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SCOUT: Cyclic Causal Discovery Under Soft Interventions with Unknown Targets

The paper proposes SCOUT, a novel framework that leverages normalizing flows to discover nonlinear cyclic causal structures and identify unknown intervention targets from soft interventional data, outperforming existing state-of-the-art methods by relaxing common assumptions such as acyclicity, Gaussian noise, and known intervention targets.

Original authors: Alpar Turkoglu, Muralikrishnna G. Sethuraman, Faramarz Fekri

Published 2026-05-19

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Alpar Turkoglu, Muralikrishnna G. Sethuraman, Faramarz Fekri

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are a detective trying to figure out how a complex machine works. You have a box full of gears, levers, and wires (variables), and you want to draw a map showing which part pushes which other part. This is called causal discovery.

Usually, detectives have a few rules that make their job easier:

The machine only moves forward (no loops where A pushes B, which pushes C, which pushes A).
The machine is quiet and predictable (Gaussian noise).
When they poke the machine to see what happens, they know exactly which button they pressed (known intervention targets).

But in the real world, machines are messy. They have feedback loops (cycles), they are noisy, and sometimes you poke them without knowing exactly which button you hit. Most existing detective tools fail when these "real world" rules are broken.

Enter SCOUT (Soft Causal discovery Under Unknown Targets). Think of SCOUT as a super-smart, flexible detective that can solve the mystery even when the machine is looping, noisy, and the detective is blindfolded regarding which button was pressed.

Here is how SCOUT works, broken down into simple concepts:

1. The "Soft" Poke vs. The "Hard" Smash

Imagine you want to see how a car engine reacts.

Hard Intervention: You smash a specific part with a hammer. It breaks, and everything connected to it stops working. This is easy to spot, but it's destructive.
Soft Intervention (What SCOUT uses): You gently nudge a part or change the oil. The engine keeps running, but it hums differently. The connections between parts are still there, but the behavior changes slightly.
The Problem: SCOUT has to figure out the engine's map and guess which part you nudged, even though you didn't tell it.

2. The "Shape-Shifting" Map (Normalizing Flows)

To understand the engine, SCOUT uses a special kind of mathematical tool called Normalizing Flows.

The Analogy: Imagine the data coming from the machine is a weird, lumpy blob of clay. SCOUT wants to turn this blob into a perfect, smooth sphere (a standard shape) so it's easy to analyze.
How it helps: SCOUT uses two types of "clay sculptors":
- Contractive Residual Flows: These act like a compression machine that squishes the data without tearing it, ensuring the machine doesn't get stuck in a loop that never ends.
- Neural Spline Flows: These are like flexible, stretchy rubber bands. They can stretch and twist the "clay" to fit almost any weird shape (non-Gaussian noise). This allows SCOUT to handle messy, unpredictable data that other tools can't process.

3. Guessing the Unknown (The "Who Pressed What?" Problem)

Since SCOUT doesn't know which button was pressed during the experiments, it has to guess.

The Analogy: Imagine you are watching a magic show where the magician changes the outcome of a trick, but you don't know which card they swapped. SCOUT keeps a "scorecard" for every possible card swap. It tries different combinations, sees which one makes the most sense of the data, and updates its guess until it finds the right one.
It does this simultaneously while drawing the map of the machine. It learns the map and the list of nudges at the same time.

4. The "Loop" Challenge

Most tools assume the machine is a straight line (A → B → C). But real systems often have loops (A → B → C → A).

The Analogy: Imagine a conversation where Person A talks to B, B talks to C, and C talks back to A. If you try to draw this as a straight line, you get confused.
SCOUT is built specifically to handle these circular conversations. It uses math to ensure that even with these loops, the system settles down into a stable state (equilibrium) that can be analyzed.

5. Did It Work? (The Results)

The authors tested SCOUT in two ways:

Fake Data (Synthetic): They built fake machines with known maps and known nudges, then hid the answers to see if SCOUT could find them. SCOUT was incredibly accurate, often getting a perfect score, even when the data was noisy or the nudges were unknown. It beat other top detective tools.
Real Data (Gene Networks): They used real data from biology (genes interacting in cells). Since we don't have the "perfect map" for these genes, they tested if SCOUT could predict what would happen if you changed a gene. SCOUT predicted the outcomes better than the other tools, proving it learned the relationships correctly.

