Generative models are popular for medical imaging tasks such as anomaly detection, feature extraction, data visualization, or image generation. Since they are parameterized by deep learning models, they are often sensitive to distribution shifts and unreliable when applied to out-of-distribution data, creating a risk of, e.g. underrepresentation bias. This behavior can be flagged using uncertainty quantification methods for generative models, but their availability remains limited. We propose SLUG: A new UQ method for VAEs that combines recent advances in Laplace approximations with stochastic trace estimators to scale gracefully with image dimensionality. We show that our UQ score -- unlike the VAE's encoder variances -- correlates strongly with reconstruction error and racial underrepresentation bias for dermatological images. We also show how pixel-wise uncertainty can detect out-of-distribution image content such as ink, rulers, and patches, which is known to induce learning shortcuts in predictive models.

Tuning scientific and probabilistic machine learning models - for example, partial differential equations, Gaussian processes, or Bayesian neural networks - often relies on evaluating functions of matrices whose size grows with the data set or the number of parameters. While the state-of-the-art for evaluating these quantities is almost always based on Lanczos and Arnoldi iterations, the present work is the first to explain how to differentiate these workhorses of numerical linear algebra efficiently. To get there, we derive previously unknown adjoint systems for Lanczos and Arnoldi iterations, implement them in JAX, and show that the resulting code can compete with Diffrax when it comes to differentiating PDEs, GPyTorch for selecting Gaussian process models and beats standard factorisation methods for calibrating Bayesian neural networks. All this is achieved without any problem-specific code optimisation.

This article proposes numerically robust algorithms for Gaussian state estimation with singular observation noise. Our approach combines a series of basis changes with Bayes' rule, transforming the singular estimation problem into a nonsingular one with reduced state dimension. In addition to ensuring low runtime and numerical stability, our proposal facilitates marginal-likelihood computations and Gauss-Markov representations of the posterior process. We analyse the proposed method's computational savings and numerical robustness and validate our findings in a series of simulations.

Hedonic games model settings in which a set of agents have to be partitioned into groups which we call coalitions. In the enemy aversion model, each agent has friends and enemies, and an agent prefers to be in a coalition with as few enemies as possible and, subject to that, as many friends as possible. A partition should be stable, i.e., no subset of agents prefer to be together rather than being in their assigned coalition under the partition. We look at two stability concepts: core stability and strict core stability. This yields several algorithmic problems: determining whether a (strictly) core stable partition exists, finding such a partition, and checking whether a given partition is (strictly) core stable. Several of these problems have been shown to be NP-complete, or even beyond NP. This motivates the study of parameterized complexity. We conduct a thorough computational study using several parameters: treewidth, number of friends, number of enemies, partition size, and coalition size. We give polynomial algorithms for restricted graph classes as well as FPT algorithms with respect to the number of friends an agent may have and the treewidth of the graph representing the friendship or enemy relations. We show W[1]-hardness or para-NP-hardness with respect to the other parameters. We conclude this paper with results in the setting in which agents can have neutral relations with each other, including hardness-results for very restricted cases.

In the last years, Federated learning (FL) has become a popular solution to train machine learning models in domains with high privacy concerns. However, FL scalability and performance face significant challenges in real-world deployments where data across devices are non-independently and identically distributed (non-IID). The heterogeneity in data distribution frequently arises from spatial distribution of devices, leading to degraded model performance in the absence of proper handling. Additionally, FL typical reliance on centralized architectures introduces bottlenecks and single-point-of-failure risks, particularly problematic at scale or in dynamic environments. To close this gap, we propose Field-Based Federated Learning (FBFL), a novel approach leveraging macroprogramming and field coordination to address these limitations through: (i) distributed spatial-based leader election for personalization to mitigate non-IID data challenges; and (ii) construction of a self-organizing, hierarchical architecture using advanced macroprogramming patterns. Moreover, FBFL not only overcomes the aforementioned limitations, but also enables the development of more specialized models tailored to the specific data distribution in each subregion. This paper formalizes FBFL and evaluates it extensively using MNIST, FashionMNIST, and Extended MNIST datasets. We demonstrate that, when operating under IID data conditions, FBFL performs comparably to the widely-used FedAvg algorithm. Furthermore, in challenging non-IID scenarios, FBFL not only outperforms FedAvg but also surpasses other state-of-the-art methods, namely FedProx and Scaffold, which have been specifically designed to address non-IID data distributions.

