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Ranking with submodular functions on a budget.

Guangyi Zhang1, Nikolaj Tatti2, Aristides Gionis1

  • 1KTH Royal Institute of Technology, Stockholm, Sweden.

Data Mining and Knowledge Discovery
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Summary
This summary is machine-generated.

This study introduces max-submodular ranking for item valuation and budget constraints. Novel algorithms provide approximation guarantees, outperforming existing methods in empirical evaluations for machine learning applications.

Keywords:
Approximation algorithmsDynamic programmingRankingSubmodular maximization

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Area of Science:

  • Machine Learning
  • Optimization Theory
  • Algorithmic Game Theory

Background:

  • Submodular maximization is crucial for machine learning tasks like viral marketing and sensor placement.
  • Existing research primarily focuses on item selection, neglecting ranking formulations.
  • Real-world applications often require ranking items rather than just selecting them.

Purpose of the Study:

  • Introduce a novel formulation for max-submodular ranking (MSR) with budget constraints.
  • Address the challenge of ranking items based on submodular valuations under budget limitations.
  • Develop practical algorithms with theoretical guarantees for the MSR problem.

Main Methods:

  • Formulation of the max-submodular ranking problem.
  • Development of algorithms for cardinality and knapsack-type budget constraints.
  • Empirical evaluation comparing proposed algorithms against baseline methods.

Main Results:

  • Proposed algorithms achieve approximation guarantees for the MSR problem.
  • Empirical results demonstrate superior performance compared to strong baselines.
  • The study validates the effectiveness of the novel ranking formulation.

Conclusions:

  • The proposed max-submodular ranking framework offers a practical solution for ranking problems with submodular valuations.
  • The developed algorithms are efficient and provide theoretical guarantees.
  • This work extends the applicability of submodular maximization to ranking scenarios in machine learning.