Most traditional causal discovery methods assume that all task-relevant variables are observed, an assumption often violated in practice. Although some recent works allow the presence of latent variables, they typically assume the absence of certain special causal relations to ensure a degree of simplicity, which might also be invalid in real-world scenarios. This paper tackles a challenging and important setting where latent and observed variables are interconnected through complex causal relations. Under a pure children assumption ensuring that latent variables leave adequate footprints in observed variables, we develop novel theoretical results, leading to an efficient causal discovery algorithm which is the first one capable of handling the setting with both latent variables and complex relations within polynomial time. Our algorithm first sequentially identifies latent variables from leaves to roots and then sequentially infers causal relations from roots to leaves. Moreover, we prove trustworthiness of our algorithm, meaning that when the assumption is invalid, it can raise an error signal rather than draw an incorrect causal conclusion, thus preventing potential damage to downstream tasks. We demonstrate the efficacy of our algorithm through experiments. Our work significantly enhances efficiency and reliability of causal discovery in complex systems. Our code is available at: https://github.com/XiuchuanLi/ICLR2025-ETCD

Causal discovery with latent variables is an important and challenging problem. To identify latent variables and infer their causal relations, most existing works rely on the assumption that latent variables have pure children. Considering that this assumption is potentially restrictive in practice and not strictly necessary in theory, in this paper, by introducing the concept of homologous surrogate, we eliminate the need for pure children in the context of causal discovery with latent variables. The homologous surrogate fundamentally differs from the pure child in the sense that the latter is characterized by having strictly restricted parents while the former allows for much more flexible parents. We formulate two assumptions involving homologous surrogates and develop theoretical results under each assumption. Under the weaker assumption, our theoretical results imply that we can determine each variable's ancestors, that is, partially recover the causal graph. The stronger assumption further enables us to determine each variable's parents exactly, that is, fully recover the causal graph. Building on these theoretical results, we derive an algorithm that fully leverages the properties of homologous surrogates for causal graph recovery. Also, we validate its efficacy through experiments. Our work broadens the applicability of causal discovery. Our code is available at: https://github.com/XiuchuanLi/ICLR2025-CDHS

Traditional causal discovery approaches typically assume the absence of latent variables, a simplification that often does not align with real-world situations. Recently, there has been a surge of causal discovery methods that explicitly consider latent variables. While some works aim to reveal causal relations between observed variables in the presence of latent variables, others seek to identify latent variables and recover the causal structure over them. The latter typically entail strong distributional and graphical assumptions, such as the non-Gaussianity, purity, and two-pure-children assumption. In this paper, we endeavor to recover the whole causal structure involving both latent and observed variables under milder assumptions. We formulate two cases, one allows entirely arbitrary distribution and requires only one pure child per latent variable, and the other requires no pure child and imposes the non-Gaussianity requirement on only a subset of variables, and they both avoid the purity assumption. We prove the identifiability of linear latent variable models in both cases, and our constructive proof leads to theoretically sound and computationally efficient algorithms.

It has been widely observed that deep neural networks are highly vulnerable to adversarial examples. Decision-based attacks could generate adversarial examples based solely on top-1 labels returned by the target model. However, they typically make excessive queries and could not bypass detection effectively. To comprehensively assess a decision-based attack, besides its query efficiency, the performance against detection is also a concern. Considering that previous detections consume massive resources and always mistakenly recognize benign video frames as malicious attacks, we design a lightweight detection calledboundary detectionto overcome the above limitations, whose success reveals serious limitations of existing decision-based attacks. To develop more powerful attacks, we first presentf-mixupas a basic method to produce candidate adversarial examples in the frequency domain. Usingf-mixupas the building block, we proposef-attackas a complete decision-based attack. With the help of several natural images,f-attackcould both work well with limited (hundreds of) queries and bypass detection effectively. Nevertheless, if the attacker could make relatively adequate (thousands of) queries and the target model is not equipped with detection,f-attackwill lag behind existing decision-based attacks. We additionally introducefrequency binary searchbased onf-mixup, which serves as a plug-and-play module for existing decision-based attacks to further improve their query efficiency. Experimental results verify the effectiveness of our proposed methods.

Recent research has revealed that deep neural networks are highly vulnerable to adversarial examples. In this paper, different from most adversarial attacks which directly modify pixels in spatial domain, we propose a novel black-box attack in frequency domain, named as f-mixup, based on the property of natural images and perception disparity between human-visual system (HVS) and convolutional neural networks (CNNs): First, natural images tend to have the bulk of their Fourier spectrums concentrated on the low frequency domain; Second, HVS is much less sensitive to high frequencies while CNNs can utilize both low and high frequency information to make predictions. Extensive experiments are conducted and show that deeper CNNs tend to concentrate more on the higher frequency domain, which may explain the contradiction between robustness and accuracy. In addition, we compared f-mixup with existing attack methods and observed that our approach possesses great advantages. Finally, we show that f-mixup can be also incorporated in training to make deep CNNs defensible against a kind of perturbations effectively.