MUSS: Multilevel Subset Selection for Relevance and Diversity

arXiv:2503.11126v4 Announce Type: replace Abstract: The problem of relevant and diverse subset selection has a wide range of applications, including recommender systems and retrieval-augmented generation (RAG). For example, in recommender systems, one is interested in selecting relevant items, while providing a diversified recommendation. Constrained subset selection problem is NP-hard, and popular approaches such as Maximum Marginal Relevance (MMR) are based on greedy selection. Many real-world applications involve large data, but the original MMR work did not consider distributed selection. This limitation was later addressed by a method called DGDS which allows for a distributed setting using random data partitioning. Here, we exploit structure in the data to further improve both scalability and performance on the target application. We propose MUSS, a novel method that uses a multilevel approach to relevant and diverse selection. In a recommender system application, our method can not only improve the performance up to $4$ percent points in precision, but is also $20$ to $80$ times faster. Our method is also capable of outperforming baselines on RAG-based question answering accuracy. We present a novel theoretical approach for analyzing this type of problems, and show that our method achieves a constant factor approximation of the optimal objective. Moreover, our analysis also resulted in a $\times 2$ tighter bound for DGDS compared to previously known bound. Our code is publicly available at https://github.com/amazon-science/muss.

Abstract:The problem of relevant and diverse subset selection has a wide range of applications, including recommender systems and retrieval-augmented generation (RAG). For example, in recommender systems, one is interested in selecting relevant items, while providing a diversified recommendation. Constrained subset selection problem is NP-hard, and popular approaches such as Maximum Marginal Relevance (MMR) are based on greedy selection. Many real-world applications involve large data, but the original MMR work did not consider distributed selection. This limitation was later addressed by a method called DGDS which allows for a distributed setting using random data partitioning. Here, we exploit structure in the data to further improve both scalability and performance on the target application. We propose MUSS, a novel method that uses a multilevel approach to relevant and diverse selection. In a recommender system application, our method can not only improve the performance up to $4$ percent points in precision, but is also $20$ to $80$ times faster. Our method is also capable of outperforming baselines on RAG-based question answering accuracy. We present a novel theoretical approach for analyzing this type of problems, and show that our method achieves a constant factor approximation of the optimal objective. Moreover, our analysis also resulted in a $\times 2$ tighter bound for DGDS compared to previously known bound. Our code is publicly available at this https URL.

Machine Learning (cs.LG)

arXiv:2503.11126 [cs.LG]

(or arXiv:2503.11126v4 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2503.11126 Focus to learn more arXiv-issued DOI via DataCite

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MUSS: Multilevel Subset Selection for Relevance and Diversity

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