As machine learning (ML) algorithms are increasingly used in medical image analysis, concerns have emerged about their potential biases against certain social groups. Although many approaches have been proposed to ensure the fairness of ML models, most existing works focus only on medical image diagnosis tasks, such as image classification and segmentation, and overlooked prognosis scenarios, which involve predicting the likely outcome or progression of a medical condition over time. To address this gap, we introduce FairTTE, the first comprehensive framework for assessing fairness in time-to-event (TTE) prediction in medical imaging. FairTTE encompasses a diverse range of imaging modalities and TTE outcomes, integrating cutting-edge TTE prediction and fairness algorithms to enable systematic and fine-grained analysis of fairness in medical image prognosis. Leveraging causal analysis techniques, FairTTE uncovers and quantifies distinct sources of bias embedded within medical imaging datasets. Our large-scale evaluation reveals that bias is pervasive across different imaging modalities and that current fairness methods offer limited mitigation. We further demonstrate a strong association between underlying bias sources and model disparities, emphasizing the need for holistic approaches that target all forms of bias. Notably, we find that fairness becomes increasingly difficult to maintain under distribution shifts, underscoring the limitations of existing solutions and the pressing need for more robust, equitable prognostic models.

Causal mediation analysis is crucial for deconstructing complex mechanisms of action. However, in current mediation analysis, complex structures derived from causal discovery lack direct interpretation of mediation pathways, while traditional mediation analysis and effect estimation are limited by the reliance on pre-specified pathways, leading to a disconnection between structure discovery and causal mechanism understanding. Therefore, a unified framework integrating structure discovery, pathway identification, and effect estimation systematically quantifies mediation pathways under structural uncertainty, enabling automated identification and inference of mediation pathways. To this end, we propose Structure-Informed Guided Mediation Analysis (SIGMA), which guides automated mediation pathway identification through probabilistic causal structure discovery and uncertainty quantification, enabling end-to-end propagation of structural uncertainty from structure learning to effect estimation. Specifically, SIGMA employs differentiable Flow-Structural Equation Models to learn structural posteriors, generating diverse Directed Acyclic Graphs (DAGs) to quantify structural uncertainty. Based on these DAGs, we introduce the Path Stability Score to evaluate the marginal probability of pathways, identifying high-confidence mediation paths. For identified mediation pathways, we integrate Efficient Influence Functions with Bayesian model averaging to fuse within-structure estimation uncertainty and between-structure effect variation, propagating uncertainty to the final effect estimates. In synthetic data experiments, SIGMA achieves state-of-the-art performance in pathway identification accuracy and effect quantification precision under structural uncertainty, concurrent multiple pathways, and nonlinear scenarios. In real-world applications using Human Phenotype Project data, SIGMA identifies mediation effects of sleep quality on cardiovascular health through inflammatory and metabolic pathways, uncovering previously unspecified multiple mediation paths.

Accurate network estimation serves as the cornerstone for understanding complex systems across scientific domains, from decoding gene regulatory networks in systems biology to identifying social relationship patterns in computational sociology. Modern applications demand methods that simultaneously address two critical challenges: capturing nonlinear dependencies between variables and reconstructing inherent hierarchical structures where higher-level entities coordinate lower-level components (e.g., functional pathways organizing gene clusters). Traditional Gaussian graphical models fundamentally fail in these aspects due to their restrictive linear assumptions and flat network representations. We propose NNBLNet, a neural network-based learning framework for bi-level network inference. The core innovation lies in hierarchical selection layers that enforce structural consistency between high-level coordinator groups and their constituent low-level connections via adaptive sparsity constraints. This architecture is integrated with a compositional neural network architecture that learn cross-level association patterns through constrained nonlinear transformations, explicitly preserving hierarchical dependencies while overcoming the representational limitations of linear methods. Crucially, we establish formal theoretical guarantees for the consistent recovery of both high-level connections and their internal low-level structures under general statistical regimes. Extensive validation demonstrates NNBLNet's effectiveness across synthetic and real-world scenarios, achieving superior F1 scores compared to competitive methods and particularly beneficial for complex systems analysis through its interpretable bi-level structure discovery.

The brain is made up of a vast set of heterogeneous regions that dynamically organize into pathways as a function of task demands. Examples of such pathways can be found in the interactions between cortical and subcortical networks during learning, or in sub-networks specializing for task characteristics such as difficulty or modality. Despite the large role these pathways play in cognition, the mechanisms through which brain regions organize into pathways remain unclear. In this work, we use an extension of the Heterogeneous Mixture-of-Experts architecture to show that heterogeneous regions do not form processing pathways by themselves, implying that the brain likely implements specific constraints which result in the reliable formation of pathways. We identify three biologically relevant inductive biases that encourage pathway formation: a routing cost imposed on the use of more complex regions, a scaling factor that reduces this cost when task performance is low, and randomized expert dropout. When comparing our resulting Mixtureof-Pathways model with the brain, we observe that the artificial pathways in our model match how the brain uses cortical and subcortical systems to learn and solve tasks of varying difficulty. In summary, we introduce a novel framework for investigating how the brain forms task-specific pathways through inductive biases, and the effects these biases have on the behavior of Mixture-of-Experts models.

Despite the promising results of disentangled representation learning in discovering latent patterns in graph-structured data, few studies have explored disentanglement for hypergraph-structured data. Integrating hyperedge disentanglement into hypergraph neural networks enables models to leverage hidden hyperedge semantics, such as unannotated relations between nodes, that are associated with labels. This paper presents an analysis of hyperedge disentanglement from a categorytheoretical perspective and proposes a novel criterion for disentanglement derived from the naturality condition. Our proof-of-concept model experimentally showed the potential of the proposed criterion by successfully capturing functional relations of genes (nodes) in genetic pathways (hyperedges).

