Kristoffer H. Hellton

Hugo L. Hammer, Vajira Thambawita, Kristoffer Herland Hellton et al.

Interpretable Mesomorphic Neural Networks (IMNs) offer a promising framework that combines the predictive power of deep neural networks with the interpretability of linear models. However, the original formulation lacks safeguards to ensure that the learned interpretations are in fact reliable. In particular, the network is free to concentrate all explanatory variance into a single weight of the linear output layer, achieving strong predictive performance while producing interpretations that are largely meaningless. Paradoxically, the L1 penalty proposed to encourage sparse solutions exacerbates this problem by further incentivizing such degenerate configurations. To address this vulnerability, we introduce Local Fidelity Regularization (LFR), a novel penalty term that prevents degenerate weight collapse by aligning the linear output weights with local data variations. This structural constraint guarantees faithful explanations and substantially improves the reliability of model interpretations. Furthermore, empirical evaluations across the OpenML benchmark suite demonstrate that LFR does not compromise accuracy for explainability; rather, it achieved improved AUROC over the unregularized IMN. By yielding results highly competitive with state-of-the-art black-box models, LFR provides the dual benefit of reliable interpretability and superior predictive performance. Source code and usage instructions are available at https://github.com/hugohammer/LFR-IMN.git.

Michael A. Riegler, Kristoffer Herland Hellton, Vajira Thambawita et al.

Selecting prior distributions in Bayesian statistics is challenging, resource-intensive, and subjective. We analyze using large-language models (LLMs) to suggest suitable, knowledge-based informative priors. We developed an extensive prompt asking LLMs not only to suggest priors but also to verify and reflect on their choices. We evaluated Claude Opus, Gemini 2.5 Pro, and ChatGPT-4o-mini on two real datasets: heart disease risk and concrete strength. All LLMs correctly identified the direction for all associations (e.g., that heart disease risk is higher for males). The quality of suggested priors was measured by their Kullback-Leibler divergence from the maximum likelihood estimator's distribution. The LLMs suggested both moderately and weakly informative priors. The moderate priors were often overconfident, resulting in distributions misaligned with the data. In our experiments, Claude and Gemini provided better priors than ChatGPT. For weakly informative priors, a key performance difference emerged: ChatGPT and Gemini defaulted to an "unnecessarily vague" mean of 0, while Claude did not, demonstrating a significant advantage. The ability of LLMs to identify correct associations shows their great potential as an efficient, objective method for developing informative priors. However, the primary challenge remains in calibrating the width of these priors to avoid over- and under-confidence.

Shih-Ting Huang, Yannick Düren, Kristoffer H. Hellton et al.

Personalized medicine has become an important part of medicine, for instance predicting individual drug responses based on genomic information. However, many current statistical methods are not tailored to this task, because they overlook the individual heterogeneity of patients. In this paper, we look at personalized medicine from a linear regression standpoint. We introduce an alternative version of the ridge estimator and target individuals by establishing a tuning parameter calibration scheme that minimizes prediction errors of individual patients. In stark contrast, classical schemes such as cross-validation minimize prediction errors only on average. We show that our pipeline is optimal in terms of oracle inequalities, fast, and highly effective both in simulations and on real data.