# Measurement error models: from nonparametric methods to deep neural networks

arXiv: https://arxiv.org/abs/2007.07498 · HTML: https://mlsanity.com/paper/2007.07498/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jul 2020.

## Built on by (most cited first, 5 of 5)

- [Deep Learning With DAGs](https://mlsanity.com/paper/2401.06864/) (2024)
- [Robust Bayesian Inference for Measurement Error Misspecification: The Berkson and Classical Cases](https://mlsanity.com/paper/2306.01468/) (2023)
- [Identifiable causal inference with noisy treatment and no side information](https://mlsanity.com/paper/2306.10614/) (2023)
- [Challenges for Predictive Modeling with Neural Network Techniques using Error-Prone Dietary Intake Data](https://mlsanity.com/paper/2311.09338/) (2023)
- [DAIF: A Data-Driven Intermediate Fusion Framework for Multimodal Supervised Learning via Approximate Message Passing](https://mlsanity.com/paper/2608.02769/) (2026)

## Abstract (arXiv)

The success of deep learning has inspired recent interests in applying neural networks in statistical inference. In this paper, we investigate the use of deep neural networks for nonparametric regression with measurement errors. We propose an efficient neural network design for estimating measurement error models, in which we use a fully connected feed-forward neural network (FNN) to approximate the regression function f(x), a normalizing flow to approximate the prior distribution of X, and an inference network to approximate the posterior distribution of X. Our method utilizes recent advances in variational inference for deep neural networks, such as the importance weight autoencoder, doubly reparametrized gradient estimator, and non-linear independent components estimation. We conduct an extensive numerical study to compare the neural network approach with classical nonparametric methods and observe that the neural network approach is more flexible in accommodating different classes of regression functions and performs superior or comparable to the best available method in nearly all settings.