# Active Feature Acquisition With Incomplete Training Data

arXiv: https://arxiv.org/abs/2609.32325 · HTML: https://mlsanity.com/paper/2609.32325/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 29 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Builds on (most cited first, 15 of 15)

- [EDDI: Efficient Dynamic Discovery of High-Value Information with Partial VAE](https://mlsanity.com/paper/1809.11142/) (2018)
- [Partially Observable Markov Decision Processes in Robotics: A Survey](https://mlsanity.com/paper/2209.10342/) (2022)
- [Learning to Maximize Mutual Information for Dynamic Feature Selection](https://mlsanity.com/paper/2301.00557/) (2023)
- [Active Feature Acquisition with Generative Surrogate Models](https://mlsanity.com/paper/2010.02433/) (2020)
- [Classification with Costly Features using Deep Reinforcement Learning](https://mlsanity.com/paper/1711.07364/) (2017)
- [Classification with Costly Features as a Sequential Decision-Making Problem](https://mlsanity.com/paper/1909.02564/) (2019)
- [Estimating Conditional Mutual Information for Dynamic Feature Selection](https://mlsanity.com/paper/2306.03301/) (2023)
- [Opportunistic Learning: Budgeted Cost-Sensitive Learning from Data Streams](https://mlsanity.com/paper/1901.00243/) (2019)
- [Acquisition Conditioned Oracle for Nongreedy Active Feature Acquisition](https://mlsanity.com/paper/2302.13960/) (2023)
- [A Survey on Active Feature Acquisition Strategies](https://mlsanity.com/paper/2502.11067/) (2025)
- [Stochastic Encodings for Active Feature Acquisition](https://mlsanity.com/paper/2508.01957/) (2025)
- [AFABench: A Generic Framework for Benchmarking Active Feature Acquisition](https://mlsanity.com/paper/2508.14734/) (2025)
- [Learning-To-Measure: In-Context Active Feature Acquisition](https://mlsanity.com/paper/2510.12624/) (2025)
- [Evaluation of Active Feature Acquisition Methods for Static Feature Settings](https://mlsanity.com/paper/2312.03619/) (2023)
- [Non-Myopic Active Feature Acquisition via Pathwise Policy Gradients](https://mlsanity.com/paper/2605.05511/) (2026)

## Abstract (arXiv)

In many prediction tasks, acquiring all features can be a prohibitively expensive or outright impossible task. Further, in many cases a static subset of features may not be enough to solve the problem sufficiently across various instances. Active Feature Acquisition (AFA) addresses these problems by formalizing the trade-off between feature cost and predictive performance during sequential feature selection. However, prior AFA work largely assumes access to complete training data, an assumption that is often violated in practice. Here we study AFA with Incomplete Training Data (AFA-ITD), showing that under missing completely at random (MCAR) data, one-step acquisition values remain unchanged, whereas multi-step values can decrease. We analyze three approaches to learning from incomplete data: aliasing, filtering, and generative restoration. We show that filtering can require a number of training instances scaling exponentially with the dimension, whereas generative restoration scales exponentially with the acquisition budget. We empirically test our theory on a controlled experiment and across common AFA datasets and find that missingness mainly damages methods that exploit multi-step acquisitions and that generative restoration is able to recover lost performance in many experiments. Code is available at https://github.com/Linusaronsson/AFA-Benchmark/tree/missing-data.