# Optimal Transfer Learning for Missing Not-at-Random Matrix Completion

arXiv: https://arxiv.org/abs/2503.00174 · HTML: https://mlsanity.com/paper/2503.00174/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 77 references that are in the map.
- First posted on arXiv 28 Feb 2025.

## Builds on (most cited first, 30 of 31)

- [Adversarial Discriminative Domain Adaptation](https://mlsanity.com/paper/1702.05464/) (2017)
- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [What is being transferred in transfer learning?](https://mlsanity.com/paper/2008.11687/) (2020)
- [Community Detection and Stochastic Block Models](https://mlsanity.com/paper/1703.10146/) (2017)
- [On the Theory of Transfer Learning: The Importance of Task Diversity](https://mlsanity.com/paper/2006.11650/) (2020)
- [Learning with Good Feature Representations in Bandits and in RL with a Generative Model](https://mlsanity.com/paper/1911.07676/) (2019)
- [Spectral Methods for Data Science: A Statistical Perspective](https://mlsanity.com/paper/2012.08496/) (2020)
- [Covid-19: Automatic detection from X-Ray images utilizing Transfer Learning with Convolutional Neural Networks](https://mlsanity.com/paper/2003.11617/) (2020)
- [Transfer Learning for Nonparametric Classification: Minimax Rate and Adaptive Classifier](https://mlsanity.com/paper/1906.02903/) (2019)
- [Noisy Matrix Completion: Understanding Statistical Guarantees for Convex Relaxation via Nonconvex Optimization](https://mlsanity.com/paper/1902.07698/) (2019)
- [Optimally tackling covariate shift in RKHS-based nonparametric regression](https://mlsanity.com/paper/2205.02986/) (2022)
- [Active Learning for Domain Adaptation: An Energy-Based Approach](https://mlsanity.com/paper/2112.01406/) (2021)
- [Causal Matrix Completion](https://mlsanity.com/paper/2109.15154/) (2021)
- [Provable Benefits of Representational Transfer in Reinforcement Learning](https://mlsanity.com/paper/2205.14571/) (2022)
- [Robust Transfer Learning with Pretrained Language Models through Adapters](https://mlsanity.com/paper/2108.02340/) (2021)
- [Missing Not at Random in Matrix Completion: The Effectiveness of Estimating Missingness Probabilities Under a Low Nuclear Norm Assumption](https://mlsanity.com/paper/1910.12774/) (2019)
- [Transfer Learning for Nonparametric Regression: Non-asymptotic Minimax Analysis and Adaptive Procedure](https://mlsanity.com/paper/2401.12272/) (2024)
- [Matrix completion with data-dependent missingness probabilities](https://mlsanity.com/paper/2106.02290/) (2021)
- [Multi-source Learning via Completion of Block-wise Overlapping Noisy Matrices](https://mlsanity.com/paper/2105.10360/) (2021)
- [Recovering shared structure from multiple networks with unknown edge distributions](https://mlsanity.com/paper/1906.07265/) (2019)
- [A Systems Theory of Transfer Learning](https://mlsanity.com/paper/2107.01196/) (2021)
- [Matrix completion with queries](https://mlsanity.com/paper/1705.00399/) (2017)
- [Tackling Combinatorial Distribution Shift: A Matrix Completion Perspective](https://mlsanity.com/paper/2307.06457/) (2023)
- [Kernel spectral joint embeddings for high-dimensional noisy datasets using duo-landmark integral operators](https://mlsanity.com/paper/2405.12317/) (2024)
- [Best Policy Identification in Linear MDPs](https://mlsanity.com/paper/2208.05633/) (2022)
- [Representational Transfer Learning for Matrix Completion](https://mlsanity.com/paper/2412.06233/) (2024)
- [Transfer Learning for Latent Variable Network Models](https://mlsanity.com/paper/2406.03437/) (2024)
- [LEARNER: A Transfer Learning Method for Low-Rank Matrix Estimation](https://mlsanity.com/paper/2412.20605/) (2024)
- [Survey of Matrix Completion Algorithms](https://mlsanity.com/paper/2204.01532/) (2022)
- [Exploiting Observation Bias to Improve Matrix Completion](https://mlsanity.com/paper/2306.04775/) (2023)

## Built on by (most cited first, 2 of 2)

- [Transfer Learning for Matrix Completion](https://mlsanity.com/paper/2507.02248/) (2025)
- [Generalization Bounds for Semi-supervised Matrix Completion with Distributional Side Information](https://mlsanity.com/paper/2511.13049/) (2025)

## Abstract (arXiv)

We study transfer learning for matrix completion in a Missing Not-at-Random (MNAR) setting that is motivated by biological problems. The target matrix Q has entire rows and columns missing, making estimation impossible without side information. To address this, we use a noisy and incomplete source matrix P, which relates to Q via a feature shift in latent space. We consider both the active and passive sampling of rows and columns. We establish minimax lower bounds for entrywise estimation error in each setting. Our computationally efficient estimation framework achieves this lower bound for the active setting, which leverages the source data to query the most informative rows and columns of Q. This avoids the need for incoherence assumptions required for rate optimality in the passive sampling setting. We demonstrate the effectiveness of our approach through comparisons with existing algorithms on real-world biological datasets.