# Active Feature Acquisition with Supervised Matrix Completion

arXiv: https://arxiv.org/abs/1802.05380 · HTML: https://mlsanity.com/paper/1802.05380/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Feb 2018.

## Built on by (most cited first, 12 of 12)

- [Missing Data Imputation and Acquisition with Deep Hierarchical Models and Hamiltonian Monte Carlo](https://mlsanity.com/paper/2202.04599/) (2022)
- [A Probabilistic Hard Attention Model For Sequentially Observed Scenes](https://mlsanity.com/paper/2111.07534/) (2021)
- [Efficient Online Estimation of Causal Effects by Deciding What to Observe](https://mlsanity.com/paper/2108.09265/) (2021)
- [Learning to Limit Data Collection via Scaling Laws: A Computational Interpretation for the Legal Principle of Data Minimization](https://mlsanity.com/paper/2107.08096/) (2021)
- [Evaluation of Active Feature Acquisition Methods for Time-varying Feature Settings](https://mlsanity.com/paper/2312.01530/) (2023)
- [Generator Assisted Mixture of Experts For Feature Acquisition in Batch](https://mlsanity.com/paper/2312.12574/) (2023)
- [Dynamic Feature Selection from Variable Feature Sets Using Features of Features](https://mlsanity.com/paper/2503.09181/) (2025)
- [Feature Acquisition using Monte Carlo Tree Search](https://mlsanity.com/paper/2212.11360/) (2022)
- [Cost-optimal Sequential Testing via Doubly Robust Q-learning](https://mlsanity.com/paper/2604.11165/) (2026)
- [Order-Agnostic Autoregressive Modelling with Missing Data](https://mlsanity.com/paper/2605.06355/) (2026)
- [Active Reference Acquisition in Few-Shot Font Generation](https://mlsanity.com/paper/2606.16502/) (2026)
- [Measure Less, Know More: Self-Supervised Test-Time Feature Acquisition](https://mlsanity.com/paper/2610.03454/) (2026)

## Abstract (arXiv)

Feature missing is a serious problem in many applications, which may lead to low quality of training data and further significantly degrade the learning performance. While feature acquisition usually involves special devices or complex process, it is expensive to acquire all feature values for the whole dataset. On the other hand, features may be correlated with each other, and some values may be recovered from the others. It is thus important to decide which features are most informative for recovering the other features as well as improving the learning performance. In this paper, we try to train an effective classification model with least acquisition cost by jointly performing active feature querying and supervised matrix completion. When completing the feature matrix, a novel target function is proposed to simultaneously minimize the reconstruction error on observed entries and the supervised loss on training data. When querying the feature value, the most uncertain entry is actively selected based on the variance of previous iterations. In addition, a bi-objective optimization method is presented for cost-aware active selection when features bear different acquisition costs. The effectiveness of the proposed approach is well validated by both theoretical analysis and experimental study.