Here the concept of Granger causality is employed to propose a new criterion for unsupervised learning that is appropriate in the case of temporally-dependent source signals. The basic idea is to identify two projections of a multivariate time series such that the Granger causality among the resulting pair of components is maximized.

The achievement of the 2030 Sustainable Development Goals (SDGs) is dependent upon strategic resource distribution. We propose a causal discovery framework using Panel Vector Autoregression, along with both country-specific fixed effects and PCMCI+ conditional independence testing on 168 countries (2000-2025) to develop the first complete causal architecture of SDG dependencies. Utilizing 8 strategically chosen SDGs, we identify a distributed causal network (i.e., no single 'hub' SDG), with 10 statistically significant Granger-causal relationships identified as 11 unique direct effects. Education to Inequality is identified as the most statistically significant direct relationship (r = -0.599; p < 0.05), while effect magnitude significantly varies depending on income levels (e.g., high-income: r = -0.65; lower-middle-income: r = -0.06; non-significant). We also reject the idea that there exists a single 'keystone' SDG. Additionally, we offer a proposed tiered priority framework for the SDGs namely, identifying upstream drivers (Education, Growth), enabling goals (Institutions, Energy), and downstream outcomes (Poverty, Health). Therefore, we conclude that effective SDG acceleration can be accomplished through coordinated multi-dimensional intervention(s), and that single-goal sequential strategies are insufficient.

Understanding causal relationships between time series variables is a fundamental problem in economics, finance, neuroscience, and many other fields. While true causality is philosophically complex and difficult to establish from observational data alone, Granger (1969) proposed a practical, testable notion of causality based on predictability: a variable X is said to "Granger-cause" another variable Y if past values of X contain information that helps predict Y beyond what is contained in past values of Y alone. Granger causality testing has found applications across diverse domains. In macroeconomics, Sims (1972) famously applied the technique to study money-income relationships, while Kraft and Kraft (1978) pioneered its use in energy economics. Financial market researchers including Hiemstra and Jones (1994) have extended the methodology to study price-volume dynamics, and neuroscientists have adapted Granger causality for brain connectivity analysis (Seth, Barrett, and Barnett 2015). The statistical foundations rest on vector autoregressive (V AR) models (Sims 1980), with comprehensive treatments available in Lütkepohl (2005) and discussions of causal interpretation in Peters, Janzing, and Schölkopf (2017). Despite its popularity, implementing Granger causality tests in R (R Core Team 2024) remains cumbersome for applied researchers.

Causal discovery with time series data remains a challenging yet increasingly important task across many scientific domains. Convergent cross mapping (CCM) and related methods have been proposed to study time series that are generated by dynamical systems, where traditional approaches like Granger causality are unreliable. However, CCM often yields inaccurate results depending upon the quality of the data. We propose the Tangent Space Causal Inference (TSCI) method for detecting causalities in dynamical systems. TSCI works by considering vector fields as explicit representations of the systems' dynamics and checks for the degree of synchronization between the learned vector fields. The TSCI approach is model-agnostic and can be used as a drop-in replacement for CCM and its generalizations. We first present a basic version of the TSCI algorithm, which is shown to be more effective than the basic CCM algorithm with very little additional computation.

Video causal reasoning aims to achieve a high-level understanding of video content from a causal perspective. However, current video reasoning tasks are limited in scope, primarily executed in a question-answering paradigm and focusing on short videos containing only a single event and simple causal relationships, lacking comprehensive and structured causality analysis for videos with multiple events. To fill this gap, we introduce a new task and dataset, Multi-Event Causal Discovery (MECD). It aims to uncover the causal relationships between events distributed chronologically across long videos. Given visual segments and textual descriptions of events, MECD requires identifying the causal associations between these events to derive a comprehensive, structured event-level video causal diagram explaining why and how the final result event occurred. To address MECD, we devise a novel framework inspired by the Granger Causality method, using an efficient mask-based event prediction model to perform an Event Granger Test, which estimates causality by comparing the predicted result event when premise events are masked versus unmasked. Furthermore, we integrate causal inference techniques such as front-door adjustment and counterfactual inference to address challenges in MECD like causality confounding and illusory causality.

Counterfactual explanations promote explainability in machine learning models by answering the question "how should the input instance be altered to obtain a desired predicted label?. The comparison of this instance before and after perturbation can enhance human interpretation. Most existing studies on counterfactual explanations are limited in tabular data or image data. In this paper, we study the problem of counterfactual explanation generation on graphs. A few studies have explored to generate counterfactual explanations on graphs, but many challenges of this problem are still not well-addressed: 1) optimizing in the discrete and disorganized space of graphs; 2) generalizing on unseen graphs; 3) maintaining the causality in the generated counterfactuals without prior knowledge of the causal model. To tackle these challenges, we propose a novel framework CLEAR which aims to generate counterfactual explanations on graphs for graph-level prediction models. Specifically, CLEAR leverages a graph variational autoencoder based mechanism to facilitate its optimization and generalization, and promotes causality by leveraging an auxiliary variable to better identify the causal model.

Hierarchical reinforcement learning (HRL) has been proven to be effective for tasks with sparse rewards, for it can improve the agent's exploration efficiency by discovering high-quality hierarchical structures (e.g., subgoals or options). However, automatically discovering high-quality hierarchical structures is still a great challenge. Previous HRL methods can only find the hierarchical structures in simple environments, as they are mainly achieved through the randomness of agent's policies during exploration. In complicated environments, such a randomness-driven exploration paradigm can hardly discover high-quality hierarchical structures because of the low exploration efficiency. In this paper, we propose CDHRL, a causality-driven hierarchical reinforcement learning framework, to build high-quality hierarchical structures efficiently in complicated environments. The key insight is that the causalities among environment variables are naturally fit for modeling reachable subgoals and their dependencies; thus, the causality is suitable to be the guidance in building high-quality hierarchical structures. Roughly, we build the hierarchy of subgoals based on causality autonomously, and utilize the subgoal-based policies to unfold further causality efficiently.

Extracting the interaction rules of biological agents from movement sequences pose challenges in various domains. Granger causality is a practical framework for analyzing the interactions from observed time-series data; however, this framework ignores the structures and assumptions of the generative process in animal behaviors, which may lead to interpretational problems and sometimes erroneous assessments of causality. In this paper, we propose a new framework for learning Granger causality from multi-animal trajectories via augmented theory-based behavioral models with interpretable data-driven models. We adopt an approach for augmenting incomplete multi-agent behavioral models described by time-varying dynamical systems with neural networks. For efficient and interpretable learning, our model leverages theory-based architectures separating navigation and motion processes, and the theory-guided regularization for reliable behavioral modeling. This can provide interpretable signs of Granger-causal effects over time, i.e., when specific others cause the approach or separation. In experiments using synthetic datasets, our method achieved better performance than various baselines. We then analyzed multi-animal datasets of mice, flies, birds, and bats, which verified our method and obtained novel biological insights.