# Transductive Matrix Completion with Calibration for Multi-Task Learning

arXiv: https://arxiv.org/abs/2302.09834 · HTML: https://mlsanity.com/paper/2302.09834/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 26 references that are in the map.
- First posted on arXiv 20 Feb 2023.

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

- [A Max-Norm Constrained Minimization Approach to 1-Bit Matrix Completion](https://mlsanity.com/paper/1309.6013/) (2013)
- [Generalized High-Dimensional Trace Regression via Nuclear Norm Regularization](https://mlsanity.com/paper/1710.08083/) (2017)
- [Collective Matrix Completion](https://mlsanity.com/paper/1807.09010/) (2018)
- [Main effects and interactions in mixed and incomplete data frames](https://mlsanity.com/paper/1806.09734/) (2018)
- [Transduction with Matrix Completion Using Smoothed Rank Function](https://mlsanity.com/paper/1805.07561/) (2018)
- [Matrix Co-completion for Multi-label Classification with Missing Features and Labels](https://mlsanity.com/paper/1805.09156/) (2018)

## Built on by (most cited first, 1 of 1)

- [Mixed Matrix Completion in Complex Survey Sampling under Heterogeneous Missingness](https://mlsanity.com/paper/2402.03954/) (2024)

## Abstract (arXiv)

Multi-task learning has attracted much attention due to growing multi-purpose research with multiple related data sources. Moreover, transduction with matrix completion is a useful method in multi-label learning. In this paper, we propose a transductive matrix completion algorithm that incorporates a calibration constraint for the features under the multi-task learning framework. The proposed algorithm recovers the incomplete feature matrix and target matrix simultaneously. Fortunately, the calibration information improves the completion results. In particular, we provide a statistical guarantee for the proposed algorithm, and the theoretical improvement induced by calibration information is also studied. Moreover, the proposed algorithm enjoys a sub-linear convergence rate. Several synthetic data experiments are conducted, which show the proposed algorithm out-performs other existing methods, especially when the target matrix is associated with the feature matrix in a nonlinear way.