Tian-Zuo Wang

Zi-Rong Li, Si-Yang Liu, Tian-Zuo Wang et al.

Causal discovery aims to recover directed causal relations from observational and interventional data, providing a basis for mechanistic understanding and reliable decision-making. Causal discovery foundation models (CDFMs) seek to amortize this problem by mapping a dataset directly to a causal graph in a single forward pass, avoiding per-dataset testing, search, or optimization. However, existing CDFMs remain limited, often failing to consistently match strong classical methods, and we find that a key bottleneck is how causal pretraining tasks are constructed. Based on this observation, we propose TabCausal, a data-driven CDFM trained with broad causal pretraining over diverse graph priors, structural mechanisms, noise models, dimensions, sample sizes, and intervention regimes. A dynamic task construction strategy composes these causal environments into varied discovery tasks, enabling more transferable structural learning from observational and mixed-interventional data. On large-scale synthetic benchmarks, TabCausal achieves better macro-averaged performance than a diverse set of causal discovery baselines. To further bridge abstract synthetic generators and realistic causal reasoning scenarios, we introduce a protocol-guided and LLM-audited semantic causal environment benchmark, where domain-grounded SCMs generate interpretable observational and interventional datasets for out-of-distribution analysis. Across both synthetic and semantic environments, TabCausal demonstrates robust structure recovery, especially under interventional evidence, highlighting broad causal pretraining as a key ingredient for transferable amortized causal discovery.

Tian-Zuo Wang, Lue Tao, Zhi-Hua Zhou

Identifying causal relations is crucial for a variety of downstream tasks. In additional to observational data, background knowledge (BK), which could be attained from human expertise or experiments, is usually introduced for uncovering causal relations. This raises an open problem that in the presence of latent variables, what causal relations are identifiable from observational data and BK. In this paper, we propose two novel rules for incorporating BK, which offer a new perspective to the open problem. In addition, we show that these rules are applicable in some typical causality tasks, such as determining the set of possible causal effects with observational data. Our rule-based approach enhances the state-of-the-art method by circumventing a process of enumerating block sets that would otherwise take exponential complexity.

Wen-Bo Du, Tian-Zuo Wang, Han-Jia Ye et al.

In machine learning, a critical class of decision-related problems concerns preventing predicted undesirable outcomes, referred to as the \textit{avoiding undesired future} (AUF) problem. To address this, the \textit{rehearsal learning} framework has been proposed to model influence relations for effective decisions. However, existing rehearsal methods rely on restrictive parametric assumptions such as linear systems or additive noise, limiting their practical applicability. In this paper, we propose the first non-parametric rehearsal learning approach for AUF without assuming specific functional forms of data generation processes. Specifically, we use kernel machinery to reformulate the AUF objective into a unified representation that disentangles desirability modeling from action-induced distributional changes. To handle the discontinuity of desirability indicator, we present a smooth Probit surrogate and provide an approximation error bound. Meanwhile, we capture the action-induced changes via conditional mean embeddings, and develop a kernel ridge regression based nested estimator for AUF objective with consistency guarantees. Such a formulation naturally accommodates nonlinear systems and non-additive noise, and empirical results on synthetic and real-data-derived semi-synthetic benchmarks demonstrate the effectiveness and flexibility of our approach.

Yu-Xuan Tao, Tian-Zuo Wang, Zhi-Hua Zhou

When a machine learning (ML) model forecasts an undesired event, one often seeks a decision to avoid it, known as the avoiding undesired future (AUF) problem. Many rehearsal learning methods have been proposed for AUF, but they rely on an underlying graph structure; learning such a graph from observational data is challenging and can incur substantial estimation error. In this work, we demonstrate that the order structure can be sufficient for AUF decision-making, and propose the first order-based rehearsal learning method. Although an order is less informative than a graph, it can be sufficient to identify the influence of decisions from observational data, suggesting that learning the entire graph is not always necessary. To learn the order, we develop an information-theoretic method that imposes no restrictions on the form of structural functions or the type of noise distributions. For AUF decision-making, we construct an order-based sampler to approximate the influence of decisions and, combined with a surrogate objective for maximizing the post-decision success probability, reduce the AUF task to a differentiable optimization problem. Experiments show that our order learning method outperforms existing methods, and that our AUF approach not only surpasses methods relying on learned graphs or learned orders, but also matches or even exceeds oracle baselines that are given the true graph.