Abstract : Big Data promises important societal progress but exacerbates the need for due process and accountability. Companies and institutions can now discriminate between users at an individual level using collected data or past behavior. Worse, today they can do so in near perfect opacity. The nascent field of web transparency aims to develop the tools and methods necessary to reveal how information is used, however today it lacks robust tools that let users and investigators identify targeting using multiple inputs. Here, we formalize for the first time the problem of detecting and identifying targeting on combinations of inputs and provide the first algorithm that is asymptotically exact. This algorithm is designed to serve as a theoretical foundational block to build future scalable and robust web transparency tools. It offers three key properties. First, our algorithm is service agnostic and applies to a variety of settings under a broad set of assumptions. Second, our algorithm's analysis delineates a theoretical detection limit that characterizes which forms of targeting can be distinguished from noise and which cannot. Third, our algorithm establishes fundamental tradeoffs that lead the way to new metrics for the science of web transparency. Understanding the tradeoff between effective targeting and targeting concealment lets us determine under which conditions predatory targeting can be made unprofitable by transparency tools.