Robust Causal Discovery under Imperfect Structural Constraints

TL;DR

RoaDs tackles robust causal discovery when prior structural constraints are imperfect. It integrates prior alignment via a surrogate model to reweight priors and employs a multi-task learning framework optimized with multi-gradient descent to balance data-driven and knowledge-driven objectives, handling both linear and nonlinear SEMs. The approach yields asymptotic consistency under consistent priors and demonstrates strong empirical robustness and efficiency across diverse noise types and constraint quality. The results on synthetic and real data indicate RoaDs reliably recovers underlying causal graphs while mitigating the adverse effects of flawed priors, offering practical impact for domains with scarce data but rich expert knowledge.

Abstract

Robust causal discovery from observational data under imperfect prior knowledge remains a significant and largely unresolved challenge. Existing methods typically presuppose perfect priors or can only handle specific, pre-identified error types. And their performance degrades substantially when confronted with flawed constraints of unknown location and type. This decline arises because most of them rely on inflexible and biased thresholding strategies that may conflict with the data distribution. To overcome these limitations, we propose to harmonizes knowledge and data through prior alignment and conflict resolution. First, we assess the credibility of imperfect structural constraints through a surrogate model, which then guides a sparse penalization term measuring the loss between the learned and constrained adjacency matrices. We theoretically prove that, under ideal assumption, the knowledge-driven objective aligns with the data-driven objective. Furthermore, to resolve conflicts when this assumption is violated, we introduce a multi-task learning framework optimized via multi-gradient descent, jointly minimizing both objectives. Our proposed method is robust to both linear and nonlinear settings. Extensive experiments, conducted under diverse noise conditions and structural equation model types, demonstrate the effectiveness and efficiency of our method under imperfect structural constraints.

Figures (20)

• Figure 1: Robustness to imperfect constraints. A single-objective baseline assigns equal weight and is misled by the flawed prior (red arrow in $\mathcal{G}_2$), whereas ours identifies the conflict and discovers DAG on the Pareto set.
• Figure 2: Pipeline. RoaDs constructs a data-driven objective from a continuous score and a knowledge-driven objective using a surrogate model to align imperfect constraints (Red arrows in figure). These are formulated as a MTL problem, which is then solved via the MGDA to recover the final causal graph.
• Figure 3: Influence of positive constraints rate $p_a$ for continuous methods ($n_v=20,n_d=2n_v,p_b,p_c=0.3,1$).
• Figure 4: Influence of imperfect constraints rate $p_b$ for continuous methods ($n_v=20,n_d=2n_v,p_a,p_c=0.3,1$).
• Figure 5: Ablation study on ER-2 ($n_v=20$, $n_d=2n_v$,$p_a,p_b,p_c = 0.3,0.3,1$, PA indicates prior alignment).

Theorems & Definitions (3)

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