Polynomial Kernel

Polynomial kernels are a class of functions used in machine learning to model relationships between data points by representing them as polynomial expansions of their features. Current research focuses on improving the efficiency of polynomial kernel methods, particularly through techniques like sketching and random feature approximations, aiming to reduce computational complexity for large datasets, as seen in the development of faster Transformer architectures. These advancements are crucial for scaling up machine learning models to handle increasingly large and complex datasets, impacting fields like natural language processing and computer vision. Furthermore, ongoing work addresses challenges related to the non-positive definiteness of certain polynomial kernels and their application in interpolation and approximation theory.