Jifan Shi

Jinling Yan, Shao-Wu Zhang, Chihao Zhang et al.

Causality inference is prone to spurious causal interactions, due to the substantial confounders in a complex system. While many existing methods based on the statistical methods or dynamical methods attempt to address misidentification challenges, there remains a notable lack of effective methods to infer causality, in particular in the presence of invisible/unobservable confounders. As a result, accurately inferring causation with invisible confounders remains a largely unexplored and outstanding issue in data science and AI fields. In this work, we propose a method to overcome such challenges to infer dynamical causality under invisible confounders (CIC method) and further reconstruct the invisible confounders from time-series data by developing an orthogonal decomposition theorem in a delay embedding space. The core of our CIC method lies in its ability to decompose the observed variables not in their original space but in their delay embedding space into the common and private subspaces respectively, thereby quantifying causality between those variables both theoretically and computationally. This theoretical foundation ensures the causal detection for any high-dimensional system even with only two observed variables under many invisible confounders, which is actually a long-standing problem in the field. In addition to the invisible confounder problem, such a decomposition actually makes the intertwined variables separable in the embedding space, thus also solving the non-separability problem of causal inference. Extensive validation of the CIC method is carried out using various real datasets, and the experimental results demonstrates its effectiveness to reconstruct real biological networks even with unobserved confounders.

Jianyang Gao, Yutong Gou, Yuexuan Xu et al.

This technical note revisits the relationship between RaBitQ and TurboQuant under a unified comparison framework. We compare the two methods in terms of methodology, theoretical guarantees, and empirical performance, using a reproducible, transparent, and symmetric setup. Our results show that, despite the claimed advantage of TurboQuant, TurboQuant does not provide a consistent improvement over RaBitQ in directly comparable settings; in many tested configurations, it performs worse than RaBitQ. We further find that several reported runtime and recall results in the TurboQuant paper could not be reproduced from the released implementation under the stated configuration. Overall, this note clarifies the shared structure and genuine differences between the two lines of work, while documenting reproducibility issues in the experimental results reported by the TurboQuant paper.

Zijian Wang, Peng Tao, Jifan Shi et al.

This study introduces Universal Delay Embedding (UDE), a pretrained foundation model designed to revolutionize time-series forecasting through principled integration of delay embedding representation and Koopman operator prediction. Leveraging Takens' embedding theorem, UDE as a dynamical representation of observed data constructs two-dimensional subspace patches from Hankel matrices, theoretically preserving dynamical and topological properties of underlying dynamical systems. Such patches are viewed as images, which can be efficiently processed by exploiting advanced deep learning technologies. Computationally, these patches further serve as tokens for learning a self-attention encoder, thus enabling accurate prediction of nonlinear time-series by a finite-dimensional Koopman operator in a linear manner in a latent space. Extensive evaluations across various benchmarks and real-world climate datasets demonstrate over 20% average reduction in mean squared error versus state-of-the-art foundation models, alongside superior generalization in fine-tuning scenarios. In particular, the learned dynamical representations and Koopman operator prediction forms from the patches exhibit exceptional interpretability, with consistent identification of topologically informative subspaces and robust encoding of domain-invariant dynamics, establishing UDE as a scalable, interpretable framework for universal time-series modeling and forecasting with broad scientific and industrial applicability.

Shirui Bian, Zezhou Wang, Siyang Leng et al.

Early-warning signals of delicate design are always used to predict critical transitions in complex systems, which makes it possible to render the systems far away from the catastrophic state by introducing timely interventions. Traditional signals including the dynamical network biomarker (DNB), based on statistical properties such as variance and autocorrelation of nodal dynamics, overlook directional interactions and thus have limitations in capturing underlying mechanisms and simultaneously sustaining robustness against noise perturbations. This paper therefore introduces a framework of causal network markers (CNMs) by incorporating causality indicators, which reflect the directional influence between variables. Actually, to detect and identify the tipping points ahead of critical transition, two markers are designed: CNM-GC for linear causality and CNM-TE for non-linear causality, as well as a functional representation of different causality indicators and a clustering technique to verify the system's dominant group. Through demonstrations using benchmark models and real-world datasets of epileptic seizure, the framework of CNMs shows higher predictive power and accuracy than the traditional DNB indicator. It is believed that, due to the versatility and scalability, the CNMs are suitable for comprehensively evaluating the systems. The most possible direction for application includes the identification of tipping points in clinical disease.

Jifan Shi, Yang Li, Juan Zhao et al.

Detecting and quantifying causality is a focal topic in the fields of science, engineering, and interdisciplinary studies. However, causal studies on non-intervention systems attract much attention but remain extremely challenging. Delay-embedding technique provides a promising approach. In this study, we propose a framework named Interventional Dynamical Causality (IntDC) in contrast to the traditional Constructive Dynamical Causality (ConDC). ConDC, including Granger causality, transfer entropy and convergence of cross-mapping, measures the causality by constructing a dynamical model without considering interventions. A computational criterion, Interventional Embedding Entropy (IEE), is proposed to measure causal strengths in an interventional manner. IEE is an intervened causal information flow but in the delay-embedding space. Further, the IEE theoretically and numerically enables the deciphering of IntDC solely from observational (non-interventional) time-series data, without requiring any knowledge of dynamical models or real interventions in the considered system. In particular, IEE can be applied to rank causal effects according to their importance and construct causal networks from data. We conducted numerical experiments to demonstrate that IEE can find causal edges accurately, eliminate effects of confounding, and quantify causal strength robustly over traditional indices. We also applied IEE to real-world tasks. IEE performed as an accurate and robust tool for causal analyses solely from the observational data. The IntDC framework and IEE algorithm provide an efficient approach to the study of causality from time series in diverse non-intervention complex systems.