相关论文: Yes, IoU loss is submodular - as a function of the…

Let $p$ be a prime number. By a result of Ozaki, the capitulations of ideals in ${\Bbb Z}_p$-extensions and the finite submodules of Iwasawa modules are closely related. In this article, we discuss this relationship in ${\Bbb…

Submodularity is a fundamental phenomenon in combinatorial optimization. Submodular functions occur in a variety of combinatorial settings such as coverage problems, cut problems, welfare maximization, and many more. Therefore, a lot of…

It has previously been an open problem whether all Boolean submodular functions can be decomposed into a sum of binary submodular functions over a possibly larger set of variables. This problem has been considered within several different…

Submodular set functions are undoubtedly among the most important building blocks of combinatorial optimization. Somewhat surprisingly, continuous counterparts of such functions have also appeared in an analytic line of research where they…

The subfactor approach to modular invariants gives insight into the fusion rule structure of the modular invariants.

We give a new and short proof of a theorem on k-hypertournament losing scores due to Zhou et al. [G. Zhou, T. Yao, K. Zhang, On score sequences of k-tournaments, European J. Comb., 21, 8 (2000) 993-1000.]

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…

The present article serves as an erratum to our paper of the same title, which was presented and published in the KDD 2014 conference. In that article, we claimed falsely that the objective function defined in Section 1.4 is non-monotone…

We study fragments of first-order logic and of least fixed point logic that allow only unary negation: negation of formulas with at most one free variable. These logics generalize many interesting known formalisms, including modal logic and…

We find it absurd that Walliser [1] essentially used the same analysis and obtained identical results as reported in [3], yet arrived at different conclusions. Namely, based on an incomplete theory and using erroneous arguments, he not only…

Distributionally robust optimization is used to tackle decision making problems under uncertainty where the distribution of the uncertain data is ambiguous. Many ambiguity sets have been proposed for continuous uncertainty that build on…

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…

We prove that if a right modular groupoid U is cancellative or has a left identity then a right modular generalised inflation of U is an inflation of U.

Networked systems are systems of interconnected components, in which the dynamics of each component are influenced by the behavior of neighboring components. Examples of networked systems include biological networks, critical…

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…

In this note, it is shown that the results claimed in the paper [1]---as well as the examples presented there---are, unfortunately, incorrect.

Solving stochastic optimization problems under partial observability, where one needs to adaptively make decisions with uncertain outcomes, is a fundamental but notoriously difficult challenge. In this paper, we introduce the concept of…

We study planning with submodular objective functions, where instead of maximizing the cumulative reward, the goal is to maximize the objective value induced by a submodular function. Our framework subsumes standard planning and submodular…

This paper demonstrates a methodology for examining the accuracy of uncertain inference systems (UIS), after their parameters have been optimized, and does so for several common UIS's. This methodology may be used to test the accuracy when…

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…