The Gaussian Radon Transform and Machine Learning
This work addresses a theoretical bottleneck for researchers in machine learning interested in probabilistic models in Banach spaces, but it appears incremental as it builds on existing frameworks without clear practical applications.
The paper tackles the problem of probabilistic interpretations in kernel-based methods by addressing the lack of a Lebesgue measure in infinite-dimensional reproducing kernel Hilbert spaces, proposing an estimation model for ridge regression using abstract Wiener spaces and interpreting support vector machine solutions via the Gaussian Radon transform.
There has been growing recent interest in probabilistic interpretations of kernel-based methods as well as learning in Banach spaces. The absence of a useful Lebesgue measure on an infinite-dimensional reproducing kernel Hilbert space is a serious obstacle for such stochastic models. We propose an estimation model for the ridge regression problem within the framework of abstract Wiener spaces and show how the support vector machine solution to such problems can be interpreted in terms of the Gaussian Radon transform.