As you said it's often not possible to explain exactly why an AI-based algorithm took a given decision (if it were we wouldn't need such a complicated algorithm

As you said it's often not possible to explain exactly why an AI-based algorithm took a given decision (if it were we wouldn't need such a complicated algorithm in the first place), but this isn't necessary either. What you need to explain to the data subject is the purpose of the automated decision making, the data you use for it and the basic logic structure of your algorithm. Again, I can only recommend to read the guidelines issued by the Article 29 working party, as they will guide the implementation and enforcement of the regulation in the member states. An overview can be found here (the relevant document is "wp251"): http://ec.europa.eu/newsroom/just/item-detail.cfm?item_id=50083 http://ec.europa.eu/newsroom/just/item-detail.cfm?item_id=50...