相关论文: Concentration of Submodular Functions and Read-k F…

A $k$-submodular function is a generalization of the submodular set function. Many practical applications can be modeled as maximizing a $k$-submodular function, such as multi-cooperative games, sensor placement with $k$ type sensors,…

Set function optimization is essential in AI and machine learning. We focus on a subadditive set function that generalizes submodularity, and examine the subadditivity of non-submodular functions. We also deal with a minimax subadditive…

Reducing reinforcement learning to supervised learning is a well-studied and effective approach that leverages the benefits of compact function approximation to deal with large-scale Markov decision processes. Independently, the boosting…

We study the relative entropy of the empirical probability vector with respect to the true probability vector in multinomial sampling of $k$ categories, which, when multiplied by sample size $n$, is also the log-likelihood ratio statistic.…

In this paper, we establish some Harnack type inequalities satisfied by positive solutions of nonlocal inhomogeneous equations arising in the description of various phenomena ranging from population dynamics to micro-magnetism. For regular…

Upper and lower bounds are obtained for the joint entropy of a collection of random variables in terms of an arbitrary collection of subset joint entropies. These inequalities generalize Shannon's chain rule for entropy as well as…

We prove an exponential decay concentration inequality to bound the tail probability of the difference between the log-likelihood of discrete random variables on a finite alphabet and the negative entropy. The concentration bound we derive…

We consider the problem of maximizing submodular functions; while this problem is known to be NP-hard, several numerically efficient local search techniques with approximation guarantees are available. In this paper, we propose a novel…

This paper considers submodular function minimization (SFM) restricted to a family of subsets. We show that SFM over complements of families with certain hierarchical structures can be solved in polynomial-time. This yields a…

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 prove several different anti-concentration inequalities for functions of independent Bernoulli-distributed random variables. First, motivated by a conjecture of Alon, Hefetz, Krivelevich and Tyomkyn, we prove some "Poisson-type"…

In this paper, we consider the minimum submodular cost allocation (MSCA) problem. The input of MSCA is $k$ non-negative submodular functions $f_1,f_2,\ldots,f_k$ on the ground set $N$ given by evaluation oracles, and the goal is to…

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…

We prove the reduction principle for asymptotics of functionals of vector random fields with weakly and strongly dependent components. These functionals can be used to construct new classes of random fields with skewed and heavy-tailed…

Adaptive sequential decision making is one of the central challenges in machine learning and artificial intelligence. In such problems, the goal is to design an interactive policy that plans for an action to take, from a finite set of $n$…

Kolmogorov's exponential inequalities are basic tools for studying the strong limit theorems such as the classical laws of the iterated logarithm for both independent and dependent random variables. This paper establishes the Kolmogorov…

Submodular function minimization is a key problem in a wide variety of applications in machine learning, economics, game theory, computer vision, and many others. The general solver has a complexity of $O(n^3 \log^2 n . E +n^4 {\log}^{O(1)}…

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…

Many transfer problems require re-using previously optimal decisions for solving new tasks, which suggests the need for learning algorithms that can modify the mechanisms for choosing certain actions independently of those for choosing…

We develop improved rearrangement algorithms to find the dependence structure that minimizes a convex function of the sum of dependent variables with given margins. We propose a new multivariate dependence measure, which can assess the…