# RECLAIM: Cyclic Causal Discovery Amid Measurement Noise

arXiv: https://arxiv.org/abs/2603.20585 · HTML: https://mlsanity.com/paper/2603.20585/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 42 references that are in the map.
- First posted on arXiv 21 Mar 2026.

## Builds on (most cited first, 17 of 17)

- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (2016)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [Residual Flows for Invertible Generative Modeling](https://mlsanity.com/paper/1906.02735/) (2019)
- [Differentiable Causal Discovery from Interventional Data](https://mlsanity.com/paper/2007.01754/) (2020)
- [Foundations of Structural Causal Models with Cycles and Latent Variables](https://mlsanity.com/paper/1611.06221/) (2016)
- [Nonparametric Identifiability of Causal Representations from Unknown Interventions](https://mlsanity.com/paper/2306.00542/) (2023)
- [Learning Linear Causal Representations from Interventions under General Nonlinear Mixing](https://mlsanity.com/paper/2306.02235/) (2023)
- [Constraint-based Causal Discovery from Multiple Interventions over Overlapping Variable Sets](https://mlsanity.com/paper/1403.2150/) (2014)
- [A Discovery Algorithm for Directed Cyclic Graphs](https://mlsanity.com/paper/1302.3599/) (2013)
- [The Bayesian Structural EM Algorithm](https://mlsanity.com/paper/1301.7373/) (2013)
- [Multi-Domain Causal Representation Learning via Weak Distributional Invariances](https://mlsanity.com/paper/2310.02854/) (2023)
- [NODAGS-Flow: Nonlinear Cyclic Causal Structure Learning](https://mlsanity.com/paper/2301.01849/) (2023)
- [Structure Learning for Cyclic Linear Causal Models](https://mlsanity.com/paper/2006.05978/) (2020)
- [Anchored Causal Inference in the Presence of Measurement Error](https://mlsanity.com/paper/1906.00928/) (2019)
- [Differentiable Cyclic Causal Discovery Under Unmeasured Confounders](https://mlsanity.com/paper/2508.08450/) (2025)
- [Sparse semiparametric canonical correlation analysis for data of mixed types](https://mlsanity.com/paper/1807.05274/) (2018)
- [MissNODAG: Differentiable Cyclic Causal Graph Learning from Incomplete Data](https://mlsanity.com/paper/2410.18918/) (2024)

## Abstract (arXiv)

Uncovering causal relationships is a fundamental problem across science and engineering. However, most existing causal discovery methods assume acyclicity and direct access to the system variables -- assumptions that fail to hold in many real-world settings. For instance, in genomics, cyclic regulatory networks are common, and measurements are often corrupted by instrumental noise. To address these challenges, we propose RECLAIM, a causal discovery framework that natively handles both cycles and measurement noise. RECLAIM learns the causal graph structure by maximizing the likelihood of the observed measurements via expectation-maximization (EM), using residual normalizing flows for tractable likelihood computation. We consider two measurement models: (i) Gaussian additive noise, and (ii) a linear measurement system with additive Gaussian noise. We provide theoretical consistency guarantees for both the settings. Experiments on synthetic data and real-world protein signaling datasets demonstrate the efficacy of the proposed method.