# Certain and Approximately Certain Models for Statistical Learning

arXiv: https://arxiv.org/abs/2402.17926 · HTML: https://mlsanity.com/paper/2402.17926/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 34 references that are in the map.
- First posted on arXiv 27 Feb 2024.

## Builds on (most cited first, 8 of 8)

- [OpenML: networked science in machine learning](https://mlsanity.com/paper/1407.7722/) (2014)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [What's a good imputation to predict with missing values?](https://mlsanity.com/paper/2106.00311/) (2021)
- [BoostClean: Automated Error Detection and Repair for Machine Learning](https://mlsanity.com/paper/1711.01299/) (2017)
- [Nearest Neighbor Classifiers over Incomplete Information: From Certain Answers to Certain Predictions](https://mlsanity.com/paper/2005.05117/) (2020)
- [Learning Over Dirty Data Without Cleaning](https://mlsanity.com/paper/2004.02308/) (2020)
- [Certifiable Robustness for Nearest Neighbor Classifiers](https://mlsanity.com/paper/2201.04770/) (2022)
- [Sparse Linear Regression With Missing Data](https://mlsanity.com/paper/1503.08348/) (2015)

## Built on by (most cited first, 1 of 1)

- [Learning Over Dirty Data with Minimal Repairs](https://mlsanity.com/paper/2503.13921/) (2025)

## Abstract (arXiv)

Real-world data is often incomplete and contains missing values. To train accurate models over real-world datasets, users need to spend a substantial amount of time and resources imputing and finding proper values for missing data items. In this paper, we demonstrate that it is possible to learn accurate models directly from data with missing values for certain training data and target models. We propose a unified approach for checking the necessity of data imputation to learn accurate models across various widely-used machine learning paradigms. We build efficient algorithms with theoretical guarantees to check this necessity and return accurate models in cases where imputation is unnecessary. Our extensive experiments indicate that our proposed algorithms significantly reduce the amount of time and effort needed for data imputation without imposing considerable computational overhead.