RECLAIM: Cyclic Causal Discovery Amid Measurement Noise

Muralikrishnna G. Sethuraman; Faramarz Fekri

cs.LGMar 21, 2026

RECLAIM: Cyclic Causal Discovery Amid Measurement Noise

Authors: Muralikrishnna G. Sethuraman, Faramarz Fekri

Organizations: School of Electrical and Computer Engineering, Georgia Institute of Technology

Abstract

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.

Figures & tables

Panel of Figure 1 — Figure 1: (a) Illustration of a causal graph $\mathcal{G}_{m}$ encoding both the system variables $\mathcal{X}$ and the measured variables $\mathcal{Y}$ for a linear measurement system. (b) Mutilated graph, $\text{do}(I)(\mathcal{G}_{m})$ , resulting from a surgical intervention on $X_{2}$ .

Panel of Figure 2 — Figure 2: Performance comparison with varying minimum noise standard deviation ( $\sigma$ ) (top), and varying number of latent nodes ( $d$ ) (bottom) for Gaussian additive noise system. Shaded regions show $\pm 1$ standard deviation over 10 trials.

Panel of Figure 3 — Figure 3: Performance comparison with varying number of measurements ( $p$ ) (top), and varying minimum noise standard deviation ( $\sigma$ ) (bottom) for Linear measurement system. Shaded regions show $\pm 1$ standard deviation over 10 trials.

Panel of Figure 4 — Figure 4: Estimated graph learnt from Sachs et al. (2005) dataset

Method	SHD
RECLAIM	19
NODAGS	22
DCDI	21
Anchored-CI	19

Table 1: Performance with respect to SHD on Sachs et al. (2005) dataset

Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 5 — Figure 5: Illustration of state evolution for different choice of $a$ and $b$ for the system defined in example A.1 . (Left) Choosing $a=0.7$ and $b=-0.8$ results in a stable system and the system reaches a fixed point. (Right) Choosing $a=1.2$ and $b=2.3$ results in an unstable system and the trajectory diverges.

Panel of Figure 6 — Figure 6: Illustration of the augmented graph $\mathcal{G}^{\mathcal{I}}$ corresponding the set of interventional targets $\mathcal{I}=\{\emptyset,\{1\},\{3\}\}$ . (b) and (c) represent the mutilated graph obtained after interventions on $X_{1}$ and $X_{3}$ respectively. The augmented graph is the union of $\mathcal{G}$ , $\text{do}(\{X_{1}\})(\mathcal{G})$ , and $\text{do}(\{X_{3}\})(\mathcal{G})$ along with the context variables $C_{1}$ and $C_{2}$ .

Panel of Figure 7 — Figure 7: Performance comparison with varying number of cycles in the latent variable graph.

Panel of Figure 8 — Figure 8: Performance comparison with varying degree of nonlinearity in the latent variable SCM.

Panel of Figure 9 — Figure 9: Performance comparison with varying latent graph sparsity.

Causal Discovery

Causal discovery infers cause-and-effect structures from observational and interventional data, distinguishing causal relationships from correlation.

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May 15, 2026J/K move · Enter open · S save

SCOUT: Cyclic Causal Discovery Under Soft Interventions with Unknown Targets

Alpar Turkoglu, Muralikrishnna G. Sethuraman, Faramarz Fekri

School of Electrical and Computer Engineering, Georgia Institute of Technology.

Causal Discovery Causal Intervention

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Learning causal relationships between variables from data is a fundamental research area with many applications across disciplines. Most existing causal discovery algorithms rely on the assumptions that (i) the underlying system is acyclic, (ii) the exogenous noise variables are Gaussian, and (iii) the intervention targets for the data-generating experiments are known. While these assumptions simplify the analysis, they are violated in real-life systems. Most existing methods that address these issues either assume the underlying model is linear or are constrained to operate in limited interventional settings. To that end, we propose SCOUT, a novel causal discovery framework for learning nonlinear cyclic causal relationships from soft interventional data with unknown targets. Our approach maximizes the data log-likelihood to recover the graph structure, using two normalizing-flow architectures: contractive residual flows and neural spline flows. Through experiments on synthetic and real-world data, we show that SCOUT outperforms state-of-the-art methods in both causal graph recovery and unknown target recovery across various interventional and noise settings.

Abstract

Causal Discovery

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