少样本多模态医学影像：一个理论框架
Few-Shot Multimodal Medical Imaging: A Theoretical Framework
AI总结：
本文提出少样本多模态医学影像的理论框架，通过样本复杂性、不确定性量化和可解释性分析，为低资源环境下的高效、可靠诊断模型设计提供理论基础。
摘要：
医学影像常常在标注数据有限的情况下运行，尤其是在罕见疾病和低资源临床环境中。现有的多模态和元学习方法在这些情况下提高了性能，但缺乏对为何或何时成功的理论解释。本文提出一个统一的理论框架，用于少样本多模态医学影像，共同表征样本复杂性、不确定性量化和可解释性。利用PAC学习、VC理论和PAC贝叶斯分析，我们推导出描述可靠性能所需最少标注样本数的界限，并通过信息增益项展示互补模态如何通过减少有效容量。我们进一步引入一个正式的指标来衡量解释的稳定性，证明解释方差以反比例于n的速度减少。还开发了一个序列贝叶斯解释，用于展示逐步后验收缩。为了说明这些想法，我们实现了受控的多模态数据集，并在少样本情况下评估了一个加法CNN MLP融合模型，确认了预测的多模态增益、在较大样本量下的模态干扰以及缩小的预测不确定性。共同来看，该框架为在低资源环境下设计数据高效、不确定性意识和可解释的诊断模型提供了原则性基础。
英文摘要：
Medical imaging often operates under limited labeled data, especially in rare disease and low resource clinical environments. Existing multimodal and meta learning approaches improve performance in these settings but lack a theoretical explanation of why or when they succeed. This paper presents a unified theoretical framework for few shot multimodal medical imaging that jointly characterizes sample complexity, uncertainty quantification, and interpretability. Using PAC learning, VC theory, and PAC Bayesian analysis, we derive bounds that describe the minimum number of labeled samples required for reliable performance and show how complementary modalities reduce effective capacity through an information gain term. We further introduce a formal metric for explanation stability, proving that explanation variance decreases at an inverse n rate. A sequential Bayesian interpretation of Chain of Thought reasoning is also developed to show stepwise posterior contraction. To illustrate these ideas, we implement a controlled multimodal dataset and evaluate an additive CNN MLP fusion model under few shot regimes, confirming predicted multimodal gains, modality interference at larger sample sizes, and shrinking predictive uncertainty. Together, the framework provides a principled foundation for designing data efficient, uncertainty aware, and interpretable diagnostic models in low resource settings.
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