Making inference about a probability measure from a collection of samples from this measure is a central topic in statistics and machine learning. We focus here on the case of probability measures on spaces of paths or sequences, that is laws of stochastic processes. Combining tools from stochastic analysis and machine learning leads to interesting mathematical objects and questions which in turn give rise to efficient estimators and algorithms. Moreover, this approach can be extened to not only capture the law but also the filtration of the stochastic process.
Personal Website of Harald Oberhauser