Predicting counterfactual outcomes in longitudinal data, where sequential treatment decisions heavily depend on evolving patient states, is critical yet notoriously challenging due to complex time-dependent confounding and inadequate uncertainty quantification in existing methods. We introduce the Causal Diffusion Model (CDM), the first denoising diffusion probabilistic approach explicitly designed to generate full probabilistic distributions of counterfactual outcomes under sequential interventions. CDM employs a novel residual denoising architecture with relational self-attention, capturing intricate temporal dependencies and multimodal outcome trajectories without requiring explicit adjustments (e.g., inverse-probability weighting or adversarial balancing) for confounding. In rigorous evaluation on a pharmacokinetic-pharmacodynamic tumor-growth simulator widely adopted in prior work, CDM consistently outperforms state-of-the-art longitudinal causal inference methods, achieving a 15-30% relative improvement in distributional accuracy (1-Wasserstein distance) while maintaining competitive or superior point-estimate accuracy (RMSE) under high-confounding regimes. By unifying uncertainty quantification and robust counterfactual prediction in complex, sequentially confounded settings, without tailored deconfounding, CDM offers a flexible, high-impact tool for decision support in medicine, policy evaluation, and other longitudinal domains.

Sparse identification of nonlinear dynamics (SINDy) has been widely used to discover the governing equations of a dynamical system from data. It uses sparse regression techniques to identify parsimonious models of unknown systems from a library of candidate functions. Therefore, it relies on the assumption that the dynamics are sparsely represented in the coordinate system used. To address this limitation, one seeks a coordinate transformation that provides reduced coordinates capable of reconstructing the original system. Recently, SINDy autoencoders have extended this idea by combining sparse model discovery with autoencoder architectures to learn simplified latent coordinates together with parsimonious governing equations. A central challenge in this framework is robustness to measurement error. Inspired by noise-separating neural network structures, we incorporate a noise-separation module into the SINDy autoencoder architecture, thereby improving robustness and enabling more reliable identification of noisy dynamical systems. Numerical experiments on the Lorenz system show that the proposed method recovers interpretable latent dynamics and accurately estimates the measurement noise from noisy observations.

As such, we prevent policies from merely exploiting heuristic rewards without improving the task reward.

Reinforcement Learning from Human Feedback (RLHF) has recently surged in popularity, particularly for aligning large language models and other AI systems with human intentions. At its core, RLHF can be viewed as a specialized instance of Preference-based Reinforcement Learning (PbRL), where the preferences specifically originate from human judgments rather than arbitrary evaluators. Despite this connection, most existing approaches in both RLHF and PbRL primarily focus on optimizing a mean reward objective, neglecting scenarios that necessitate risk-awareness, such as AI safety, healthcare, and autonomous driving. These scenarios often operate under a one-episode-reward setting, which makes conventional risk-sensitive objectives inapplicable.

Injective multiset functions have a key role in the theoretical study of machine learning on multisets and graphs.

However, such pessimism for out-of-sample data could be too restricted and sample inefficient, as not all out-of-sample(unseen) states are not generalizable [20].