# Harmonization with Flow-based Causal Inference

arXiv: https://arxiv.org/abs/2106.06845 · HTML: https://mlsanity.com/paper/2106.06845/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 38 references that are in the map.
- First posted on arXiv 12 Jun 2021.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Causality for Machine Learning](https://mlsanity.com/paper/1911.10500/) (2019)
- [Deep Structural Causal Models for Tractable Counterfactual Inference](https://mlsanity.com/paper/2006.06485/) (2020)
- [Invariant Representations without Adversarial Training](https://mlsanity.com/paper/1805.09458/) (2018)
- [Detect and Correct Bias in Multi-Site Neuroimaging Datasets](https://mlsanity.com/paper/2002.05049/) (2020)
- [Invertible Generative Modeling using Linear Rational Splines](https://mlsanity.com/paper/2001.05168/) (2020)
- [Scanner Invariant Representations for Diffusion MRI Harmonization](https://mlsanity.com/paper/1904.05375/) (2019)
- [Image-level Harmonization of Multi-Site Data using Image-and-Spatial Transformer Networks](https://mlsanity.com/paper/2006.16741/) (2020)
- [Medical Image Harmonization Using Deep Learning Based Canonical Mapping: Toward Robust and Generalizable Learning in Imaging](https://mlsanity.com/paper/2010.05355/) (2020)

## Built on by (most cited first, 14 of 14)

- [Causal Machine Learning for Healthcare and Precision Medicine](https://mlsanity.com/paper/2205.11402/) (2022)
- [Learning Disentangled Representations in the Imaging Domain](https://mlsanity.com/paper/2108.12043/) (2021)
- [Normalizing Flows for Interventional Density Estimation](https://mlsanity.com/paper/2209.06203/) (2022)
- [A Review of Causality for Learning Algorithms in Medical Image Analysis](https://mlsanity.com/paper/2206.05498/) (2022)
- [Bias in Machine Learning Models Can Be Significantly Mitigated by Careful Training: Evidence from Neuroimaging Studies](https://mlsanity.com/paper/2205.13421/) (2022)
- [Structured Neural Networks for Density Estimation and Causal Inference](https://mlsanity.com/paper/2311.02221/) (2023)
- [Applications of Generative Adversarial Networks in Neuroimaging and Clinical Neuroscience](https://mlsanity.com/paper/2206.07081/) (2022)
- [A Survey of Deep Causal Models and Their Industrial Applications](https://mlsanity.com/paper/2209.08860/) (2022)
- [A Systematic Review of Generalization Research in Medical Image Classification](https://mlsanity.com/paper/2403.12167/) (2024)
- [Harmonizing Flows: Unsupervised MR harmonization based on normalizing flows](https://mlsanity.com/paper/2301.11551/) (2023)
- [Harmonizing Flows: Leveraging normalizing flows for unsupervised and source-free MRI harmonization](https://mlsanity.com/paper/2407.15717/) (2024)
- [Adapting Machine Learning Diagnostic Models to New Populations Using a Small Amount of Data: Results from Clinical Neuroscience](https://mlsanity.com/paper/2308.03175/) (2023)
- [Causal Transfer in Medical Image Analysis](https://mlsanity.com/paper/2603.24388/) (2026)
- [Causal-Adversarial Probing of Clinical Covariates for Prostate MRI Grading](https://mlsanity.com/paper/2607.14720/) (2026)

## Abstract (arXiv)

Heterogeneity in medical data, e.g., from data collected at different sites and with different protocols in a clinical study, is a fundamental hurdle for accurate prediction using machine learning models, as such models often fail to generalize well. This paper leverages a recently proposed normalizing-flow-based method to perform counterfactual inference upon a structural causal model (SCM), in order to achieve harmonization of such data. A causal model is used to model observed effects (brain magnetic resonance imaging data) that result from known confounders (site, gender and age) and exogenous noise variables. Our formulation exploits the bijection induced by flow for the purpose of harmonization. We infer the posterior of exogenous variables, intervene on observations, and draw samples from the resultant SCM to obtain counterfactuals. This approach is evaluated extensively on multiple, large, real-world medical datasets and displayed better cross-domain generalization compared to state-of-the-art algorithms. Further experiments that evaluate the quality of confounder-independent data generated by our model using regression and classification tasks are provided.