Research in high-dimensional statistics vs. machine learning?
This makes me think right off the bat of Gaussian processes.

The GP was initially developed by geostatisticians in the 1970s as a model for the distribution of resources over a geographic area; this process is known as kriging (or also Gaussian process regression). But more recently GPs have been used pretty widely in the movement/control/robotics area to model movements and trajectories of robotic limbs etc. over time.

Statistically, GPs are treated as priors over vectors of infinite dimension, such that the distribution of any subset of the values of a vector is Gaussian distributed. There's an online book if you want to read more!