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We study the problem of maximizing a non-monotone submodular function under multiple knapsack constraints. We propose a simple discrete greedy algorithm to approach this problem, and prove that it yields strong approximation guarantees for…

Graph convolutional networks are a popular class of deep neural network algorithms which have shown success in a number of relational learning tasks. Despite their success, graph convolutional networks exhibit a number of peculiar features,…

Algorithmic fairness has aroused considerable interests in data mining and machine learning communities recently. So far the existing research has been mostly focusing on the development of quantitative metrics to measure algorithm…

In this paper, we generalize the minimum flow decomposition problem (MFD) to incorporate uncertain edge capacities and tackle it from the perspective of robust optimization. In the classical flow decomposition problem, a network flow is…

In this paper we take a problem of unsupervised nodes clustering on graphs and show how recent advances in attention models can be applied successfully in a "hard" regime of the problem. We propose an unsupervised algorithm that encodes…

This paper proposes a novel algorithm for the problem of structural image segmentation through an interactive model-based approach. Interaction is expressed in the model creation, which is done according to user traces drawn over a given…

Inspired by the works in linkage theory of modules, we define the concept of linkage of sheaves of modules as a generalization of linkage of modules. Thus, we expressed it in geometry algebraic language. We show that the linkedness of…

One-dimensional signal decomposition is a well-established and widely used technique across various scientific fields. It serves as a highly valuable pre-processing step for data analysis. While traditional decomposition techniques often…

In the realm of generative models for graphs, extensive research has been conducted. However, most existing methods struggle with large graphs due to the complexity of representing the entire joint distribution across all node pairs and…

The modular decomposition of a graph is a canonical representation of its modules. Algorithms for computing the modular decomposition of directed and undirected graphs differ significantly, with the undirected case being simpler, and…

The principle underlying this paper is the basic observation that the problem of simultaneously solving a large class of composite monotone inclusions and their duals can be reduced to that of finding a zero of the sum of a maximally…

Clustering a graph means identifying internally dense subgraphs which are only sparsely interconnected. Formalizations of this notion lead to measures that quantify the quality of a clustering and to algorithms that actually find…

The coupling of some types of oscillators requires the mediation of a physical link between them, rendering the distance between oscillators a critical factor to achieve synchronization. In this paper we propose and explore a greedy…

Flexible grid topology has become a key enabler of flexibility in modern power grids, particularly for congestion management. Studying the effects of combinatorial topological changes is therefore of significant interest, though it remains…

Convolutional neural networks utilize a hierarchy of neural network layers. The statistical aspects of information concentration in successive layers can bring an insight into the feature abstraction process. We analyze the saliency maps of…

Time series forecasting represents a significant and challenging task across various fields. Recently, methods based on mode decomposition have dominated the forecasting of complex time series because of the advantages of capturing local…

Identifying breakpoints in piecewise regression is critical in enhancing the reliability and interpretability of data fitting. In this paper, we propose novel algorithms based on the greedy algorithm to accurately and efficiently identify…

Kernel based methods provide a way to reconstruct potentially high-dimensional functions from meshfree samples, i.e., sampling points and corresponding target values. A crucial ingredient for this to be successful is the distribution of the…

We study the problem of scheduling sensors in a resource-constrained linear dynamical system, where the objective is to select a small subset of sensors from a large network to perform the state estimation task. We formulate this problem as…

Submodular functions -- functions exhibiting diminishing returns -- are central to machine learning. When the objective is monotone and non-negative, the greedy algorithm achieves a tight $63\%$ approximation. But many practical objectives…