Niko Beerenwinkel

Paweł Czyż, Frederic Grabowski, Julia E. Vogt et al. · eth-zurich

Mutual information is a general statistical dependency measure which has found applications in representation learning, causality, domain generalization and computational biology. However, mutual information estimators are typically evaluated on simple families of probability distributions, namely multivariate normal distribution and selected distributions with one-dimensional random variables. In this paper, we show how to construct a diverse family of distributions with known ground-truth mutual information and propose a language-independent benchmarking platform for mutual information estimators. We discuss the general applicability and limitations of classical and neural estimators in settings involving high dimensions, sparse interactions, long-tailed distributions, and high mutual information. Finally, we provide guidelines for practitioners on how to select appropriate estimator adapted to the difficulty of problem considered and issues one needs to consider when applying an estimator to a new data set.

Paweł Czyż, Frederic Grabowski, Julia E. Vogt et al. · eth-zurich

The pointwise mutual information profile, or simply profile, is the distribution of pointwise mutual information for a given pair of random variables. One of its important properties is that its expected value is precisely the mutual information between these random variables. In this paper, we analytically describe the profiles of multivariate normal distributions and introduce a novel family of distributions, Bend and Mix Models, for which the profile can be accurately estimated using Monte Carlo methods. We then show how Bend and Mix Models can be used to study the limitations of existing mutual information estimators, investigate the behavior of neural critics used in variational estimators, and understand the effect of experimental outliers on mutual information estimation. Finally, we show how Bend and Mix Models can be used to obtain model-based Bayesian estimates of mutual information, suitable for problems with available domain expertise in which uncertainty quantification is necessary.

Gonzalo Cardenal-Antolin, Jacques Fellay, Bashkim Jaha et al.

Large language models (LLMs) are emerging as valuable tools to support clinicians in routine decision-making. HIV management is a compelling use case due to its complexity, including diverse treatment options, comorbidities, and adherence challenges. However, integrating LLMs into clinical practice raises concerns about accuracy, potential harm, and clinician acceptance. Despite their promise, AI applications in HIV care remain underexplored, and LLM benchmarking studies are scarce. This study evaluates the current capabilities of LLMs in HIV management, highlighting their strengths and limitations. We introduce HIVMedQA, a benchmark designed to assess open-ended medical question answering in HIV care. The dataset consists of curated, clinically relevant questions developed with input from an infectious disease physician. We evaluated seven general-purpose and three medically specialized LLMs, applying prompt engineering to enhance performance. Our evaluation framework incorporates both lexical similarity and an LLM-as-a-judge approach, extended to better reflect clinical relevance. We assessed performance across key dimensions: question comprehension, reasoning, knowledge recall, bias, potential harm, and factual accuracy. Results show that Gemini 2.5 Pro consistently outperformed other models across most dimensions. Notably, two of the top three models were proprietary. Performance declined as question complexity increased. Medically fine-tuned models did not always outperform general-purpose ones, and larger model size was not a reliable predictor of performance. Reasoning and comprehension were more challenging than factual recall, and cognitive biases such as recency and status quo were observed. These findings underscore the need for targeted development and evaluation to ensure safe, effective LLM integration in clinical care.

Fritz Bayer, Drago Plecko, Niko Beerenwinkel et al.

Clustering algorithms may unintentionally propagate or intensify existing disparities, leading to unfair representations or biased decision-making. Current fair clustering methods rely on notions of fairness that do not capture any information on the underlying causal mechanisms. We show that optimising for non-causal fairness notions can paradoxically induce direct discriminatory effects from a causal standpoint. We present a clustering approach that incorporates causal fairness metrics to provide a more nuanced approach to fairness in unsupervised learning. Our approach enables the specification of the causal fairness metrics that should be minimised. We demonstrate the efficacy of our methodology using datasets known to harbour unfair biases.

Fritz M. Bayer, Giusi Moffa, Niko Beerenwinkel et al.

Inference of the marginal probability distribution is defined as the calculation of the probability of a subset of the variables and is relevant for handling missing data and hidden variables. While inference of the marginal probability distribution is crucial for various problems in machine learning and statistics, its exact computation is generally not feasible for categorical variables in Bayesian networks due to the NP-hardness of this task. We develop a divide-and-conquer approach using the graphical properties of Bayesian networks to split the computation of the marginal probability distribution into sub-calculations of lower dimensionality, thus reducing the overall computational complexity. Exploiting this property, we present an efficient and scalable algorithm for calculating the marginal probability distribution for categorical variables. The novel method is compared against state-of-the-art approximate inference methods in a benchmarking study, where it displays superior performance. As an immediate application, we demonstrate how our method can be used to classify incomplete data against Bayesian networks and use this approach for identifying the cancer subtype of kidney cancer patient samples.

Polina Suter, Jack Kuipers, Giusi Moffa et al.

The R package BiDAG implements Markov chain Monte Carlo (MCMC) methods for structure learning and sampling of Bayesian networks. The package includes tools to search for a maximum a posteriori (MAP) graph and to sample graphs from the posterior distribution given the data. A new hybrid approach to structure learning enables inference in large graphs. In the first step, we define a reduced search space by means of the PC algorithm or based on prior knowledge. In the second step, an iterative order MCMC scheme proceeds to optimize within the restricted search space and estimate the MAP graph. Sampling from the posterior distribution is implemented using either order or partition MCMC. The models and algorithms can handle both discrete and continuous data. The BiDAG package also provides an implementation of MCMC schemes for structure learning and sampling of dynamic Bayesian networks.