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**publisher and metadata sources**).We consider the budget allocation problem over bipartite influence model proposed by Alon et al. (Alon et al., 2012). This problem can be viewed as the well-known influence maximization problem with… Continue Reading

We consider a generalization of the submodular cover problem based on the concept of diminishing return property on the integer lattice. We are motivated by real scenarios in machine learning that… Continue Reading

The problem of maximizing non-negative monotone submodular functions under a certain constraint has been intensively studied in the last decade. In this paper, we address the problem for functions… Continue Reading

We consider non-monotone DR-submodular function maximization, where DR-submodularity (diminishing return submodularity) is an extension of submodularity for functions over the integer lattice based… Continue Reading

For an undirected/directed hypergraph $G=(V,E)$, its Laplacian $L_G\colon\mathbb{R}^V\to \mathbb{R}^V$ is defined such that its ``quadratic form'' $\boldsymbol{x}^\top L_G(\boldsymbol{x})$ captures… Continue Reading

For a given matrix subspace, how can we find a basis that consists of low-rank matrices? This is a generalization of the sparse vector problem. It turns out that when the subspace is spanned by… Continue Reading

While several feature scoring methods are proposed to explain the output of complex machine learning models, most of them lack formal mathematical definitions. In this study, we propose a novel… Continue Reading

The problem of maximizing non-negative monotone submodular functions under a certain constraint has been intensively studied in the last decade. In this paper, we address the problem for functions… Continue Reading

The problem of maximizing non-negative monotone submodular functions under a certain constraint has been intensively studied in the last decade. In this paper, we address the problem for functions… Continue Reading

As is well known, the smallest possible ratio between the spectral norm and the Frobenius norm of an $m \times n$ matrix with $m \le n$ is $1/\sqrt{m}$ and is (up to scalar scaling) attained only by… Continue Reading