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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., Comment: 23 pages, 5 figures

Inferring causal links or subgraphs corresponding to a specific phenotype or label based solely on measured data is an important yet challenging task, which is also different from inferring causal nodes. While Graph Neural Network (GNN) Explainers have shown potential in subgraph identification, existing methods with GNN often offer associative rather than causal insights. This lack of transparency and explainability hinders our understanding of their results and also underlying mechanisms. To address this issue, we propose a novel method of causal link/subgraph inference, called CIDER: Counterfactual-Invariant Diffusion-based GNN ExplaineR, by implementing both counterfactual and diffusion implementations. In other words, it is a model-agnostic and task-agnostic framework for generating causal explanations based on a counterfactual-invariant and diffusion process, which provides not only causal subgraphs due to counterfactual implementation but reliable causal links due to the diffusion process. Specifically, CIDER is first formulated as an inference task that generatively provides the two distributions of one causal subgraph and another spurious subgraph. Then, to enhance the reliability, we further model the CIDER framework as a diffusion process. Thus, using the causal subgraph distribution, we can explicitly quantify the contribution of each subgraph to a phenotype/label in a counterfactual manner, representing each subgraph's causal strength. From a causality perspective, CIDER is an interventional causal method, different from traditional association studies or observational causal approaches, and can also reduce the effects of unobserved confounders. We evaluate CIDER on both synthetic and real-world datasets, which all demonstrate the superiority of CIDER over state-of-the-art methods.

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. To address this challenge, we propose a framework named Interventional Dynamical Causality (IntDC) for such non-intervention systems, along with its computational criterion, Interventional Embedding Entropy (IEE), to quantify causality. The IEE criterion 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. Demonstrations of performance showed the accuracy and robustness of IEE on benchmark simulated systems as well as real-world systems, including the neural connectomes of C. elegans, COVID-19 transmission networks in Japan, and regulatory networks surrounding key circadian genes.

The Waddington landscape serves as a metaphor illustrating the developmental process of cells, likening it to a small ball rolling down various trajectories into valleys. Constructing an epigenetic landscape of this nature aids in visualizing and gaining insights into cell differentiation. Development encompasses intricate processes involving both cell differentiation and cell cycles. However, current landscape methods solely focus on constructing a potential landscape for cell differentiation, neglecting the accompanying cell cycle. This paper introduces a novel method that simultaneously constructs two types of potential landscapes using single-cell RNA sequencing data. Specifically, it presents the natural Helmholtz-Hodge decomposition (nHHD) of a continuous vector field within a bounded domain in n-dimensional Euclidean space. This decomposition uniquely breaks down the vector field into a gradient field, a rotation field, and a harmonic field. Utilizing this approach, the RNA velocity vector field is separated into a curl-free component representing cell differentiation and a curl component representing the cell cycle. By calculating the corresponding potential functions, potential landscapes for both cell differentiation and the cell cycle are obtained. Finally, the efficacy of this method is demonstrated through its application to synthetic and real datasets.

Making an accurate prediction of an unknown system only from a short-term time series is difficult due to the lack of sufficient information, especially in a multi-step-ahead manner. However, a high-dimensional short-term time series contains rich dynamical information, and also becomes increasingly available in many fields. In this work, by exploiting spatiotemporal information (STI) transformation scheme that transforms such high-dimensional/spatial information to temporal information, we developed a new method called MT-GPRMachine to achieve accurate prediction from a short-term time series. Specifically, we first construct a specific multi-task GPR which is multiple linked STI mappings to transform high dimensional/spatial information into temporal/dynamical information of any given target variable, and then makes multi step-ahead prediction of the target variable by solving those STI mappings. The multi-step-ahead prediction results on various synthetic and real-world datasets clearly validated that MT-GPRMachine outperformed other existing approaches.

Making predictions in a robust way is a difficult task only based on the observed data of a nonlinear system. In this work, a neural network computing framework, the spatiotemporal information conversion machine (STICM), was developed to efficiently and accurately render a multistep-ahead prediction of a time series by employing a spatial-temporal information (STI) transformation. STICM combines the advantages of both the STI equation and the temporal convolutional network, which maps the high-dimensional/spatial data to the future temporal values of a target variable, thus naturally providing the prediction of the target variable. From the observed variables, the STICM also infers the causal factors of the target variable in the sense of Granger causality, which are in turn selected as effective spatial information to improve the prediction robustness of time-series. The STICM was successfully applied to both benchmark systems and real-world datasets, all of which show superior and robust performance in multistep-ahead prediction, even when the data were perturbed by noise. From both theoretical and computational viewpoints, the STICM has great potential in practical applications in artificial intelligence (AI) or as a model-free method based only on the observed data, and also opens a new way to explore the observed high-dimensional data in a dynamical manner for machine learning., Comment: 28 pages, 6 figures

Given the existing COVID-19 pandemic worldwide, it is critical to systematically study the interactions between hosts and coronaviruses including SARS-Cov, MERS-Cov, and SARS-CoV-2 (cause of COVID-19). We first created four host-pathogen interaction (HPI)-Outcome postulates, and generated a HPI-Outcome model as the basis for understanding host-coronavirus interactions (HCI) and their relations with the disease outcomes. We hypothesized that ontology can be used as an integrative platform to classify and analyze HCI and disease outcomes. Accordingly, we annotated and categorized different coronaviruses, hosts, and phenotypes using ontologies and identified their relations. Various COVID-19 phenotypes are hypothesized to be caused by the backend HCI mechanisms. To further identify the causal HCI-outcome relations, we collected 35 experimentally-verified HCI protein-protein interactions (PPIs), and applied literature mining to identify additional host PPIs in response to coronavirus infections. The results were formulated in a logical ontology representation for integrative HCI-outcome understanding. Using known PPIs as baits, we also developed and applied a domain-inferred prediction method to predict new PPIs and identified their pathological targets on multiple organs. Overall, our proposed ontology-based integrative framework combined with computational predictions can be used to support fundamental understanding of the intricate interactions between human patients and coronaviruses (including SARS-CoV-2) and their association with various disease outcomes., Comment: 32 pages, 1 table, 6 figures

Natural systems are typically nonlinear and complex, and it is of great interest to be able to reconstruct a system in order to understand its mechanism, which can not only recover nonlinear behaviors but also predict future dynamics. Due to the advances of modern technology, big data becomes increasingly accessible and consequently the problem of reconstructing systems from measured data or time series plays a central role in many scientific disciplines. In recent decades, nonlinear methods rooted in state space reconstruction have been developed, and they do not assume any model equations but can recover the dynamics purely from the measured time series data. In this review, the development of state space reconstruction techniques will be introduced and the recent advances in systems prediction and causality inference using state space reconstruction will be presented. Particularly, the cutting-edge method to deal with short-term time series data will be focused. Finally, the advantages as well as the remaining problems in this field are discussed., Comment: 19 pages, 9 figures, it has been accepted for publication in SCIENCE CHINA Mathematics