# Efficient and Accurate Top-K Recovery from Choice Data

arXiv: https://arxiv.org/abs/2206.11995 · HTML: https://mlsanity.com/paper/2206.11995/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 34 references that are in the map.
- First posted on arXiv 23 Jun 2022.

## Builds on (most cited first, 6 of 6)

- [Simple, Robust and Optimal Ranking from Pairwise Comparisons](https://mlsanity.com/paper/1512.08949/) (2015)
- [Spectral Method and Regularized MLE Are Both Optimal for Top-K Ranking](https://mlsanity.com/paper/1707.09971/) (2017)
- [Spectral MLE: Top-K Rank Aggregation from Pairwise Comparisons](https://mlsanity.com/paper/1504.07218/) (2015)
- [Learning Mixtures of Plackett-Luce Models](https://mlsanity.com/paper/1603.07323/) (2016)
- [Learning Mixtures of Plackett-Luce Models from Structured Partial Orders](https://mlsanity.com/paper/1910.11721/) (2019)
- [On Top-k Selection from m-wise Partial Rankings via Borda Counting](https://mlsanity.com/paper/2204.05742/) (2022)

## Abstract (arXiv)

The intersection of learning to rank and choice modeling is an active area of research with applications in e-commerce, information retrieval and the social sciences. In some applications such as recommendation systems, the statistician is primarily interested in recovering the set of the top ranked items from a large pool of items as efficiently as possible using passively collected discrete choice data, i.e., the user picks one item from a set of multiple items. Motivated by this practical consideration, we propose the choice-based Borda count algorithm as a fast and accurate ranking algorithm for top K-recovery i.e., correctly identifying all of the top K items. We show that the choice-based Borda count algorithm has optimal sample complexity for top-K recovery under a broad class of random utility models. We prove that in the limit, the choice-based Borda count algorithm produces the same top-K estimate as the commonly used Maximum Likelihood Estimate method but the former's speed and simplicity brings considerable advantages in practice. Experiments on both synthetic and real datasets show that the counting algorithm is competitive with commonly used ranking algorithms in terms of accuracy while being several orders of magnitude faster.