# Causal Inference with Noisy and Missing Covariates via Matrix Factorization

arXiv: https://arxiv.org/abs/1806.00811 · HTML: https://mlsanity.com/paper/1806.00811/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jun 2018.

## Built on by (most cited first, 30 of 30)

- [Causal Matrix Completion](https://mlsanity.com/paper/2109.15154/) (2021)
- [Evaluation Methods and Measures for Causal Learning Algorithms](https://mlsanity.com/paper/2202.02896/) (2022)
- [Estimating Treatment Effects from Irregular Time Series Observations with Hidden Confounders](https://mlsanity.com/paper/2303.02320/) (2023)
- [Deconfounding Temporal Autoencoder: Estimating Treatment Effects over Time Using Noisy Proxies](https://mlsanity.com/paper/2112.03013/) (2021)
- [Partial Identification with Noisy Covariates: A Robust Optimization Approach](https://mlsanity.com/paper/2202.10665/) (2022)
- [Intact-VAE: Estimating Treatment Effects under Unobserved Confounding](https://mlsanity.com/paper/2101.06662/) (2021)
- [To Impute or not to Impute? Missing Data in Treatment Effect Estimation](https://mlsanity.com/paper/2202.02096/) (2022)
- [Causal Inference with Treatment Measurement Error: A Nonparametric Instrumental Variable Approach](https://mlsanity.com/paper/2206.09186/) (2022)
- [DeCaFlow: A deconfounding causal generative model](https://mlsanity.com/paper/2503.15114/) (2025)
- [Identifiable Energy-based Representations: An Application to Estimating Heterogeneous Causal Effects](https://mlsanity.com/paper/2108.03039/) (2021)
- [Matrix Completion with Model-free Weighting](https://mlsanity.com/paper/2106.05850/) (2021)
- [Deep Treatment-Adaptive Network for Causal Inference](https://mlsanity.com/paper/2112.13502/) (2021)
- [Towards Principled Causal Effect Estimation by Deep Identifiable Models](https://mlsanity.com/paper/2109.15062/) (2021)
- [Debiasing Multimodal Models via Causal Information Minimization](https://mlsanity.com/paper/2311.16941/) (2023)
- [Causal Inference with Latent Variables: Recent Advances and Future Prospectives](https://mlsanity.com/paper/2406.13966/) (2024)
- [Adjustment for Confounding using Pre-Trained Representations](https://mlsanity.com/paper/2506.14329/) (2025)
- [Estimating Treatment Effects in Continuous Time with Hidden Confounders](https://mlsanity.com/paper/2302.09446/) (2023)
- [Entropy Minimizing Matrix Factorization](https://mlsanity.com/paper/2103.13487/) (2021)
- [Causal Inference in Possibly Nonlinear Factor Models](https://mlsanity.com/paper/2008.13651/) (2020)
- [Conservative Policy Construction Using Variational Autoencoders for Logged Data with Missing Values](https://mlsanity.com/paper/2109.03747/) (2021)
- [Substitute adjustment via recovery of latent variables](https://mlsanity.com/paper/2403.00202/) (2024)
- [Variational Temporal Deconfounder for Individualized Treatment Effect Estimation from Longitudinal Observational Data](https://mlsanity.com/paper/2207.11251/) (2022)
- [Causal Inference (C-inf) -- closed form worst case typical phase transitions](https://mlsanity.com/paper/2301.00793/) (2023)
- [Causal Inference (C-inf) -- asymmetric scenario of typical phase transitions](https://mlsanity.com/paper/2301.00801/) (2023)
- [Disentangled Latent Representation Learning for Tackling the Confounding M-Bias Problem in Causal Inference](https://mlsanity.com/paper/2312.05404/) (2023)
- [Matrix Completion via Residual Spectral Matching](https://mlsanity.com/paper/2412.10005/) (2024)
- [Beyond Correlation: Causal Multi-View Unsupervised Feature Selection Learning](https://mlsanity.com/paper/2509.13763/) (2025)
- [An Interdisciplinary and Cross-Task Review on Missing Data Imputation](https://mlsanity.com/paper/2511.01196/) (2025)
- [Data-Poisoning Audits for Causal Effect Estimation](https://mlsanity.com/paper/2607.19692/) (2026)
- [Synthetic Nearest Neighbors: Extending Synthetic Controls for Matrix Completion with Missing Not at Random Data](https://mlsanity.com/paper/2609.13586/) (2026)

## Abstract (arXiv)

Valid causal inference in observational studies often requires controlling for confounders. However, in practice measurements of confounders may be noisy, and can lead to biased estimates of causal effects. We show that we can reduce the bias caused by measurement noise using a large number of noisy measurements of the underlying confounders. We propose the use of matrix factorization to infer the confounders from noisy covariates, a flexible and principled framework that adapts to missing values, accommodates a wide variety of data types, and can augment many causal inference methods. We bound the error for the induced average treatment effect estimator and show it is consistent in a linear regression setting, using Exponential Family Matrix Completion preprocessing. We demonstrate the effectiveness of the proposed procedure in numerical experiments with both synthetic data and real clinical data.