Active Seriation: Efficient Ordering Recovery with Statistical Guarantees

TL;DR

This paper introduces an active seriation method that adaptively queries pairwise similarities to efficiently recover an unknown item ordering with statistical guarantees, even from partial information.

Contribution

It proposes a novel active seriation algorithm with provable guarantees for accurate ordering recovery under a separation condition.

Findings

Algorithm recovers the true ordering with high probability.

Optimal bounds on the number of observations needed.

Guarantees hold even with partial initial information.

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.