Research map / Probabilistic and scientific modeling / Causal discovery
Differentiable Causal Discovery for Latent Hierarchical Causal Models
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes identifiability results for nonlinear latent hierarchical causal models without deterministic-latent assumptions, and a differentiable (VAE + Gumbel-softmax mask) causal discovery method that recovers the latent hierarchy from data.
Problem
Causal discovery with latent variables in nonlinear hierarchical models is hard: existing methods rely on iterative discrete searches that scale poorly, assume linearity or invertibility, and require latent variables and noise to be deterministic functions of observed variables.
Approach
A rank-of-Jacobian criterion on E[y|x] identifies the minimal number of latent variables d-separating measured sets, enabling identifiability without deterministic latents; the structure matrix is learned end-to-end in a VAE with relaxed binary masks, a pure-children structural constraint, and an independence loss on noise.
Key results
- On four synthetic latent hierarchical graphs, the method achieves SHD 0.67-1.17 and F1 0.95-0.97, versus best baseline KONG/HUANG with F1 around 0.63-0.79.
- On CMNIST 'Reverse' test set, the method reaches 0.979 accuracy vs 0.916 for Causal VAE and 0.854 for Autoencoder.
- The learned hierarchy on MNIST contains 62 latent variables, demonstrating scalability to high-dimensional image data.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the proposed differentiable causal discovery method instead of KONG | Latent hierarchical causal discovery · Tree (LeakyReLU) | SHD: 5.83 -> 0.67 | Helped |
| Use the proposed differentiable causal discovery method instead of HUANG | Latent hierarchical causal discovery · V-structure (LeakyReLU) | F1: 0.72 -> 0.97 | Helped |
| Use the proposed differentiable causal discovery method instead of HUANG | Latent hierarchical causal discovery · Tree (Tanh) | SHD: 4.50 -> 1.00 | Helped |
| Use the proposed differentiable causal discovery method instead of KONG | Latent hierarchical causal discovery · V-structure (Tanh) | F1: 0.79 -> 0.95 | Helped |
| Learn representations with the proposed method instead of an autoencoder | Logistic regression on CMNIST latent representations · CMNIST Reverse test | accuracy: 0.854 -> 0.979 | Helped |
| Learn representations with the proposed method instead of Graph VAE | Logistic regression on CMNIST latent representations · CMNIST Blue test | accuracy: 0.766 -> 0.753 | No clear effect |
| Omit MINE-based independence enforcement for exogenous variables (ablation) | Image-data Hierarchical VAE · Image data | final output | No clear effect |
Surprising findings
- Causal VAE/Graph VAE and some baselines reach higher accuracy than the method on the CMNIST 'black' test set (Graph VAE 0.766 vs ours 0.753), which the authors acknowledge.
- Several baselines (GIN, DeCAMFounder) recover almost no edges, giving F1 near zero on the synthetic benchmarks.
Limitations
- Requires the two-pure-children condition and equal-path-length structure, and does not handle measured variables with children.
- Evaluation of SHD requires O(|Z|!) permutation search, which is intractable for large graphs.
- Downstream transfer accuracy on CMNIST does not uniformly beat task-specific baselines.
Experimental setup
Datasets: MNIST CMNIST CelebA synthetic SEM data
Benchmarks: synthetic latent hierarchical graphs (trees and v-structures) CMNIST CelebA
Metrics: SHD F1 runtime (seconds) test accuracy
Baselines: KONG HUANG GIN DeCAMFounder Autoencoder VAE beta-VAE Causal VAE Graph VAE
Builds on: NOTEARS variational autoencoder Gumbel-softmax MINE
Closest papers by meaning
- THE ROBUSTNESS OF DIFFERENTIABLE CAUSAL DISCOVERY IN MISSPECIFIED SCENARIOS (ICLR 2025 · similarity 0.92)
- Identification of Causal Structure with Latent Variables Based on Higher Order Cumulants (AAAI 2024 · similarity 0.91)
- Local Identifying Causal Relations in the Presence of Latent Variables (ICML 2025 · similarity 0.91)
- Identification of Latent Confounders via Investigating the Tensor Ranks of the Nonlinear Observations (ICML 2025 · similarity 0.91)
- Local Causal Structure Learning in the Presence of Latent Variables (ICML 2024 · similarity 0.91)
- Identifiable Latent Polynomial Causal Models through the Lens of Change (ICLR 2024 · similarity 0.91)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.