Nima Negarandeh

Foundation models (FMs) have achieved substantial success in generalizing across tasks without problem-specific training or fine-tuning. However, many critical applications in mechanics and computational science require not only accurate predictions but also reliable uncertainty quantification (UQ). Herein we investigate the UQ capabilities of tabular FMs in regression tasks through a comprehensive empirical study comparing Tabular Prior-Data Fitted Networks (TabPFN) against Gaussian processes (GPs). We systematically evaluate these two methods across a host of regression problems with varying complexity, dataset sizes, and input dimensionalities. We use a default setting to build all the GPs and for a fair comparison against TabPFN v2.5. Our findings highlight an important trade-off between explicit and learned priors: while TabPFN achieves highly competitive performance for complex, high-dimensional problems with sufficient data, GPs often provide superior predictive accuracy and UQ in data-scarce settings. Moreover, when the chosen kernel constitutes a good prior for the underlying function, GP performance can substantially exceed that of TabPFN. Our results can be reproduced from https://github.com/kianswarehouse/GPvsPFN.

Background Understanding whether commonly available metabolic, demographic, and behavioral factors can explain variability in brain structure may support the development of accessible predictive approaches. This study aims to evaluate the ability of machine learning regression models to predict brain structural measures in young, neurologically healthy adults using clinically accessible risk factors. Methods Data were drawn from the Human Connectome Project Young Adults dataset, including 1082 participants aged 22–37. Predictors comprised metabolic measures (systolic and diastolic blood pressure, hematocrit, body mass index, hemoglobin A1C, thyroid stimulating hormone) and demographic/behavioral variables (age, gender, race, education level, smoking history, alcohol use). Brain structural parameters from MRI included gray matter (GM) and white matter (WM) volumes, surface areas, and cortical thickness. Distance correlation (dcor) guided feature selection, followed by machine learning modeling. Model performance was evaluated using normalized mean absolute error (NMAE), normalized root-mean-squared error (NRMSE), and coefficient of determination (R²). SHAP values were used for feature interpretation. Results XGBoost consistently outperformed other algorithms, showing strong predictive accuracy for total brain segmentation, supratentorial, and total GM volumes (NMAE < 0.35, R² > 0.80). In contrast, cortical surface predictions (left superior frontal) showed moderate performance (NMAE > 0.50, R² < 0.60). SHAP analysis highlighted age, gender, education level, and diastolic and systolic blood pressure as the most influential predictors of brain structure. Conclusions The findings highlight the methodological value of regression-based approaches for estimating brain structural variability and support their potential role as complementary tools for brain health research.