Visual reinforcement learning has shown promise in various real-world applications. However, deploying policies in complex real-world environments with visual perturbations remains a significant challenge. We notice that humans tend to filter information at the object level prior to decision-making, facilitating efficient skill transfer across different contexts. Inspired by this, we introduce Focus-ThenReuse (FTR), a method utilizing a novel object selection mechanism to focus on task-relevant objects, and directly reuse the simulation-trained policy on them.

Causal mediation analysis is crucial for deconstructing complex mechanisms of action. However, in current mediation analysis, complex structures derived from causal discovery lack direct interpretation of mediation pathways, while traditional mediation analysis and effect estimation are limited by the reliance on pre-specified pathways, leading to a disconnection between structure discovery and causal mechanism understanding. Therefore, a unified framework integrating structure discovery, pathway identification, and effect estimation systematically quantifies mediation pathways under structural uncertainty, enabling automated identification and inference of mediation pathways. To this end, we propose Structure-Informed Guided Mediation Analysis (SIGMA), which guides automated mediation pathway identification through probabilistic causal structure discovery and uncertainty quantification, enabling end-to-end propagation of structural uncertainty from structure learning to effect estimation. Specifically, SIGMA employs differentiable Flow-Structural Equation Models to learn structural posteriors, generating diverse Directed Acyclic Graphs (DAGs) to quantify structural uncertainty. Based on these DAGs, we introduce the Path Stability Score to evaluate the marginal probability of pathways, identifying high-confidence mediation paths. For identified mediation pathways, we integrate Efficient Influence Functions with Bayesian model averaging to fuse within-structure estimation uncertainty and between-structure effect variation, propagating uncertainty to the final effect estimates. In synthetic data experiments, SIGMA achieves state-of-the-art performance in pathway identification accuracy and effect quantification precision under structures uncertainty, concurrent multiple pathways, and nonlinear scenarios. In real-world applications using Human Phenotype Project data, SIGMA identifies mediation effects of sleep quality on cardiovascular health through inflammatory and metabolic pathways, uncovering previously unspecified multiple mediation paths.

Alzheimer's disease (AD) is marked by cognitive decline along with the widespread of tau aggregates across the brain cortex. Due to the challenges of imaging pathology spreading flows \textit{in vivo}, however, quantitative analysis on the cortical pathways of tau propagation and its interaction with the cascade of amyloid-beta (A$\beta$) plaques lags behind the experimental insights of underlying pathophysiological mechanisms. To address this challenge, we present a physics-informed neural network, empowered by mean-field theory, to uncover the biologically meaningful spreading pathways of tau aggregates between two longitudinal snapshots. Following the notion of `prion-like' mechanism in AD, we first formulate the dynamics of tau propagation as a mean-field game (MFG), where the spread of tau aggregate at each location (aka.

Automated systems built on artificial intelligence (AI) are increasingly deployed across high-stakes domains, raising critical concerns about fairness and the perpetuation of demographic disparities that exist in the world. In this context, causal inference provides a principled framework for reasoning about fairness, as it links observed disparities to underlying mechanisms and aligns naturally with human intuition and legal notions of discrimination. Prior work on causal fairness primarily focuses on the standard machine learning setting, where a decision-maker constructs a single predictive mechanism $f_{\widehat Y}$ for an outcome variable $Y$, while inheriting the causal mechanisms of all other covariates from the real world. The generative AI setting, however, is markedly more complex: generative models can sample from arbitrary conditionals over any set of variables, implicitly constructing their own beliefs about all causal mechanisms rather than learning a single predictive function. This fundamental difference requires new developments in causal fairness methodology. We formalize the problem of causal fairness in generative AI and unify it with the standard ML setting under a common theoretical framework. We then derive new causal decomposition results that enable granular quantification of fairness impacts along both (a) different causal pathways and (b) the replacement of real-world mechanisms by the generative model's mechanisms. We establish identification conditions and introduce efficient estimators for causal quantities of interest, and demonstrate the value of our methodology by analyzing race and gender bias in large language models across different datasets.

Mediation analysis (Robins & Greenland 1992, Pearl 2001, Imai, Keele & Tingley 2010, Tchetgen Tchetgen & Shpitser 2012) provides a principled framework for investigating causal mechanisms by decomposing the effect of a treatment A on an outcome Y into pathways operating through a mediator of interest M. Classical mediation analysis focuses on the natural indirect effect, corresponding to the pathway from Ato Y through M, and the natural direct effect, corresponding to pathways not through M. These estimands are well understood when a single mediator is present and strong identification assumptions hold. However, in many applications, there exist multiple intermediate variables between treatment and outcome. In such settings, conventional mediation analysis typically requires the absence of treatment-induced mediator-outcome confounders--often referred to as recanting witnesses--as well as the absence of unmeasured confounding. Under these circumstances, commonly used identification assumptions such as sequential ignorability (Imai, Keele & Yamamoto 2010) or nonparametric structural equation models with independent errors (NPSEM-IE) (Pearl 2009) no longer suffice to identify natural indirect effects (Avin et al. 2005, Tchetgen Tchetgen & VanderWeele 2014). Figure 1 illustrates this issue: the recanting witness D is directly affected by A and simultaneously confounds the relationship between M and Y. Such treatment-induced confounding is common in epidemiologic studies, particularly when the mediator of interest occurs long after the treatment initiation (Robins 1999). A motivating example arises in studies of preterm birth. Mediation analysis has been widely used to explore whether adequate prenatal care (A) reduces the risk of preterm birth (Y) through preeclampsia (M) (Vansteelandt & VanderWeele 2012, VanderWeele et al. 2014, Xia & Chan 2023).