Related papers: Monotonic Decompositions of Submodular Set Functio…
The research problem in this work is the relaxation of maximizing non-negative submodular plus modular with the entire real number domain as its value range over a family of down-closed sets. We seek a feasible point $\mathbf{x}^*$ in the…
We introduce two new "degree of complementarity" measures, which we refer to, respectively, as supermodular width and superadditive width. Both are formulated based on natural witnesses of complementarity. We show that both measures are…
We analyze the performance of the greedy algorithm, and also a discrete semi-gradient based algorithm, for maximizing the sum of a suBmodular and suPermodular (BP) function (both of which are non-negative monotone non-decreasing) under two…
We study the mixed-integer epigraph of a special class of convex functions with non-convex indicator constraints, which are often used to impose logical constraints on the support of the solutions. The class of functions we consider are…
The paper extends the widely used in optimisation theory decoupling techniques to infinite collections of functions. Extended concepts of uniform lower semicontinuity and firm uniform lower semicontinuity are discussed. The main theorems…
We investigate a class of composite nonconvex functions, where the outer function is the sum of univariate extended-real-valued convex functions and the inner function is the limit of difference-of-convex functions. A notable feature of…
Using polarity, we give an outer polyhedral approximation for the epigraph of set functions. For a submodular function, we prove that the corresponding polar relaxation is exact; hence, it is equivalent to the Lov\'asz extension. The polar…
In this work, we study the classical problem of maximizing a submodular function subject to a matroid constraint. We develop deterministic algorithms that are very parsimonious with respect to querying the submodular function, for both the…
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…
Functional decomposition is a powerful tool for systems analysis because it can reduce a function of arbitrary input dimensions to the sum and superposition of functions of a single variable, thereby mitigating (or potentially avoiding) the…
It is observed that the conjugacy growth series of the infinite finitary symmetric group with respect to the generating set of transpositions is the generating series of the partition function. Other conjugacy growth series are computed,…
Submodular maximization constitutes a prominent research topic in combinatorial optimization and theoretical computer science, with extensive applications across diverse domains. While substantial advancements have been achieved in…
We study the arity gap of functions of several variables defined on an arbitrary set A and valued in another set B. The arity gap of such a function is the minimum decrease in the number of essential variables when variables are identified.…
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…
We introduce an algebraic model, based on the determinantal expansion of the product of two matrices, to test combinatorial reductions of set functions. Each term of the determinantal expansion is deformed through a monomial factor in d…
The maximum a posteriori (MAP) configuration of binary variable models with submodular graph-structured energy functions can be found efficiently and exactly by graph cuts. Max-product belief propagation (MP) has been shown to be suboptimal…
Stochastic optimization of continuous objectives is at the heart of modern machine learning. However, many important problems are of discrete nature and often involve submodular objectives. We seek to unleash the power of stochastic…
An order theoretic and algebraic framework for the extended real numbers is established which includes extensions of the usual difference to expressions involving $-\infty$ and/or $+\infty$, so-called residuations. Based on this,…
In this paper, we study the problem of maximizing continuous submodular functions that naturally arise in many learning applications such as those involving utility functions in active learning and sensing, matrix approximations and network…
We study universal approximation of continuous functionals on compact subsets of products of Hilbert spaces. We prove that any such functional can be uniformly approximated by models that first take finitely many continuous linear…