This paper considers the problem of estimating the unknown intervention targets in a causal directed acyclic graph from observational and interventional data. The focus is on soft interventions in linear structural equation models (SEMs). Current approaches to causal structure learning either work with known intervention targets or use hypothesis testing to discover the unknown intervention targets even for linear SEMs. This severely limits their scalability and sample complexity. This paper proposes a scalable and efficient algorithm that consistently identifies all intervention targets.

We provide explicit, finite-sample guarantees for learning causal representations from data with a sublinear number of environments. Causal representation learning seeks to provide a rigourous foundation for the general representation learning problem by bridging causal models with latent factor models in order to learn interpretable representations with causal semantics. Despite a blossoming theory of identifiability in causal representation learning, estimation and finite-sample bounds are less well understood. We show that causal representations can be learned with only a logarithmic number of unknown, multi-node interventions, and that the intervention targets need not be carefully designed in advance. Through a careful perturbation analysis, we provide a new analysis of this problem that guarantees consistent recovery of (a) the latent causal graph, (b) the mixing matrix and representations, and (c) \emph{unknown} intervention targets.

Intervention Target Estimation (ITE) is vital for both understanding and decision-making in complex systems, yet it remains underexplored. Current ITE methods are hampered by their inability to learn from distinct intervention instances collaboratively and to incorporate rich insights from labeled data, which leads to inefficiencies such as the need for re-estimation of intervention targets with minor data changes or alterations in causal graphs. In this paper, we propose DeepITE, an innovative deep learning framework designed around a variational graph autoencoder. DeepITE can concurrently learn from both unlabeled and labeled data with different intervention targets and causal graphs, harnessing correlated information in a self or semi-supervised manner. The model's inference capabilities allow for the immediate identification of intervention targets on unseen samples and novel causal graphs, circumventing the need for retraining. Our extensive testing confirms that DeepITE not only surpasses 13 baseline methods in the Recall@k metric but also demonstrates expeditious inference times, particularly on large graphs. Moreover, incorporating a modest fraction of labeled data (5-10\%) substantially enhances DeepITE's performance, further solidifying its practical applicability. Our source code is available at https://github.com/alipay/DeepITE.

Intervention Target Estimation (ITE) is vital for both understanding and decision-making in complex systems, yet it remains underexplored.

Our primary focus is the identification of the latent structure in measurement models without parametric assumptions such as linearity or Gaussianity.

Often, observational data alone is not enough to uniquely identify a system's causal structure.

Other concurrent works address, e.g., learning from soft interventions with polynomial mixing [