How can you automate collecting curriculum vitae data?

I'm doing a machine learning project, for which I need data from thousands of curriculum vitae. For this, I need to collect data from the employees of some 50 specific companies. From each company, I require data from thousands of employees. This data simply consists of what positions they have previously held, and with which company; what qualifications they have (e.g. Computer Science BSc from University of Oxford); and what skills they have.

Initially I thought about using a webscraper on LinkedIn, but this is apparently very difficult for technical and legal reasons.

So what other viable solutions are there?