# DAG-CLIP: A DAG Learning Framework in the Presence of Latent Variables

arXiv: https://arxiv.org/abs/2610.06086 · HTML: https://mlsanity.com/paper/2610.06086/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 74 references that are in the map.
- First posted on arXiv 5 Oct 2026.

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

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [Causal Inference and Causal Explanation with Background Knowledge](https://mlsanity.com/paper/1302.4972/) (2013)
- [DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterization](https://mlsanity.com/paper/2209.08037/) (2022)
- [Learning Equivalence Classes of Bayesian Networks Structures](https://mlsanity.com/paper/1302.3566/) (2013)
- [On Causal Discovery with Equal Variance Assumption](https://mlsanity.com/paper/1807.03419/) (2018)
- [Latent Hierarchical Causal Structure Discovery with Rank Constraints](https://mlsanity.com/paper/2210.01798/) (2022)
- [High-dimensional consistency in score-based and hybrid structure learning](https://mlsanity.com/paper/1507.02608/) (2015)
- [Concave Penalized Estimation of Sparse Gaussian Bayesian Networks](https://mlsanity.com/paper/1401.0852/) (2014)
- [Vintage Factor Analysis with Varimax Performs Statistical Inference](https://mlsanity.com/paper/2004.05387/) (2020)
- [Item Response Theory -- A Statistical Framework for Educational and Psychological Measurement](https://mlsanity.com/paper/2108.08604/) (2021)
- [Integer Programming for Causal Structure Learning in the Presence of Latent Variables](https://mlsanity.com/paper/2102.03129/) (2021)
- [Discovery and inference of a causal network with hidden confounding](https://mlsanity.com/paper/2309.09420/) (2023)
- [Improving Bayesian Network Structure Learning in the Presence of Measurement Error](https://mlsanity.com/paper/2011.09776/) (2020)
- [Learning linear non-Gaussian directed acyclic graph with diverging number of nodes](https://mlsanity.com/paper/2111.00740/) (2021)
- [Ordinal Causal Discovery](https://mlsanity.com/paper/2201.07396/) (2022)
- [Permutation-Based Rank Test in the Presence of Discretization and Application in Causal Discovery with Mixed Data](https://mlsanity.com/paper/2501.18990/) (2025)
- [Learning Bayesian Networks from Ordinal Data](https://mlsanity.com/paper/2010.15808/) (2020)
- [Discrete Causal Representation Learning](https://mlsanity.com/paper/2603.25017/) (2026)
- [Score-Based Causal Discovery of Latent Variable Causal Models](https://mlsanity.com/paper/2605.20396/) (2026)
- [Learning Attribute Patterns in High-Dimensional Structured Latent Attribute Models](https://mlsanity.com/paper/1904.04378/) (2019)
- [Learning and scoring Gaussian latent variable causal models with unknown additive interventions](https://mlsanity.com/paper/2101.06950/) (2021)
- [Inference for a Large Directed Acyclic Graph with Unspecified Interventions](https://mlsanity.com/paper/2110.03805/) (2021)
- [Latent Conjunctive Bayesian Network: Unify Attribute Hierarchy and Bayesian Network for Cognitive Diagnosis](https://mlsanity.com/paper/2301.03665/) (2023)
- [Causal Discovery with Generalized Linear Models through Peeling Algorithms](https://mlsanity.com/paper/2310.16698/) (2023)
- [Learning Bayesian networks: a copula approach for mixed-type data](https://mlsanity.com/paper/2312.13168/) (2023)
- [Score-based Greedy Search for Structure Identification of Partially Observed Linear Causal Models](https://mlsanity.com/paper/2510.04378/) (2025)
- [Beyond Vintage Rotation: Bias-Free Sparse Representation Learning with Oracle Inference](https://mlsanity.com/paper/2602.22590/) (2026)
- [When Composite Likelihood Meets Stochastic Approximation](https://mlsanity.com/paper/2310.04165/) (2023)

## Abstract (arXiv)

Learning directed acyclic graphs (DAGs) to uncover causal mechanisms has attracted substantial attention in machine learning. While most existing methods focus exclusively on observed variables, many variables of substantive interest are latent constructs defined by statistical measurement models. Such constructs are particularly common in the social and behavioral sciences. In this paper, we propose a general statistical framework for DAG learning when some or all nodes of the graph are latent variables, accommodating non-Gaussian manifest variables such as binary and categorical data in the measurement model. To overcome the computational burden of high-dimensional integration in standard marginal likelihoods, we develop DAG learning via Composite-Likelihood-based screening and Iterative Pruning (DAG-CLIP), a two-step composite-likelihood-based learning algorithm. This algorithm first solves a smooth acyclicity-constrained optimization problem to screen out misspecified DAG structures, and subsequently performs BIC-guided composite-likelihood backward deletion within the Markov equivalence class (MEC) space to identify a sparse DAG. We establish the statistical consistency of the algorithm in recovering the MEC of the true DAG, and demonstrate its effectiveness through extensive simulation studies and a real-world application to large-scale educational survey data.