Armenian Journal of Mathematics, 15(5)
2023; 1–9
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Optimality of the Least Sum of Logarithms in the Problem of Matching Map Recovery in the Presence of Noise and Outliers

Tigran Galstyan*, Arshak Minasyan

Received: 2024-12-04 · Published: 2023-03-30

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CC BY 4.0 This work is licensed under a Creative Commons Attribution 4.0 International License.
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Original title
Optimality of the Least Sum of Logarithms in the Problem of Matching Map Recovery in the Presence of Noise and Outliers
Authors
Tigran Galstyan, Arshak Minasyan
Source journal
Armenian Journal of Mathematics, 15(5)
Published
2023-03-30
Licence
Creative Commons Attribution 4.0 International
Original
https://doi.org/10.52737/18291163-2023.15.5-1-9

Abstract

We consider the problem of estimating the matching map between two sets of feature-vectors observed in a noisy environment and contaminated by outliers. It was already known in the literature that in the outlier-free setting, the least sum of squares (LSS) and the least sum of logarithms (LSL) are both minimax-rate-optimal. It has been recently proved that the optimality properties of the LSS continue to hold in the case the data sets contain outliers. In this work, we show that the same is true for the LSL as well. Therefore, LSL has the same desirable properties as the LSS, and, in addition, it is minimax-rate-optimal in the outlier-free setting with heteroscedastic noise.
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