Active Seriation: Efficient Ordering Recovery with Statistical Guarantees

2026-03-16

AI Summary

This work addresses the problem of recovering an unknown ranking of items from noisy observations corresponding to partial entries of an underlying permutation-Robinson matrix. To this end, the authors propose an active seriation method that adaptively queries pairwise similarities to efficiently reconstruct the latent order of $n$ items, operating effectively under both no-prior and partial-prior settings. The approach provides, for the first time within an active ranking framework, theoretical guarantees for correct recovery with high probability. Under a uniform separation condition, the method simultaneously achieves optimal sample complexity and minimax-optimal error probability, thereby attaining theoretically optimal performance.

Technology Category

• Machine Learning: Learning Preferences or Rankings
• Planning, Routing, and Scheduling: Activity and Plan Recognition
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Active seriation aims at recovering an unknown ordering of $n$ items by adaptively querying pairwise similarities. The observations are noisy measurements of entries of an underlying $n$ x $n$ permuted Robinson matrix, whose permutation encodes the latent ordering. The framework allows the algorithm to start with partial information on the latent ordering, including seriation from scratch as a special case. We propose an active seriation algorithm that provably recovers the latent ordering with high probability. Under a uniform separation condition on the similarity matrix, optimal performance guarantees are established, both in terms of the probability of error and the number of observations required for successful recovery.

Problem

• active seriation
• ordering recovery
• Robinson matrix
• noisy observations
• latent ordering

Innovation

• Active seriation
• Robinson matrix
• adaptive querying
• statistical guarantees
• ordering recovery