Does anyone know of good resources for studying machine learning or data science given a strong mathematical background? I'm transitioning careers from pure math research into industry. I know very little about machine learning, but I know the crap out of linear algebra and real analysis (and other, less relevant fields). It'd be great to have some sources that leverage that without assuming much prior CS knowledge.
There are many new methods cropping up that most people in the data science hype train will be full-on unable to access, including methods on manifolds (even kernel methods on manifolds) and algebraic-topological methods (persistent homology) with enough maths to give Kagglers the screaming meemies. I'm using some of those for $(redacted, the plan is to make money). Don't follow the crowd.
I think with hindsight, it's great to have a broad spectrum of methods available to you, but if you focus too much on methods at the hard-math end of the spectrum just for the sake of an intellectual challenge, you can end up fixated on an exotic solution looking for a problem while the rest of the field moves on, rather than doing useful engineering people care about.
Maybe you find a niche where something exotic really helps, maybe you don't -- maybe for research this is a risk worth taking. But just something to keep in mind.
IMO: breadth is good. Mathematical maturity helps. If one sticks around one finds uses for interesting maths eventually, but not worth trying to force it.
Another avenue for people who want to use some hardcore math: try and use it to find some good theory around why things which work well, work well. Not an easy task either by any means.