# Spherical Regression under Mismatch Corruption with Application to Automated Knowledge Translation

arXiv: https://arxiv.org/abs/1810.05679 · HTML: https://mlsanity.com/paper/1810.05679/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Oct 2018.

## Built on by (most cited first, 7 of 7)

- [Multi-source Learning via Completion of Block-wise Overlapping Noisy Matrices](https://mlsanity.com/paper/2105.10360/) (2021)
- [Permuted and Unlinked Monotone Regression in ℝd: an approach based on mixture modeling and optimal transport](https://mlsanity.com/paper/2201.03528/) (2022)
- [Linear regression with partially mismatched data: local search with theoretical guarantees](https://mlsanity.com/paper/2106.02175/) (2021)
- [Shuffled linear regression through graduated convex relaxation](https://mlsanity.com/paper/2209.15608/) (2022)
- [Regularization for Shuffled Data Problems via Exponential Family Priors on the Permutation Group](https://mlsanity.com/paper/2111.01767/) (2021)
- [Knowledge-Embedded Latent Projection for Robust Representation Learning](https://mlsanity.com/paper/2602.16709/) (2026)
- [Alternating minimization algorithm with initialization analysis for r-local and k-sparse unlabeled sensing](https://mlsanity.com/paper/2211.07621/) (2022)

## Abstract (arXiv)

Motivated by a series of applications in data integration, language translation, bioinformatics, and computer vision, we consider spherical regression with two sets of unit-length vectors when the data are corrupted by a small fraction of mismatch in the response-predictor pairs. We propose a three-step algorithm in which we initialize the parameters by solving an orthogonal Procrustes problem to estimate a translation matrix mathbbW ignoring the mismatch. We then estimate a mapping matrix aiming to correct the mismatch using hard-thresholding to induce sparsity, while incorporating potential group information. We eventually obtain a refined estimate for mathbbW by removing the estimated mismatched pairs. We derive the error bound for the initial estimate of mathbbW in both fixed and high-dimensional setting. We demonstrate that the refined estimate of mathbbW achieves an error rate that is as good as if no mismatch is present. We show that our mapping recovery method not only correctly distinguishes one-to-one and one-to-many correspondences, but also consistently identifies the matched pairs and estimates the weight vector for combined correspondence. We examine the finite sample performance of the proposed method via extensive simulation studies, and with application to the unsupervised translation of medical codes using electronic health records data.