# Hybrid Methods for Robust Tabular Data Imputation

arXiv: https://arxiv.org/abs/2609.39613 · HTML: https://mlsanity.com/paper/2609.39613/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 24 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Builds on (most cited first, 7 of 7)

- [Hyperparameters and Tuning Strategies for Random Forest](https://mlsanity.com/paper/1804.03515/) (2018)
- [What's a good imputation to predict with missing values?](https://mlsanity.com/paper/2106.00311/) (2021)
- [On the consistency of supervised learning with missing values](https://mlsanity.com/paper/1902.06931/) (2019)
- [Random Forest Missing Data Algorithms](https://mlsanity.com/paper/1701.05305/) (2017)
- [Imputation for prediction: beware of diminishing returns](https://mlsanity.com/paper/2407.19804/) (2024)
- [Gradient descent with adaptive stepsize converges (nearly) linearly under fourth-order growth](https://mlsanity.com/paper/2409.19791/) (2024)
- [Adaptive Singular Value Thresholding](https://mlsanity.com/paper/1705.00715/) (2017)

## Abstract (arXiv)

Missing data are a fundamental challenge in statistical analysis and machine learning, as the choice of imputation method substantially impacts downstream inference. In this work, we propose two hybrid imputation methods called NuclearForest and SoftForest, which combine nuclear-norm-based low-rank initialization using Singular Value Thresholding (SVT) and SoftImpute, respectively, with a non-iterative Random Forest refinement. For the SVT-based component, we further introduce an adaptive step-size rule, prove adaptive step-size bounds, and establish convergence for the corresponding zero-initialized iteration. The low-rank initialization provides a structured warm start that captures the global covariance patterns in the data, while the subsequent Random Forest step recovers residual nonlinear signals encoding local dependencies. We conduct an extensive benchmark on diverse datasets from different application domains, comparing the proposed methods with seven established imputation methods under the Missing Completely at Random (MCAR), Missing at Random (MAR), and Missing Not at Random (MNAR) mechanisms across varying missingness rates. Our results demonstrate that NuclearForest and SoftForest match or exceed the imputation fidelity of state-of-the-art iterative methods such as MissForest, while significantly reducing computational cost. In particular, they achieve speedups of approximately 5.81 times and 9.52 times over MissForest by replacing iterative cycles with a single refinement step. Our approach effectively exploits the low-rank structure of real-world tabular data and accommodates mixed-type variables, providing an efficient and robust solution for data imputation in bioinformatics, economics, and beyond.