# Why Not to Use Zero Imputation? Correcting Sparsity Bias in Training Neural Networks

arXiv: https://arxiv.org/abs/1906.00150 · HTML: https://mlsanity.com/paper/1906.00150/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jun 2019.

## Built on by (most cited first, 16 of 16)

- [Uncovering the Missing Pattern: Unified Framework Towards Trajectory Imputation and Prediction](https://mlsanity.com/paper/2303.16005/) (2023)
- [FedNI: Federated Graph Learning with Network Inpainting for Population-Based Disease Prediction](https://mlsanity.com/paper/2112.10166/) (2021)
- [Tabular Transfer Learning via Prompting LLMs](https://mlsanity.com/paper/2408.11063/) (2024)
- [Don't Pay Attention to the Noise: Learning Self-supervised Representations of Light Curves with a Denoising Time Series Transformer](https://mlsanity.com/paper/2207.02777/) (2022)
- [How Deep is your Guess? A Fresh Perspective on Deep Learning for Medical Time-Series Imputation](https://mlsanity.com/paper/2407.08442/) (2024)
- [Network-wide Freeway Traffic Estimation Using Sparse Sensor Data: A Dirichlet Graph Auto-Encoder Approach](https://mlsanity.com/paper/2503.15845/) (2025)
- [Collaborative Reflection-Augmented Autoencoder Network for Recommender Systems](https://mlsanity.com/paper/2201.03158/) (2022)
- [Survival Analysis for Idiopathic Pulmonary Fibrosis using CT Images and Incomplete Clinical Data](https://mlsanity.com/paper/2203.11391/) (2022)
- [MSTF: Multiscale Transformer for Incomplete Trajectory Prediction](https://mlsanity.com/paper/2407.05671/) (2024)
- [MAIN: Multihead-Attention Imputation Networks](https://mlsanity.com/paper/2102.05428/) (2021)
- [Self-Normalizing Foundation Model for Enhanced Multi-Omics Data Analysis in Oncology](https://mlsanity.com/paper/2405.08226/) (2024)
- [Cloned Identity Detection in Social-Sensor Clouds based on Incomplete Profiles](https://mlsanity.com/paper/2411.01329/) (2024)
- [AugMask: Training Diffusion Models on Incomplete Tabular Data via Stochastic Augmentation and Masking](https://mlsanity.com/paper/2606.03347/) (2026)
- [Temporal Dynamic Embedding for Irregularly Sampled Time Series](https://mlsanity.com/paper/2504.05768/) (2025)
- [FGSSNet: Feature-Guided Semantic Segmentation of Real World Floorplans](https://mlsanity.com/paper/2507.10343/) (2025)
- [An Interdisciplinary and Cross-Task Review on Missing Data Imputation](https://mlsanity.com/paper/2511.01196/) (2025)

## Abstract (arXiv)

Handling missing data is one of the most fundamental problems in machine learning. Among many approaches, the simplest and most intuitive way is zero imputation, which treats the value of a missing entry simply as zero. However, many studies have experimentally confirmed that zero imputation results in suboptimal performances in training neural networks. Yet, none of the existing work has explained what brings such performance degradations. In this paper, we introduce the variable sparsity problem (VSP), which describes a phenomenon where the output of a predictive model largely varies with respect to the rate of missingness in the given input, and show that it adversarially affects the model performance. We first theoretically analyze this phenomenon and propose a simple yet effective technique to handle missingness, which we refer to as Sparsity Normalization (SN), that directly targets and resolves the VSP. We further experimentally validate SN on diverse benchmark datasets, to show that debiasing the effect of input-level sparsity improves the performance and stabilizes the training of neural networks.