Main question: What connections are there between machine learning and stochastics (Probability theory, analysis, processes, SDEs)?
Background: I've just been accepted into a master's programme for stochastic analysis. My original plan was to focus mostly on SDEs. I can still switch to other fields, such as statistics, or optimisation (and I do realize those would be much better choices for ML), but I am quite certain my heart lies in stochastics, as I simply love measure theory, topology, probability theory, etc.
I recently also got seriously interested in machine learning. It intrigued me so much that I now feel I might feel like I've missed something if I don't (at least partially) get into that field.
I do however understand joining those two might not be possible and that my preferences might change over time, so as an additional question (a very soft one, or even just a suggestion for additional comments):
If you were to suggest fields as close to stochastics as possible which have a greater connection to ML, which ones whould they be?
Thank you for answers!