Learning Rate Should Scale Inversely with High-Order Data Moments in High-Dimensional Online Independent Component Analysis
This work addresses the sensitivity of ICA algorithms to non-Gaussian data structures, which is an incremental improvement for researchers in signal processing and machine learning dealing with high-dimensional data.
The paper tackled the problem of slower convergence in online Independent Component Analysis (ICA) due to high-order data moments, showing that as these moments increase, the algorithm requires a lower learning rate and better initial alignment, with a critical learning rate threshold identified for effective learning.
We investigate the impact of high-order moments on the learning dynamics of an online Independent Component Analysis (ICA) algorithm under a high-dimensional data model composed of a weighted sum of two non-Gaussian random variables. This model allows precise control of the input moment structure via a weighting parameter. Building on an existing ordinary differential equation (ODE)-based analysis in the high-dimensional limit, we demonstrate that as the high-order moments increase, the algorithm exhibits slower convergence and demands both a lower learning rate and greater initial alignment to achieve informative solutions. Our findings highlight the algorithm's sensitivity to the statistical structure of the input data, particularly its moment characteristics. Furthermore, the ODE framework reveals a critical learning rate threshold necessary for learning when moments approach their maximum. These insights motivate future directions in moment-aware initialization and adaptive learning rate strategies to counteract the degradation in learning speed caused by high non-Gaussianity, thereby enhancing the robustness and efficiency of ICA in complex, high-dimensional settings.