# Closing the loop in learning with missing data

arXiv: https://arxiv.org/abs/2608.09030 · HTML: https://mlsanity.com/paper/2608.09030/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 31 references that are in the map.
- First posted on arXiv 10 Aug 2026.

## Builds on (most cited first, 9 of 9)

- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Data-driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations](https://mlsanity.com/paper/1505.05116/) (2015)
- [Online Learning with Feedback Graphs: Beyond Bandits](https://mlsanity.com/paper/1502.07617/) (2015)
- [ReMasker: Imputing Tabular Data with Masked Autoencoding](https://mlsanity.com/paper/2309.13793/) (2023)
- [Distributionally Robust Optimization with Probabilistic Group](https://mlsanity.com/paper/2303.05809/) (2023)
- [Multiclass Online Learnability under Bandit Feedback](https://mlsanity.com/paper/2308.04620/) (2023)
- [Partial Feedback Online Learning](https://mlsanity.com/paper/2601.21462/) (2026)

## Abstract (arXiv)

What should a machine learning model learn when data is missing during training? We look at the learning process from a dynamical systems perspective, cast data missingness as a structured loss of actuation that limits controllability of the parameter error dynamics, and ultimately derive adaptation mechanisms with Lyapunov stability characteristics that throttle model updates in ways that preserve learning coherence under partial, intermittent observability. Under recurrent excitation, our analysis provides ISS-type residual-to-state bounds with respect to a bounded closed-loop mismatch between the loss residual and the preconditioned update geometry. We evaluate the efficacy of our directional observability-aware adaptive learning approach on multimodal contexts, reinforcing its premise in promoting learning coherence and stability even in pathologically sparse domains and problems.