I have a lot of books on measure theoretic probability theory, functional analysis, graduate level topology, convex optimization, stochastic calculus, numerical analysis using a functional analysis framework, statistical theory, Bayesian Analysis, decision theory, elements of statistical learning, abstract algebra, advanced linear algebra, PDEs and information theory
I want to learn as much of these topics as possible over the next 12 years while machine learning advances, but I wonder how many of these advanced topics are actually used in Machine Learning today?
Particuarly, I want to study deep and reinforcement learning that does NOT need training data sets except for mathematical structures. I.e., Imagine an algorithm that knows which approach to take and learns to classify objects by topology, then further classifies them by geometry, and ever further by color, periodicity, symmetry etc.
For example, even if you trained the algorithm on recognizing squares, it would be able to distinguish a circle as being similar but fundamentally different. Maybe it could also learn to put pictures of limbs together and generalize them into the shape of a person while figuring out how they interact.