In prototype-based federated learning, the exchange of model parameters between clients and the master server is replaced by transmission of prototypes or quantized versions of the data samples to the aggregation server. A fully decentralized deployment of prototype-based learning, without a central agregartor of prototypes, is more robust upon network failures and reacts faster to changes in the statistical distribution of the data, suggesting potential advantages and quick adaptation in dynamic learning tasks, e.g., when the data sources are IoT devices or when data is non-iid. In this paper, we consider the problem of designing a communication-efficient decentralized learning system based on prototypes. We address the challenge of prototype redundancy by leveraging on a twofold data compression technique, i.e., sending only update messages if the prototypes are informationtheoretically useful (via the Jensen-Shannon distance), and using clustering on the prototypes to compress the update messages used in the gossip protocol. We also use parallel instead of sequential gossiping, and present an analysis of its age-of-information (AoI). Our experimental results show that, with these improvements, the communications load can be substantially reduced without decreasing the convergence rate of the learning algorithm. Federated Learning (FL) [1], [2], [3] and Decentralized Federated Learning (DFL) [4], [5] provide good approaches for distributed machine learning system where the main focus is the minimization of a global loss function using different versions of a model created by multiple clients. These approaches have been extensively studied in the literature and applied, traditionally, to process private data in areas such as health and banking. In this paper, differently to these well-known approaches, we focus on the analysis and implementation of a decentralized machine learning system based on prototypes. On the one hand, our choice of prototype-based algorithms is motivated by the advantages of these prototypes as compact representation of the data, capturing the essential features and patterns within the dataset.

Singing is one of the most cherished forms of human entertainment. However, creating a beautiful song requires an accompaniment that complements the vocals and aligns well with the song instruments and genre. With advancements in deep learning, previous research has focused on generating suitable accompaniments but often lacks precise alignment with the desired instrumentation and genre. To address this, we propose a straightforward method that enables control over the accompaniment through text prompts, allowing the generation of music that complements the vocals and aligns with the song instrumental and genre requirements. Through extensive experiments, we successfully generate 10-second accompaniments using vocal input and text control.

The adoption of increasingly complex deep models has fueled an urgent need for insight into how these models make predictions. Counterfactual explanations form a powerful tool for providing actionable explanations to practitioners. Previously, counterfactual explanation methods have been designed by traversing the latent space of generative models. Yet, these latent spaces are usually greatly simplified, with most of the data distribution complexity contained in the decoder rather than the latent embedding. Thus, traversing the latent space naively without taking the nonlinear decoder into account can lead to unnatural counterfactual trajectories. We introduce counterfactual explanations obtained using a Riemannian metric pulled back via the decoder and the classifier under scrutiny. This metric encodes information about the complex geometric structure of the data and the learned representation, enabling us to obtain robust counterfactual trajectories with high fidelity, as demonstrated by our experiments in real-world tabular datasets.

The language technology moonshot moment of Generative, Large Language Models (GLLMs) was not limited to English: These models brought a surge of technological applications, investments and hype to low-resource languages as well. However, the capabilities of these models in languages such as Danish were until recently difficult to verify beyond qualitative demonstrations due to a lack of applicable evaluation corpora. We present a GLLM benchmark to evaluate Danoliteracy, a measure of Danish language and cultural competency, across eight diverse scenarios such Danish citizenship tests and abstractive social media question answering. This limited-size benchmark is found to produce a robust ranking that correlates to human feedback at $\rho \sim 0.8$ with GPT-4 and Claude Opus models achieving the highest rankings. Analyzing these model results across scenarios, we find one strong underlying factor explaining $95\%$ of scenario performance variance for GLLMs in Danish, suggesting a $g$ factor of model consistency in language adaption.

Despite substantial progress in recent years, probabilistic solvers with adaptive step sizes can still not solve memory-demanding differential equations -- unless we care only about a single point in time (which is far too restrictive; we want the whole time series). Counterintuitively, the culprit is the adaptivity itself: Its unpredictable memory demands easily exceed our machine's capabilities, making our simulations fail unexpectedly and without warning. Still, dropping adaptivity would abandon years of progress, which can't be the answer. In this work, we solve this conundrum. We develop an adaptive probabilistic solver with fixed memory demands building on recent developments in robust state estimation. Switching to our method (i) eliminates memory issues for long time series, (ii) accelerates simulations by orders of magnitude through unlocking just-in-time compilation, and (iii) makes adaptive probabilistic solvers compatible with scientific computing in JAX.