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!

  • 1
    $\begingroup$ Check out linear dynamical systems cs.brown.edu/research/pubs/theses/masters/2009/gbarayor.pdf Ornstein-Uhlenbeck processes are big here. $\endgroup$ – user237393 May 7 '15 at 10:26
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    $\begingroup$ Check out chapters 6, 10, 11, and 13. 6 deals with gaussian processes, 10 with stochastic Dynamical systems, 11 with Sampling/ simulation, and 13 with sequential data/ random walks and such rmki.kfki.hu/~banmi/elte/… All have their origins in stochastics. Secondly, if you like measure theory, then you'd be great at continuous optimization in function spaces. And topology would lend itself nicely to kernel methods. $\endgroup$ – user237393 May 7 '15 at 10:38
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    $\begingroup$ @user237393 thank you! This looks really promising! Makes me quite hopeful in joining these two. $\endgroup$ – Dahn May 7 '15 at 14:38
  • $\begingroup$ The lack of activity on this question, however, does not :( $\endgroup$ – Dahn May 11 '15 at 18:43

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