Summary

SCOUT is a new tool that lets scientists map out complex, looping systems (like genes or ecosystems) even when:

The data is messy and unpredictable.
The system has feedback loops.
They don't know exactly which part of the system they changed during experiments.

It does this by using flexible mathematical "sculptors" to reshape the data and a smart guessing game to figure out both the map and the experiments simultaneously.

Technical Summary: SCOUT – Cyclic Causal Discovery Under Soft Interventions with Unknown Targets

1. Problem Statement

Causal discovery aims to infer the underlying causal structure of a system from data. However, existing algorithms face significant limitations when applied to complex, real-world systems. Most current methods rely on three restrictive assumptions:

Acyclicity: The underlying causal graph is a Directed Acyclic Graph (DAG), ignoring feedback loops common in biological and economic systems.
Gaussianity: Exogenous noise variables are assumed to be Gaussian, which often fails to capture the complexity of real-world distributions.
Known Intervention Targets: The specific variables targeted during interventional experiments are assumed to be known, whereas in many practical scenarios (e.g., high-throughput biological screens), these targets are unknown.

Furthermore, existing methods addressing these issues individually often fail to combine them. For instance, methods handling cyclic graphs often assume linearity or hard (surgical) interventions, while those handling soft interventions often assume acyclicity or known targets. This paper addresses the challenge of learning non-linear, cyclic causal relationships from soft interventional data where the intervention targets are unknown and the noise is non-Gaussian.

2. Methodology: The SCOUT Framework

The authors propose SCOUT, a novel framework that formulates causal discovery as a continuous optimization problem maximizing the data log-likelihood. The framework integrates several advanced components to handle the specific challenges of cycles, non-linearity, and unknown targets.

2.1. Structural Equation Modeling (SEM) with Cycles

The system is modeled using a structural equation model (SEM) that allows for directed cycles:
$X = f(X) + \epsilon$
where $X$ represents the random variables, $f$ represents the non-linear causal mechanisms, and $\epsilon$ represents exogenous noise. To ensure the system is well-posed and admits a unique solution under equilibrium conditions, the authors assume the causal mechanism $f$ is contractive. This allows the definition of an invertible forward map $X \mapsto \epsilon = (id - f)(X)$ .

2.2. Modeling Soft Interventions

The framework handles soft interventions, where the connectivity of a node with its parents is preserved, but the causal mechanism or noise characteristics change. For $K$ experiments with unknown targets, the model is expressed as:
$X = U_k(f(X) + \epsilon) + (I_d - U_k)(\tilde{f}(X) + \tilde{\epsilon})$
Here, $U_k$ is a diagonal matrix indicating which variables are not intervened upon in experiment $k$ . Crucially, $U_k$ (and thus the intervention targets) is treated as an unknown parameter to be learned alongside the graph structure.

2.3. Normalizing Flows for Non-Gaussian Noise

To handle non-Gaussian noise and learn the causal mechanisms, SCOUT employs Normalizing Flows in two stages:

Contractive Residual Flows: The causal mechanism $f$ is parameterized by a neural network. To satisfy the contractivity assumption required for solvability, the network weights are constrained using spectral normalization. The adjacency matrix of the graph is learned via a Gumbel-softmax relaxation.
Neural Spline Flows (NSF): Since the noise $\epsilon$ may be non-Gaussian, the framework uses a piecewise rational quadratic CDF transformation (Neural Spline Flow) to map the noise $\epsilon$ to a standard normal distribution $z$ . This allows the model to capture complex noise distributions while maintaining tractable likelihood computation.

2.4. Unknown Target Inference

To identify unknown intervention targets, SCOUT introduces an intervention target matrix $T^I \in \{0, 1\}^{K \times d}$ . Similar to the graph adjacency matrix, the entries of $T^I$ are sampled from a Gumbel-softmax distribution and optimized via straight-through gradient estimation. A sparsity regularizer is applied to encourage sparse intervention targets.

