Honestly, I've found that getting a job in a field that I'm interested in is a much faster way to learn. You have the advantage of working with people already in the field, an existing codebase and set of data to tap into, and clear projects with deadlines and impact to the bottom line.
Example: Machine Learning. I learned much more in a few weeks at a job at a Machine Learning company than I ever did trying working through Elements of Statistical Learning on my own.
If you can prove that you're smart and capable of contributing to the bottom line, it's very possible to get hired with the assumption that you'll quickly pick up anything you need to know.
Eg, at a previous job I'd saved the company $3MM/year using a technology I'd never really worked with before. With that kind of track record this company was happy to hire me even if I didn't have direct ML experience.
Example: Machine Learning. I learned much more in a few weeks at a job at a Machine Learning company than I ever did trying working through Elements of Statistical Learning on my own.