AI 中文总结
针对标准ICA在处理非线性预处理特征时假设不成立的问题，提出AdaptICA框架，通过轮廓互信息准则联合学习变换与去混合结构，建立相关理论结果，经模拟和应用验证，能自适应选择变换结构，兼具恢复更多独立可解释源及保留标准ICA的优势。
AI 中文摘要
独立成分分析（ICA）广泛用于从信号和成像数据中恢复潜在结构，但标准ICA假设观测测量尺度保持线性混合结构。对于通过非线性预处理产生的特征，如运动想象脑电图中的频段特定功率，该假设可能不成立。我们提出了AdaptICA，这是一个基于自适应变换的框架，它使用轮廓互信息准则联合学习分组的逐分量变换和去混合结构。由于变换和去混合参数可能相互补偿，它们的联合估计带来了新的可识别性和渐近挑战。我们建立了变换估计器的可识别性、一致性和渐近正态性，以及变换和去混合估计器的联合强一致性。AdaptICA能自适应地选择变换结构，并将恒等变换作为候选，在不需要尺度调整时可简化为标准ICA。大量模拟支持了理论结果。应用表明，当变换有益时，AdaptICA可以恢复更多独立且可解释的源，而在原始测量尺度适当时保留标准ICA。
英文摘要
Independent component analysis (ICA) is widely used to recover latent structure from signal and imaging data, but standard ICA assumes that the observed measurement scale preserves a linear mixing structure. This assumption may fail for features produced through nonlinear preprocessing, such as band-specific power in motor-imagery EEG. We propose AdaptICA, an adaptive transformation-based framework that jointly learns grouped componentwise transformations and the demixing structure using a profiled mutual-information criterion. Because the transformation and demixing parameters may compensate for one another, their joint estimation introduces new identifiability and asymptotic challenges. We establish identifiability, consistency, and asymptotic normality of the transformation estimator, together with joint strong consistency of the transformation and demixing estimators. AdaptICA selects the transformation structure data-adaptively and includes the identity transformation as a candidate, thereby reducing to standard ICA when no scale adjustment is needed. Extensive simulations support the theoretical results. Applications demonstrate that AdaptICA can recover more independent and interpretable sources when transformation is beneficial while retaining standard ICA when the original measurement scale is adequate.
Comments35 pages, 3 figures
