[toxikitty_]

A lot of data scientists these days (me included) are former academics with backgrounds in numerical simulation in fields like chemistry, physics, mechanical engineering etc.

They live and breath numerical linear algebra and are comfortable reading advanced theoretical books or papers.

It's easy for them to pick up the basics needed to pass interviews and find a data science job. How would they go about adding some rigor to their understanding of ML and statistics?

[sidlls]

I wouldn't expect the majority of data science jobs to be particularly focused on the math behind the algorithms. Rudimentary understanding of probability and how to translate the jargon into your academic background's jargon is more important than deep understanding for these jobs. Passing the interviews for these jobs is one thing. Unless you're specifically looking for jobs that focus on generating new modeling techniques or algorithms for computational statistics, expect to be far removed from even basic linear algebra in actual practice. Source: me. I fall in your described bucket and have worked in data science/machine learning jobs in both contexts (new modeling techniques/stats versus application of off-the-shelf tools).

[martingoodson]

I personally love this for statistical inference: http://www.springer.com/cn/book/9780387402727

and this for statistical ML: http://statweb.stanford.edu/~tibs/ElemStatLearn/