Distances between probability distributions are a key component of many statistical machine learning tasks, from two-sample testing to generative modeling, among others. We introduce a novel distance between measures that compares them through a Schatten norm of their kernel covariance operators. We show that this new distance is an integral probability metric that can be framed between a Maximum Mean Discrepancy (MMD) and a Wasserstein distance. In particular, we show that it avoids some pitfalls of MMD, by being more discriminative and robust to the choice of hyperparameters. Moreover, it benefits from some compelling properties of kernel methods, that can avoid the curse of dimensionality for their sample complexity. We provide an algorithm to compute the distance in practice by introducing an extension of kernel matrix for difference of distributions that could be of independent interest. Those advantages are illustrated by robust approximate Bayesian computation under contamination as well as particle flow simulations.

Assisting medical students with clinical reasoning (CR) during clinical scenario training remains a persistent challenge in medical education. This paper presents the design and architecture of the Fuzzy Supervisor Agent (FSA), a novel component for the Multi-Agent Educational Clinical Scenario Simulation (MAECSS) platform. The FSA leverages a Fuzzy Inference System (FIS) to continuously interpret student interactions with specialized clinical agents (e.g., patient, physical exam, diagnostic, intervention) using pre-defined fuzzy rule bases for professionalism, medical relevance, ethical behavior, and contextual distraction. By analyzing student decision-making processes in real-time, the FSA is designed to deliver adaptive, context-aware feedback and provides assistance precisely when students encounter difficulties. This work focuses on the technical framework and rationale of the FSA, highlighting its potential to provide scalable, flexible, and human-like supervision in simulation-based medical education. Future work will include empirical evaluation and integration into broader educational settings. More detailed design and implementation is open sourced here.

Unlike classification, whose goal is to estimate the class of each data point in a dataset, prevalence estimation or quantification is a task that aims to estimate the distribution of classes in a dataset. The two main tasks in prevalence estimation are to adjust for bias, due to the prevalence in the training dataset, and to quantify the uncertainty in the estimate. The standard methods used to quantify uncertainty in prevalence estimates are bootstrapping and Bayesian quantification methods. It is not clear which approach is ideal in terms of precision (i.e. the width of confidence intervals) and coverage (i.e. the confidence intervals being well-calibrated). Here, we propose Precise Quantifier (PQ), a Bayesian quantifier that is more precise than existing quantifiers and with well-calibrated coverage. We discuss the theory behind PQ and present experiments based on simulated and real-world datasets. Through these experiments, we establish the factors which influence quantification precision: the discriminatory power of the underlying classifier; the size of the labeled dataset used to train the quantifier; and the size of the unlabeled dataset for which prevalence is estimated. Our analysis provides deep insights into uncertainty quantification for quantification learning.

In scientific domains -- from biology to the social sciences -- many questions boil down to \textit{What effect will we observe if we intervene on a particular variable?} If the causal relationships (e.g.~a causal graph) are known, it is possible to estimate the intervention distributions. In the absence of this domain knowledge, the causal structure must be discovered from the available observational data. However, observational data are often compatible with multiple causal graphs, making methods that commit to a single structure prone to overconfidence. A principled way to manage this structural uncertainty is via Bayesian inference, which averages over a posterior distribution on possible causal structures and functional mechanisms. Unfortunately, the number of causal structures grows super-exponentially with the number of nodes in the graph, making computations intractable. We propose to circumvent these challenges by using meta-learning to create an end-to-end model: the Model-Averaged Causal Estimation Transformer Neural Process (MACE-TNP). The model is trained to predict the Bayesian model-averaged interventional posterior distribution, and its end-to-end nature bypasses the need for expensive calculations. Empirically, we demonstrate that MACE-TNP outperforms strong Bayesian baselines. Our work establishes meta-learning as a flexible and scalable paradigm for approximating complex Bayesian causal inference, that can be scaled to increasingly challenging settings in the future.

We propose Bayesian Hierarchical Invariant Prediction (BHIP) reframing Invariant Causal Prediction (ICP) through the lens of Hierarchical Bayes. We leverage the hierarchical structure to explicitly test invariance of causal mechanisms under heterogeneous data, resulting in improved computational scalability for a larger number of predictors compared to ICP. Moreover, given its Bayesian nature BHIP enables the use of prior information. In this paper, we test two sparsity inducing priors: horseshoe and spike-and-slab, both of which allow us a more reliable identification of causal features. We test BHIP in synthetic and real-world data showing its potential as an alternative inference method to ICP.

