# Graph Resistance and Learning from Pairwise Comparisons

@inproceedings{Hendrickx2019GraphRA, title={Graph Resistance and Learning from Pairwise Comparisons}, author={Julien M. Hendrickx and Alexander Olshevsky and Venkatesh Saligrama}, booktitle={ICML}, year={2019} }

We consider the problem of learning the qualities of a collection of items by performing noisy comparisons among them. [...] Key Method We prove that, after a known transition period, the relevant graph-theoretic quantity is the square root of the resistance of the comparison graph. Specifically, we provide an algorithm that is minimax optimal. The algorithm has a relative error decay that scales with the square root of the graph resistance, and provide a matching lower bound (up to log factors). The… Expand

#### 5 Citations

Minimax Rate for Learning From Pairwise Comparisons

- 2019

We consider the problem of learning the qualities w1, . . . , wn of a collection of items by performing noisy comparisons among them. We assume there is a fixed “comparison graph” and every… Expand

Minimax Rate for Learning From Pairwise Comparisons in the BTL Model

- Computer Science, Mathematics
- ICML
- 2020

It is shown that the determination of the minimax rate is achieved by a simple algorithm based on weighted least squares, with weights determined from the empirical outcomes of the comparisons, which can be implemented in nearly linear time in the total number of comparisons. Expand

Ranking a Set of Objects: A Graph Based Least-Square Approach

- Computer Science
- IEEE Transactions on Network Science and Engineering
- 2021

A class of non-adaptive ranking algorithms that rely on a least-squares optimization criterion for the estimation of qualities are proposed and shown to be asymptotically optimal. Expand

Rank Aggregation from Pairwise Comparisons in the Presence of Adversarial Corruptions

- Computer Science
- ICML
- 2020

This paper considers a setting where pairwise comparisons are initially generated according to a BTL model, but a fraction of these comparisons are corrupted adversarially prior to being reported to us, and provides a novel algorithm that provably filters out the adversarial corruption from data under reasonable conditions on data generation and corruption. Expand

The Performance of the MLE in the Bradley-Terry-Luce Model in $\ell_{\infty}$-Loss and under General Graph Topologies

- Mathematics
- 2021

The Bradley-Terry-Luce (BTL) model is a popular statistical approach for estimating the global ranking of a collection of items of interest using pairwise comparisons. To ensure accurate ranking, it… Expand

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