submodular function
Phrase Table Pruning via Submodular Function Maximization
... Phrase table pruning is the act of re- moving phrase pairs from a phrase table to make it smaller, ideally removing the least useful phrases first. We propose a phrase table pruning method that formu- lates the task as a ...
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Towards Abstractive Multi Document Summarization Using Submodular Function Based Framework, Sentence Compression and Merging
... We consider the relevance of the summary as the summation of the importance scores of the sentences in it. First, we utilize the Markov ran- dom walk model used by (Hong and Nenkova, 2014; Mihalcea and Tarau, 2004) to ...
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Provable Fast Greedy Compressive Summarization with Any Monotone Submodular Function
... be submodular if g(A ∪ B) + g(A ∩ B) ≤ g(A) + g(B) holds for any A, B ⊆ V ...Set function g is mono- tone if g(A) ≤ g(B) for any A ⊆ ...monotone submodular func- tions such that g( ∅ ) = ...coverage ...
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Active-set Methods for Submodular Minimization Problems
... ordered partition of the underlying ground set V = { 1, . . . , n } . The main insight of this paper is that given the main polytope associated with a submodular function (namely the base polytope described ...
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Robust Submodular Observation Selection
... A previous version of this paper appeared in (Krause et al., 2007a). The present version is signifi- cantly extended, providing new theoretical analyses (described in Section 7, Section 9), new exam- ples demonstrating ...
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Submodular stochastic probing on matroids
... E [f (A)] under this distribution, while the value of F (y) is the value of E [f(A)] under the particular distribution that places each element i in A independently. However, the following allows us to relate the value ...
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Greedy Maximization of Functions with Bounded Curvature under Partition Matroid Constraints
... a submodular function given k as a cardinality constraint is equivalent to finding a set U , with | U | ≤ k, that maximizes f (U ...sider submodular maximization under partition matroid con- ...
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Submodular Optimization based Diverse Paraphrasing and its Effectiveness in Data Augmentation
... monotone submodular func- tion maximization (Fujishige, 2005; Krause and Golovin; Bach et ...the submodular objective offers better flexibility in terms of controlling diversity as well as ...monotone ...
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A Class of Submodular Functions for Document Summarization
... to submodular function optimization, but also the widely used ROUGE evaluation is closely related to submodular ...ing submodular optimization problem can be solved efficiently and ...
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Subtree Extractive Summarization via Submodular Maximization
... nondecreasing submodular function maxi- mization with a cost ...cost function to represent the cost, which indicates the length of word tokens in the ...
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Submodular Optimization over Streams with Inhomogeneous Decays
... Constrained Submodular Function Maxi- mization. Submodular optimization lies at the core of many data mining and machine learning ...years, submodular optimization has been applied to a wide ...
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Multi document Summarization via Budgeted Maximization of Submodular Functions
... underlying function is submod- ular. It has been shown that any submodular func- tion can be minimized in polynomial time (Schri- jver, 2000)(Iwata et ...monotone submodular function under a ...
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Convex Analysis for Minimizing and Learning Submodular Set Functions
... of submodular functions: on one hand there are very basic or specialized functions that admit simple and practical minimization algorithms, but are fairly limited in what they can describe, and, on the other, ...
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Word Alignment via Submodular Maximization over Matroids
... Vondr´ak (2008) shows a continuous greedy al- gorithm followed by pipage rounding with approx- imation factor 1 − 1/e (≈ 0.63) for maximizing a monotone submodular function subject to a ma- troid ...
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Subspace Selection via DR-Submodular Maximization on Lattices
... In this paper, we formulated the subspace selection prob- lem as optimization problem over lattices. By introducing new “DR-submodularities” on lattices, named directional DR-submodularities, we successfully identified ...
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Summarization of Multi Document Topic Hierarchies using Submodular Mixtures
... a submodular optimization problem on a topic hierarchy using the documents as ...a submodular function that expresses coherence between the chosen topics and this ...
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Monotone submodular maximization over a matroid via non oblivious local search
... monotone submodular optimization over a matroid ...objective function, but on a related auxiliary potential function, which is also monotone and ...potential function gives more weight to ...
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Hardness of submodular cost allocation : lattice matching and a simplex coloring conjecture
... Facility Location problem considered by Svitkina and Tardos [24] who gave an O(log |V |)- approximation and a matching hardness via a reduction from Set Cover. Following previous work, Chekuri and Ene [3, 2] considered ...
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Balancing Relevance and Diversity in Online Bipartite Matching via Submodularity
... Online Submodular Bipar- tite Matching (OSBM) problem, where the goal is to maxi- mize a submodular function f over the set of matched ...coverage function) and relevance (e.g., the ...
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New algorithms for distributed submodular maximization
... a submodular function f , and (possibly) a set of constraints, we aim to find a feasible set S maximizing f ...on submodular maximization, the community has a good understanding of the problem under ...
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