A new multi-view regression approach with an application to customer wallet estimation

Motivated by the problem of customer wallet estimation, we propose a new setting for multi-view regression, where we learn a completely unobserved target (in our case, customer wallet) by modeling it as a "central link" in a directed graphical model, connecting multiple sets of observed variables. The resulting conditional independence allows us to reduce the maximum discriminative likelihood estimation problem to a convex optimization problem for exponential linear models. We show that under certain modeling assumptions, in particular, when there exist two conditionally independent views and the noise is Gaussian, this problem can be reduced to a single least squares regression. Thus, for this specific, but widely applicable setting, the "unsupervised" multi-view problem can be solved via a simple supervised learning approach. This reduction also allows us to test the statistical independence assumptions underlying the graphical model and perform variable selection. We demonstrate the effectiveness of our approach on our motivating problem of customer wallet estimation and on simulation data.