2.5. Optimization and Score Function

The objective is to maximize a regularized log-likelihood score function:
$S(G, I) = \sup_{\theta} \sum_{k=1}^K \mathbb{E}_{X \sim p^{(k)}} [\log p_{I_k, G}(X)] - \lambda_G |G| - \lambda_I |I|$
Computing the log-determinant of the Jacobian for cyclic systems is computationally challenging. SCOUT addresses this using an unbiased estimator based on the power series expansion of the log-determinant (Neumann series), combined with the Hutchinson trace estimator and a random truncation strategy to ensure unbiasedness.

3. Key Contributions

The paper makes the following specific contributions:

Novel Framework: SCOUT is the first framework to simultaneously accommodate non-linear mechanisms, directed cycles, non-Gaussian additive noise, and soft interventions with unknown targets.
Theoretical Guarantees: The authors prove that exact maximization of the proposed score function identifies the interventional equivalence class of the ground-truth graph and the ground-truth intervention family, under assumptions of contractivity and faithfulness.
Scalable Architecture: By utilizing continuous optimization and normalizing flows, the method avoids the combinatorial search space typical of discrete causal discovery.
Comprehensive Evaluation: The framework is benchmarked against state-of-the-art methods (NODAGS-Flow, LLC, BACKSHIFT) on both synthetic and real-world datasets.

4. Experimental Results

The authors evaluated SCOUT on synthetic data and two real-world datasets: Perturb-CITE-seq (gene expression data) and SERGIO (simulated single-cell gene expression).

4.1. Synthetic Data Performance

Graph Recovery: SCOUT achieved near-perfect graph recovery (AUPRC $\approx$ 1.0) across various settings involving Gaussian, Exponential, and Gumbel noise, and shift, scale, and noisy function interventions. It significantly outperformed baselines, particularly in non-Gaussian and cyclic settings where other methods failed or degraded.
Target Recovery: SCOUT successfully recovered unknown intervention targets, achieving perfect AUPRC for shift and scale interventions. While performance dipped for "noisy function" interventions (due to limited distributional shifts), it still outperformed the BACKSHIFT baseline.
Scalability: As the number of nodes increased from 10 to 70, SCOUT maintained high performance, whereas baselines like BACKSHIFT and LLC showed significant degradation.
Ablation Studies: Removing the Neural Spline Flow (NSF) layer resulted in a significant drop in performance for non-Gaussian noise, confirming the necessity of NSF for modeling complex noise distributions.

4.2. Real-World Data

Perturb-CITE-seq: On gene regulatory network data, SCOUT demonstrated superior predictive performance (measured by Interventional Negative Log-Likelihood) compared to NODAGS-Flow and LLC across different cell conditions (Co-culture, Control, IFN- $\gamma$ ). This suggests that accounting for non-Gaussian noise improves predictive accuracy in biological systems.
SERGIO: In a close-to-real-world simulation, SCOUT achieved near-perfect intervention target recovery (AUPRC 0.978) and outperformed baselines in graph identification, even though the ground truth mechanism was not strictly contractive.

5. Significance and Claims

The paper claims that SCOUT substantially broadens the scope of causal discovery for realistic experimental settings. By relaxing the assumptions of acyclicity, Gaussianity, and known targets, the framework enables the analysis of complex systems with feedback loops and heterogeneous noise, which are prevalent in fields like biology and systems engineering.

The authors emphasize that their approach provides a consistent method for recovering the Markov equivalence class of the ground-truth graph and the intervention targets. They acknowledge limitations, such as the requirement for contractive mechanisms to ensure solvability and the difficulty of recovering targets when interventions induce minimal distributional changes (e.g., noisy function interventions). Future work is suggested to include handling confounders, more realistic measurement noise models, and scaling to larger graph models.

The paper concludes that SCOUT represents a significant step forward in making causal discovery applicable to the complex, cyclic, and non-Gaussian systems often found in modern scientific data.