Estimating causal quantities from observational data is crucial for understanding the safety and effectiveness of medical treatments. However, to make reliable inferences, medical practitioners require not only estimating averaged causal quantities, such as the conditional average treatment effect, but also understanding the randomness of the treatment effect as a random variable. This randomness is referred to as aleatoric uncertainty and is necessary for understanding the probability of benefit from treatment or quantiles of the treatment effect. Yet, the aleatoric uncertainty of the treatment effect has received surprisingly little attention in the causal machine learning community. To fill this gap, we aim to quantify the aleatoric uncertainty of the treatment effect at the covariate-conditional level, namely, the conditional distribution of the treatment effect (CDTE).

In this work, we address risk-averse Bayes-adaptive reinforcement learning. We pose the problem of optimising the conditional value at risk (CVaR) of the total return in Bayes-adaptive Markov decision processes (MDPs). We show that a policy optimising CVaR in this setting is risk-averse to both the epistemic uncertainty due to the prior distribution over MDPs, and the aleatoric uncertainty due to the inherent stochasticity of MDPs. We reformulate the problem as a two-player stochastic game and propose an approximate algorithm based on Monte Carlo tree search and Bayesian optimisation. Our experiments demonstrate that our approach significantly outperforms baseline approaches for this problem.

In-context learning enables transformers to adapt to new tasks from a few examples at inference time, while grokking highlights that this generalization can emerge abruptly only after prolonged training. We study task generalization and grokking in in-context learning using a Bayesian perspective, asking what enables the delayed transition from memorization to generalization. Concretely, we consider modular arithmetic tasks in which a transformer must infer a latent linear function solely from in-context examples and analyze how predictive uncertainty evolves during training. We combine approximate Bayesian techniques to estimate the posterior distribution and we study how uncertainty behaves across training and under changes in task diversity, context length, and context noise. We find that epistemic uncertainty collapses sharply when the model groks, making uncertainty a practical label-free diagnostic of generalization in transformers. Additionally, we provide theoretical support with a simplified Bayesian linear model, showing that asymptotically both delayed generalization and uncertainty peaks arise from the same underlying spectral mechanism, which links grokking time to uncertainty dynamics.

Estimating and disentangling epistemic uncertainty, uncertainty that is reducible with more training data, and aleatoric uncertainty, uncertainty that is inherent to the task at hand, is critically important when applying machine learning to high-stakes applications such as medical imaging and weather forecasting. Conditional diffusion models' breakthrough ability to accurately and efficiently sample from the posterior distribution of a dataset now makes uncertainty estimation conceptually straightforward: One need only train and sample from a large ensemble of diffusion models. Unfortunately, training such an ensemble becomes computationally intractable as the complexity of the model architecture grows. In this work we introduce a new approach to ensembling, hyper-diffusion models (HyperDM), which allows one to accurately estimate both epistemic and aleatoric uncertainty with a single model. Unlike existing single-model uncertainty methods like Monte-Carlo dropout and Bayesian neural networks, HyperDM offers prediction accuracy on par with, and in some cases superior to, multi-model ensembles. Furthermore, our proposed approach scales to modern network architectures such as Attention U-Net and yields more accurate uncertainty estimates compared to existing methods.

We study post-calibration uncertainty for trained ensembles of classifiers. Specifically, we consider both aleatoric (label noise) and epistemic (model) uncertainty. Among the most popular and widely used calibration methods in classification are temperature scaling (i.e., pool-then-calibrate) and conformal methods. However, the main shortcoming of these calibration methods is that they do not balance the proportion of aleatoric and epistemic uncertainty. Not balancing these uncertainties can severely misrepresent predictive uncertainty, leading to overconfident predictions in some input regions while being underconfident in others. To address this shortcoming, we present a simple but powerful calibration algorithm Joint Uncertainty Calibration (JUCAL) that jointly calibrates aleatoric and epistemic uncertainty. JUCAL jointly calibrates two constants to weight and scale epistemic and aleatoric uncertainties by optimizing the negative log-likelihood (NLL) on the validation/calibration dataset. JUCAL can be applied to any trained ensemble of classifiers (e.g., transformers, CNNs, or tree-based methods), with minimal computational overhead, without requiring access to the models' internal parameters. We experimentally evaluate JUCAL on various text classification tasks, for ensembles of varying sizes and with different ensembling strategies. Our experiments show that JUCAL significantly outperforms SOTA calibration methods across all considered classification tasks, reducing NLL and predictive set size by up to 15% and 20%, respectively. Interestingly, even applying JUCAL to an ensemble of size 5 can outperform temperature-scaled ensembles of size up to 50 in terms of NLL and predictive set size, resulting in up to 10 times smaller inference costs. Thus, we propose JUCAL as a new go-to method for calibrating ensembles in classification.

Stochastic simulation is widely used to study complex systems composed of various interconnected subprocesses, such as input processes, routing and control logic, optimization routines, and data-driven decision modules. In practice, these subprocesses may be inherently unknown or too computationally intensive to directly embed in the simulation model. Replacing these elements with estimated or learned approximations introduces a form of epistemic uncertainty that we refer to as submodel uncertainty. This paper investigates how submodel uncertainty affects the estimation of system performance metrics. We develop a framework for quantifying submodel uncertainty in stochastic simulation models and extend the framework to digital-twin settings, where simulation experiments are repeatedly conducted with the model initialized from observed system states. Building on approaches from input uncertainty analysis, we leverage bootstrapping and Bayesian model averaging to construct quantile-based confidence or credible intervals for key performance indicators. We propose a tree-based method that decomposes total output variability and attributes uncertainty to individual submodels in the form of importance scores. The proposed framework is model-agnostic and accommodates both parametric and nonparametric submodels under frequentist and Bayesian modeling paradigms. A synthetic numerical experiment and a more realistic digital-twin simulation of a contact center illustrate the importance of understanding how and how much individual submodels contribute to overall uncertainty.

However, the design of methods for learning credal set predictors remains a challenging problem. In this paper, we make use of conformal prediction for this purpose.