对比表格基础模型与高斯过程的不确定性量化能力，发现数据少时高斯过程更优。
On the Uncertainty Quantification Ability of Tabular Foundation Models
- 用表格基础模型与高斯过程对比，评估其在回归任务中的不确定性量化能力。
- 数据充足时表格模型表现接近最优，数据稀少时高斯过程预测更准且不确定性更可靠。
- 当核函数与真实函数匹配时，高斯过程性能显著优于表格模型，适合小样本场景。
基础模型（FMs）在无需特定任务训练或微调的情况下实现了跨任务的良好泛化。然而，机械与计算科学中的许多关键应用不仅需要精确预测，还需可靠的不确定性量化（UQ）。本文通过系统实证研究，比较了表格先验-数据拟合网络（TabPFN）与高斯过程（GPs）在回归任务中的UQ能力。我们在多种复杂度、数据集大小和输入维度的回归问题上进行评估，并采用默认设置构建所有高斯过程以公平对比TabPFN v2.5。结果表明：显式先验与学习先验之间存在重要权衡——当数据充足时，TabPFN在复杂高维问题中表现极具竞争力；而在数据稀缺情况下，高斯过程通常提供更高的预测精度和更可靠的不确定性估计。此外，当所选核函数与底层函数构成良好先验时，高斯过程性能可显著超越TabPFN。实验代码已公开于https://github.com/kianswarehouse/GPvsPFN。
原文摘要 · Abstract (English)
Foundation models (FMs) have achieved substantial success in generalizing across tasks without problemspecific 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.
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