Learning to Infer Unobserved Behaviors: Estimating User's Preference for
  a Site over Other Sites
Atanu R Sinha Tanay Anand Paridhi Maheshwari A V Lakshmy Vishal Jain
A site's recommendation system relies on knowledge of its users' preferences
to offer relevant recommendations to them. These preferences are for attributes
that comprise items and content shown on the site, and are estimated from the
data of users' interactions with the site. Another form of users' preferences
is material too, namely, users' preferences for the site over other sites,
since that shows users' base level propensities to engage with the site.
Estimating users' preferences for the site, however, faces major obstacles
because (a) the focal site usually has no data of its users' interactions with
other sites; these interactions are users' unobserved behaviors for the focal
site; and (b) the Machine Learning literature in recommendation does not offer
a model of this situation. Even if (b) is resolved, the problem in (a) persists
since without access to data of its users' interactions with other sites, there
is no ground truth for evaluation. Moreover, it is most useful when (c) users'
preferences for the site can be estimated at the individual level, since the
site can then personalize recommendations to individual users. We offer a
method to estimate individual user's preference for a focal site, under this
premise. In particular, we compute the focal site's share of a user's online
engagements without any data from other sites. We show an evaluation framework
for the model using only the focal site's data, allowing the site to test the
model. We rely upon a Hierarchical Bayes Method and perform estimation in two
different ways - Markov Chain Monte Carlo and Stochastic Gradient with Langevin
Dynamics. Our results find good support for the approach to computing
personalized share of engagement and for its evaluation.