# Learning Latent Structural Causal Models

arXiv: https://arxiv.org/abs/2210.13583 · HTML: https://mlsanity.com/paper/2210.13583/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 58 of its 96 references that are in the map.
- First posted on arXiv 24 Oct 2022.

## Builds on (most cited first, 30 of 58)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (2021)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [GFlowNet Foundations](https://mlsanity.com/paper/2111.09266/) (2021)
- [AdaBelief Optimizer: Adapting Stepsizes by the Belief in Observed Gradients](https://mlsanity.com/paper/2010.07468/) (2020)
- [Inductive Biases for Deep Learning of Higher-Level Cognition](https://mlsanity.com/paper/2011.15091/) (2020)
- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [Contrastive Learning Inverts the Data Generating Process](https://mlsanity.com/paper/2102.08850/) (2021)
- [Differentiable Causal Discovery from Interventional Data](https://mlsanity.com/paper/2007.01754/) (2020)
- [Towards Causal Representation Learning](https://mlsanity.com/paper/2102.11107/) (2021)
- [DYNOTEARS: Structure Learning from Time-Series Data](https://mlsanity.com/paper/2002.00498/) (2020)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [Learning Bayesian Networks: The Combination of Knowledge and Statistical Data](https://mlsanity.com/paper/1302.6815/) (2013)
- [Learning Latent Permutations with Gumbel-Sinkhorn Networks](https://mlsanity.com/paper/1802.08665/) (2018)
- [A Meta-Transfer Objective for Learning to Disentangle Causal Mechanisms](https://mlsanity.com/paper/1901.10912/) (2019)
- [Bayesian Structure Learning with Generative Flow Networks](https://mlsanity.com/paper/2202.13903/) (2022)
- [CausalGAN: Learning Causal Implicit Generative Models with Adversarial Training](https://mlsanity.com/paper/1709.02023/) (2017)
- [Interventional Causal Representation Learning](https://mlsanity.com/paper/2209.11924/) (2022)
- [Weakly supervised causal representation learning](https://mlsanity.com/paper/2203.16437/) (2022)
- [CITRIS: Causal Identifiability from Temporal Intervened Sequences](https://mlsanity.com/paper/2202.03169/) (2022)
- [Learning Neural Causal Models from Unknown Interventions](https://mlsanity.com/paper/1910.01075/) (2019)
- [DiBS: Differentiable Bayesian Structure Learning](https://mlsanity.com/paper/2105.11839/) (2021)
- [Masked Gradient-Based Causal Structure Learning](https://mlsanity.com/paper/1910.08527/) (2019)
- [Discovering Causal Signals in Images](https://mlsanity.com/paper/1605.08179/) (2016)

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

- [Bayesian learning of Causal Structure and Mechanisms with GFlowNets and Variational Bayes](https://mlsanity.com/paper/2211.02763/) (2022)
- [LCA-on-the-Line: Benchmarking Out-of-Distribution Generalization with Class Taxonomies](https://mlsanity.com/paper/2407.16067/) (2024)
- [Neuro-Causal Factor Analysis](https://mlsanity.com/paper/2305.19802/) (2023)
- [Differentiable Causal Discovery For Latent Hierarchical Causal Models](https://mlsanity.com/paper/2411.19556/) (2024)
- [Diffusion Based Causal Representation Learning](https://mlsanity.com/paper/2311.05421/) (2023)

## Abstract (arXiv)

Causal learning has long concerned itself with the accurate recovery of underlying causal mechanisms. Such causal modelling enables better explanations of out-of-distribution data. Prior works on causal learning assume that the high-level causal variables are given. However, in machine learning tasks, one often operates on low-level data like image pixels or high-dimensional vectors. In such settings, the entire Structural Causal Model (SCM) -- structure, parameters, textitand high-level causal variables -- is unobserved and needs to be learnt from low-level data. We treat this problem as Bayesian inference of the latent SCM, given low-level data. For linear Gaussian additive noise SCMs, we present a tractable approximate inference method which performs joint inference over the causal variables, structure and parameters of the latent SCM from random, known interventions. Experiments are performed on synthetic datasets and a causally generated image dataset to demonstrate the efficacy of our approach. We also perform image generation from unseen interventions, thereby verifying out of distribution generalization for the proposed causal model.