Invariant Kernel

Invariant kernels, particularly translation-invariant kernels, are functions defining similarity between data points, crucial for various machine learning methods like kernel ridge regression and self-supervised learning. Current research focuses on understanding the optimal estimation rates of these kernels, analyzing the impact of adaptive bandwidth selection on model performance (including the phenomenon of "benign overfitting"), and developing efficient algorithms for their application, such as those leveraging orthonormal expansions. This work is significant because it improves the theoretical understanding and practical efficiency of kernel methods, impacting diverse fields from statistical inference to image processing and beyond.