How to Design Robust Algorithms using Noisy Comparison Oracle

TL;DR

This paper develops robust algorithms for clustering and neighbor search using noisy comparison oracles, providing theoretical guarantees and empirical validation under adversarial and probabilistic noise models.

Contribution

It introduces new algorithms for clustering and neighbor search that operate reliably with noisy comparison queries, along with theoretical analysis and empirical evaluation.

Findings

Algorithms achieve strong approximation guarantees.

Methods are effective under both adversarial and probabilistic noise.

Empirical results validate theoretical claims on real datasets.

Abstract

Metric based comparison operations such as finding maximum, nearest and farthest neighbor are fundamental to studying various clustering techniques such as $k$-center clustering and agglomerative hierarchical clustering. These techniques crucially rely on accurate estimation of pairwise distance between records. However, computing exact features of the records, and their pairwise distances is often challenging, and sometimes not possible. We circumvent this challenge by leveraging weak supervision in the form of a comparison oracle that compares the relative distance between the queried points such as `Is point u closer to v or w closer to x?'. However, it is possible that some queries are easier to answer than others using a comparison oracle. We capture this by introducing two different noise models called adversarial and probabilistic noise. In this paper, we study various problems that include finding maximum, nearest/farthest neighbor search under these noise models. Building upon the techniques we develop for these comparison operations, we give robust algorithms for k-center clustering and agglomerative hierarchical clustering. We prove that our algorithms achieve good approximation guarantees with a high probability and analyze their query complexity. We evaluate the effectiveness and efficiency of our techniques empirically on various real-world datasets.