We establish a fundamental connection between optimal structure learning and optimal conditional independence testing by showing that the minimax optimal rate for structure learning problems is determined by the minimax rate for conditional independence testing in these problems. This is accomplished by establishing a general reduction between these two problems in the case of poly-forests, and demonstrated by deriving optimal rates for several examples, including Bernoulli, Gaussian and nonparametric models. Furthermore, we show that the optimal algorithm in these settings is a suitable modification of the PC algorithm. This theoretical finding provides a unified framework for analyzing the statistical complexity of structure learning through the lens of minimax testing.

Energy-based probabilistic models learned by maximizing the likelihood of the data are limited by the intractability of the partition function. A widely used workaround is to maximize the pseudo-likelihood, which replaces the global normalization with tractable local normalizations. Here we show that, in the zero-temperature limit, a network trained to maximize pseudo-likelihood naturally implements an associative memory: if the training set is small, patterns become fixed-point attractors whose basins of attraction exceed those of any classical Hopfield rule. We explain quantitatively this effect on uncorrelated random patterns. Moreover, we show that, for different structured datasets coming from computer science (random feature model, MNIST), physics (spin glasses) and biology (proteins), as the number of training examples increases the learned network goes beyond memorization, developing meaningful attractors with non-trivial correlations with test examples, thus showing the ability to generalize. Our results therefore reveal pseudo-likelihood works both as an efficient inference tool and as a principled mechanism for memory and generalization.

Monte-Carlo tree search (MCTS) has driven many recent breakthroughs in deep reinforcement learning (RL). However, scaling MCTS to parallel compute has proven challenging in practice which has motivated alternative planners like sequential Monte-Carlo (SMC). Many of these SMC methods adopt particle filters for smoothing through a reformulation of RL as a policy inference problem. Yet, persisting design choices of these particle filters often conflict with the aim of online planning in RL, which is to obtain a policy improvement at the start of planning. Drawing inspiration from MCTS, we tailor SMC planners specifically for RL by improving data generation within the planner through constrained action sampling and explicit terminal state handling, as well as improving policy and value target estimation. This leads to our Trust-Region Twisted SMC (TRT-SMC), which shows improved runtime and sample-efficiency over baseline MCTS and SMC methods in both discrete and continuous domains.

-- In disaster response or surveillance operations, quickly identifying areas needing urgent attention is critical, but deploying response teams to every location is inefficient or often impossible. Effective performance in this domain requires coordinating a multi-robot inspection team to prioritize inspecting locations more likely to need immediate response, while also minimizing travel time. This is particularly challenging because robots must directly observe the locations to determine which ones require additional attention. This work introduces a multi-robot planning framework for coordinated time-critical multi-robot search under uncertainty. Our approach uses a graph neural network to estimate the likelihood of PoIs needing attention from noisy sensor data and then uses those predictions to guide a multi-robot model-based planner to determine the cost-effective plan. Simulated experiments demonstrate that our planner improves performance at least by 16.3%, 26.7%, and 26.2% for 1, 3, and 5 robots, respectively, compared to non-learned and learned baselines. In scenarios like disaster aftermath inspection or critical surveillance operations, quickly traveling to and inspecting affected areas is crucial for an efficient response.

We present COMPASS, a novel simulation-based inference framework that combines score-based diffusion models with transformer architectures to jointly perform parameter estimation and Bayesian model comparison across competing Galactic Chemical Evolution (GCE) models. COMPASS handles high-dimensional, incomplete, and variable-size stellar abundance datasets. Applied to high-precision elemental abundance measurements, COMPASS evaluates 40 combinations of nucleosynthetic yield tables. The model strongly favours Asymptotic Giant Branch yields from NuGrid and core-collapse SN yields used in the IllustrisTNG simulation, achieving near-unity cumulative posterior probability. Using the preferred model, we infer a steep high-mass IMF slope and an elevated Supernova Ia normalization, consistent with prior solar neighbourhood studies but now derived from fully amortized Bayesian inference. Our results demonstrate that modern SBI methods can robustly constrain uncertain physics in astrophysical simulators and enable principled model selection when analysing complex, simulation-based data.