{0,1\}^n$. We use intersection cuts to tighten a…

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…

We define the supermodular rank of a function on a lattice. This is the smallest number of terms needed to decompose it into a sum of supermodular functions. The supermodular summands are defined with respect to different partial orders. We…