# Learning Individual Models for Imputation (Technical Report)

arXiv: https://arxiv.org/abs/2004.03436 · HTML: https://mlsanity.com/paper/2004.03436/

## Key facts

- Cited by 7 papers in the map (data through 7 Oct 2026).
- First posted on arXiv 7 Apr 2020.

## Built on by (most cited first, 7 of 7)

- [On the Relation between Prediction and Imputation Accuracy under Missing Covariates](https://mlsanity.com/paper/2112.05248/) (2021)
- [Differentiable and Scalable Generative Adversarial Models for Data Imputation](https://mlsanity.com/paper/2201.03202/) (2022)
- [Multi-Variate Time Series Forecasting on Variable Subsets](https://mlsanity.com/paper/2206.12626/) (2022)
- [Multi-scale Temporal Fusion Transformer for Incomplete Vehicle Trajectory Prediction](https://mlsanity.com/paper/2409.00904/) (2024)
- [Towards Practical Benchmarking of Data Cleaning Techniques: On Generating Authentic Errors via Large Language Models](https://mlsanity.com/paper/2507.10934/) (2025)
- [SEGAN: semi-supervised learning approach for missing data imputation](https://mlsanity.com/paper/2405.13089/) (2024)
- [GIG: Graph Data Imputation With Graph Differential Dependencies](https://mlsanity.com/paper/2410.15747/) (2024)

## Abstract (arXiv)

Missing numerical values are prevalent, e.g., owing to unreliable sensor reading, collection and transmission among heterogeneous sources. Unlike categorized data imputation over a limited domain, the numerical values suffer from two issues: (1) sparsity problem, the incomplete tuple may not have sufficient complete neighbors sharing the same/similar values for imputation, owing to the (almost) infinite domain; (2) heterogeneity problem, different tuples may not fit the same (regression) model. In this study, enlightened by the conditional dependencies that hold conditionally over certain tuples rather than the whole relation, we propose to learn a regression model individually for each complete tuple together with its neighbors. Our IIM, Imputation via Individual Models, thus no longer relies on sharing similar values among the k complete neighbors for imputation, but utilizes their regression results by the aforesaid learned individual (not necessary the same) models. Remarkably, we show that some existing methods are indeed special cases of our IIM, under the extreme settings of the number l of learning neighbors considered in individual learning. In this sense, a proper number l of neighbors is essential to learn the individual models (avoid over-fitting or under-fitting). We propose to adaptively learn individual models over various number l of neighbors for different complete tuples. By devising efficient incremental computation, the time complexity of learning a model reduces from linear to constant. Experiments on real data demonstrate that our IIM with adaptive learning achieves higher imputation accuracy than the existing approaches.