arXiv subjects

Kristoffer Herland Hellton

Publications and source records attributed to Kristoffer Herland Hellton.

3 recordsLinked to original sources

arXiv2026

Fridge: focused fine-tuning of ridge regression for personalize predictions

Statistical prediction methods typically require some form of fine-tuning of tuning parameter(s), with $K$-fold cross-validation as the canonical procedure. For ridge regression there exist numerous procedures, but common for all, including cross-validation, is that one single parameter is chosen for all future predictions. We propose instead to calculate a unique tuning parameter for each individual for which we wish to predict an outcome. This generates an individualized prediction by focusing on the vector of covariates of a specific individual. The focused ridge -- fridge -- procedure is introduced with a two-part contribution: 1) first we define an oracle tuning parameter minimizing the mean squared prediction error of a specific covariate vector, 2) then we propose to estimate this tuning parameter by using plug-in estimates of the regression coefficients and error variance parameter. The procedure is extended to logistic ridge regression by utilizing parametric bootstrap. For high-dimensional data, we propose to use ridge regression with cross-validation as the plug-in estimate, and simulations show that fridge gives smaller average prediction error than ridge with cross-validation for both simulated and real data. We illustrate the new concept for both linear and logistic regression models in two applications of personalized medicine: predicting individual risk and treatment response based on gene expression data. The method is implemented in the R package "fridge".

stat.ME↗

arXiv2026

Improved Predictive Performance and Interpretability for Mesomorphic Neural Networks Using Local Fidelity Regularization

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.

cs.LG↗

arXiv2025

Using Large Language Models to Suggest Informative Prior Distributions in Bayesian Statistics

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.

stat.ME↗