相关论文: IoU is not submodular

We introduce a method to learn a mixture of submodular "shells" in a large-margin setting. A submodular shell is an abstract submodular function that can be instantiated with a ground set and a set of parameters to produce a submodular…

The purpose of this paper is to introduce into consideration an analogue of the concentration index in the class of subharmonic functions of infinite order. The one in the case of finite order is used in the interpolation theory.

In this paper, we study feature cross search as a fundamental primitive in feature engineering. The importance of feature cross search especially for the linear model has been known for a while, with well-known textbook examples. In this…

A real-valued set function is (additively) approximately submodular if it satisfies the submodularity conditions with an additive error. Approximate submodularity arises in many settings, especially in machine learning, where the function…

Multimodular functions, primarily used in the literature of queueing theory, discrete-event systems, and operations research, constitute a fundamental function class in discrete convex analysis. The objective of this paper is to clarify the…

Submodular functions, as well as the sub-class of decomposable submodular functions, and their optimization appear in a wide range of applications in machine learning, recommendation systems, and welfare maximization. However, optimization…

In this article we determine the coefficient bounds for functions in certain subclasses of analytic functions defined by subordination which are related to the well-known classes of starlike and convex functions. The main results deal with…

As a popular machine learning method, neural networks can be used to solve many complex tasks. Their strong generalization ability comes from the representation ability of the basic neuron model. The most popular neuron is the MP neuron,…

Let $D=(V,A)$ be a digraph. For an integer $k\geq 1$, a $k$-arc-connected flip is an arc subset of $D$ such that after reversing the arcs in it the digraph becomes (strongly) $k$-arc-connected. The first main result of this paper introduces…

Submodular functions are at the core of many machine learning and data mining tasks. The underlying submodular functions for many of these tasks are decomposable, i.e., they are sum of several simple submodular functions. In many data…

Let I and J be homogeneous ideals in a standard graded polynomial ring. We study upper bounds of the Hilbert function of the intersection of I and g(J), where g is a general change of coordinates. Our main result gives a generalization of…

We examine hypergeometric functions in the finite field, p-adic and classical settings. In each setting, we prove a formula which splits the hypergeometric function into a sum of lower order functions whose arguments differ by roots of…

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…

Although microservices have physically isolated modules, they have failed to prevent the propagation and diffusion of dependencies. To trace the root cause of the inter-module coupling, this paper, starting from the impact assessment…

We propose a semantically grounded theory of session types which relies on intersection and union types. We argue that intersection and union types are natural candidates for modeling branching points in session types and we show that the…

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…

The UNet architecture has transformed image segmentation. UNet's versatility and accuracy have driven its widespread adoption, significantly advancing fields reliant on machine learning problems with images. In this work, we give a clear…

Given a factorable function f, we propose a procedure that constructs a concave underestimator of f that is tight at a given point. These underestimators can be used to generate intersection cuts. A peculiarity of these underestimators is…

Selective classification (or classification with a reject option) pairs a classifier with a selection function to determine whether or not a prediction should be accepted. This framework trades off coverage (probability of accepting a…

Submodular functions are a special class of set functions which naturally model the notion of representativeness, diversity, coverage etc. and have been shown to be computationally very efficient. A lot of past work has applied submodular…