# Consistency of Neural Causal Partial Identification

arXiv: https://arxiv.org/abs/2405.15673 · HTML: https://mlsanity.com/paper/2405.15673/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 55 references that are in the map.
- First posted on arXiv 24 May 2024.

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

- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018)
- [Nearly-tight VC-dimension and pseudodimension bounds for piecewise linear neural networks](https://mlsanity.com/paper/1703.02930/) (2017)
- [Parseval Networks: Improving Robustness to Adversarial Examples](https://mlsanity.com/paper/1704.08847/) (2017)
- [Optimal approximation of continuous functions by very deep ReLU networks](https://mlsanity.com/paper/1802.03620/) (2018)
- [CausalGAN: Learning Causal Implicit Generative Models with Adversarial Training](https://mlsanity.com/paper/1709.02023/) (2017)
- [Training robust neural networks using Lipschitz bounds](https://mlsanity.com/paper/2005.02929/) (2020)
- [The Causal-Neural Connection: Expressiveness, Learnability, and Inference](https://mlsanity.com/paper/2107.00793/) (2021)
- [Faster Wasserstein Distance Estimation with the Sinkhorn Divergence](https://mlsanity.com/paper/2006.08172/) (2020)
- [Counterfactual Probabilities: Computational Methods, Bounds and Applications](https://mlsanity.com/paper/1302.6784/) (2013)
- [Partial Counterfactual Identification from Observational and Experimental Data](https://mlsanity.com/paper/2110.05690/) (2021)
- [Neural Causal Models for Counterfactual Identification and Estimation](https://mlsanity.com/paper/2210.00035/) (2022)
- [Differential Properties of Sinkhorn Approximation for Learning with Wasserstein Distance](https://mlsanity.com/paper/1805.11897/) (2018)
- [Generative Interventions for Causal Learning](https://mlsanity.com/paper/2012.12265/) (2020)
- [An Automated Approach to Causal Inference in Discrete Settings](https://mlsanity.com/paper/2109.13471/) (2021)
- [CLIP: Cheap Lipschitz Training of Neural Networks](https://mlsanity.com/paper/2103.12531/) (2021)
- [Estimating average causal effects from patient trajectories](https://mlsanity.com/paper/2203.01228/) (2022)
- [A Class of Algorithms for General Instrumental Variable Models](https://mlsanity.com/paper/2006.06366/) (2020)
- [Stochastic Causal Programming for Bounding Treatment Effects](https://mlsanity.com/paper/2202.10806/) (2022)
- [A General Method for Deriving Tight Symbolic Bounds on Causal Effects](https://mlsanity.com/paper/2003.10702/) (2020)
- [Partial Identification of Treatment Effects with Implicit Generative Models](https://mlsanity.com/paper/2210.08139/) (2022)
- [A Neural Framework for Generalized Causal Sensitivity Analysis](https://mlsanity.com/paper/2311.16026/) (2023)
- [Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Model](https://mlsanity.com/paper/2306.01424/) (2023)
- [Nonparametric Bounds and Sensitivity Analysis of Treatment Effects](https://mlsanity.com/paper/1503.01598/) (2015)
- [Instrumentality Tests Revisited](https://mlsanity.com/paper/1301.2258/) (2013)
- [Towards Bounding Causal Effects under Markov Equivalence](https://mlsanity.com/paper/2311.07259/) (2023)
- [High-Dimensional Distribution Generation Through Deep Neural Networks](https://mlsanity.com/paper/2107.12466/) (2021)
- [On Partial Identification of the Pure Direct Effect](https://mlsanity.com/paper/1509.01652/) (2015)

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

- [Information-Theoretic Causal Bounds under Unmeasured Confounding](https://mlsanity.com/paper/2601.17160/) (2026)
- [Computational Identifiability](https://mlsanity.com/paper/2606.19361/) (2026)
- [Counterfactual identifiability beyond global monotonicity: non-monotone triangular structural causal models](https://mlsanity.com/paper/2605.04413/) (2026)
- [Representable but Unlearned: Encoding Rank and the Interaction-Prediction Floor](https://mlsanity.com/paper/2609.36208/) (2026)
- [Counterfactual Rollouts for Offline Contrastive Goal-Conditioned Reinforcement Learning](https://mlsanity.com/paper/2610.14953/) (2026)

## Abstract (arXiv)

Recent progress in Neural Causal Models (NCMs) showcased how identification and partial identification of causal effects can be automatically carried out via training of neural generative models that respect the constraints encoded in a given causal graph [Xia et al. 2022, Balazadeh et al. 2022]. However, formal consistency of these methods has only been proven for the case of discrete variables or only for linear causal models. In this work, we prove the consistency of partial identification via NCMs in a general setting with both continuous and categorical variables. Further, our results highlight the impact of the design of the underlying neural network architecture in terms of depth and connectivity as well as the importance of applying Lipschitz regularization in the training phase. In particular, we provide a counterexample showing that without Lipschitz regularization this method may not be asymptotically consistent. Our results are enabled by new results on the approximability of Structural Causal Models (SCMs) via neural generative models, together with an analysis of the sample complexity of the resulting architectures and how that translates into an error in the constrained optimization problem that defines the partial identification bounds.