# Latent Causal Invariant Model

arXiv: https://arxiv.org/abs/2011.02203 · HTML: https://mlsanity.com/paper/2011.02203/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Nov 2020.

## Built on by (most cited first, 9 of 9)

- [Nonlinear Invariant Risk Minimization: A Causal Approach](https://mlsanity.com/paper/2102.12353/) (2021)
- [Learning Domain Invariant Representations for Generalizable Person Re-Identification](https://mlsanity.com/paper/2103.15890/) (2021)
- [Causal Hidden Markov Model for Time Series Disease Forecasting](https://mlsanity.com/paper/2103.16391/) (2021)
- [Domain Generalization -- A Causal Perspective](https://mlsanity.com/paper/2209.15177/) (2022)
- [A Survey of Deep Causal Models and Their Industrial Applications](https://mlsanity.com/paper/2209.08860/) (2022)
- [Raising the Bar in Graph OOD Generalization: Invariant Learning Beyond Explicit Environment Modeling](https://mlsanity.com/paper/2502.10706/) (2025)
- [β-Intact-VAE: Identifying and Estimating Causal Effects under Limited Overlap](https://mlsanity.com/paper/2110.05225/) (2021)
- [Domain Invariant Model with Graph Convolutional Network for Mammogram Classification](https://mlsanity.com/paper/2204.09954/) (2022)
- [Context-LGM: Leveraging Object-Context Relation for Context-Aware Object Recognition](https://mlsanity.com/paper/2110.04042/) (2021)

## Abstract (arXiv)

Current supervised learning can learn spurious correlation during the data-fitting process, imposing issues regarding interpretability, out-of-distribution (OOD) generalization, and robustness. To avoid spurious correlation, we propose a Latent Causal Invariance Model (LaCIM) which pursues causal prediction. Specifically, we introduce latent variables that are separated into (a) output-causative factors and (b) others that are spuriously correlated to the output via confounders, to model the underlying causal factors. We further assume the generating mechanisms from latent space to observed data to be causally invariant. We give the identifiable claim of such invariance, particularly the disentanglement of output-causative factors from others, as a theoretical guarantee for precise inference and avoiding spurious correlation. We propose a Variational-Bayesian-based method for estimation and to optimize over the latent space for prediction. The utility of our approach is verified by improved interpretability, prediction power on various OOD scenarios (including healthcare) and robustness on security.