In the original published article, there were typographical errors in mathematical formulas (Equations 58, 59, 73, and 74). The equations were derived and implemented correctly in the computer program; however, mistakes occurred during the writing of the paper. Corrections have been made to Equations 58, 59 in Section 4.2.2 EM-ALS algorithm and Equations 73, 74 in Section 4.3.2 EM-ALS for learning multi-class TN classifiers.
Equations 58, 59, 73, and 74 previously stated:
The corrected Equations appear below:
1 Derivation of corrections
Here we only show the derivation of Equation (58). The remaining three corrections can be derived in a similar manner.
First, Equation 58 is the weighted least squares solution for
where we put , , , and ⊘ stands for entry-wise division. Let us put and , the cost function is rewritten as
Note that . Optimality condition is given by
Finally, the minimizer is given in closed form as
The original article has been updated.
Statements
Publisher’s note
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Summary
Keywords
expectation-maximization (EM), majorization-minimization (MM), alternating least squares (ALS), tensor networks, tensor train, logistic regression, Pólya-Gamma (PG) augmentation
Citation
Yamauchi N, Hontani H and Yokota T (2025) Corrigendum: Expectation-maximization alternating least squares for tensor network logistic regression. Front. Appl. Math. Stat. 11:1629658. doi: 10.3389/fams.2025.1629658
Received
16 May 2025
Accepted
03 June 2025
Published
01 July 2025
Volume
11 - 2025
Edited and reviewed by
Yannan Chen, South China Normal University, China
Updates
Copyright
© 2025 Yamauchi, Hontani and Yokota.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Tatsuya Yokota t.yokota@nitech.ac.jp
Disclaimer
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.