Digital advertising revenue in the United States is reported to be US$27.45bn for the first half of 2015 and has experienced a compound annual growth rate of 17% from 2005 to 2014 (Interactive Advertising Bureau (IAB), 2014). Digital advertising exposes marketers to the full tracks of users' conversion paths (i.e., sequence and timing of, as well as engagement in, advertising channels that have reached them) in addition to their demographic information, shopping preferences, and a lot of other relevant information. By analyzing these data, marketers have the potential to gain better insights into how advertisements have an impact on the users and consequently affect their purchasing activity. These insights further help to make smarter decisions in advertising investment planning.

A variety of online channels, including search, display, digital video, and so on, are employed in digital advertising campaigns. Each individual user is usually exposed to multiple advertising channels before making any purchasing decision. Therefore, a fundamental problem in measuring advertising effectiveness and efficiency is to quantify how revenue should be attributed to multiple touch-points along users' conversion paths. The attribution problem studied in this article can be formulated as follows. Given a sequence of revenue records (y ) and users' exposure history to P advertising channels (x1,…xP), we quantify how y should be attributed to xjs and report attribution values ϕxj for j = 1,.., P. We use these notations consistently for all of the methods discussed throughout this article.