SOURCE-LINKED INTELLIGENCE

Generalized Splines and Gaussian Processes

arXiv · AI, language, vision and robotics · article · Aug 28, 2026 · UTC

For finite-dimensional linear inverse problems where the variables are Gaussian, it is well-known that the minimum-mean-square error estimator takes the form of a regularized least-squares data fit. In this chapter, we show that this equivalence extends to a much broader infinite-dimensional setting where generalized splines take the role of linear regressors and generalized Gaussian processes on a nuclear space $S$ are the counterpart of Gaussian random vectors. The scope of this extension is of the same nature as the switch from the classic notion of function to that of a distribution, also

Read original source ↗ Open in workspace

recordType

paper

region

Global