Accountability is the ability to provide good reasons in order to explain and to justify actions, decisions, and policies for a (hypothetical) forum of persons or organizations. Since decision-makers, both in the private and in the public sphere, increasingly rely on algorithms operating on Big Data for their decision-making, special mechanisms of accountability concerning the making and deployment of algorithms in that setting become gradually more urgent. In the upcoming General Data Protection Regulation, the importance of accountability and closely related concepts, such as transparency, as guiding protection principles, is emphasized. Yet, the accountability mechanisms inherent in the regulation cannot be appropriately applied to algorithms operating on Big Data and their societal impact. First, algorithms are complex. Second, algorithms often operate on a random group-level, which may pose additional difficulties when interpreting and articulating the risks of algorithmic decision-making processes. In light of the possible significance of the impact on human beings, the complexities and the broader scope of algorithms in a big data setting call for accountability mechanisms that transcend the mechanisms that are now inherent in the regulation.