> The controller should find simple ways to tell the data subject about the rationale behind, or the criteria relied on in reaching the decision without necessarily always attempting a complex explanation of the algorithms used or disclosure of the full algorithm. The information provided should, however, be meaningful to the data subject.
There's also a detailed example in the document that should make it clearer what kind of explanation is required (and what is not required). Again, personally I understand that it's not clear what exactly will be required here, but titling an article "Will GDPR Make Machine Learning Illegal?" is just an attempt to garner attention by instilling (unfounded) fear.
[1]: http://ec.europa.eu/newsroom/just/document.cfm?doc_id=47963