Uplift Modeling from Separate Labels
Uplift modeling is aimed at estimating the incremental impact of an action on an individual's behavior, which is useful in various application domains such as targeted marketing (advertisement campaigns) and personalized medicine (medical treatments). Conventional methods of uplift modeling require every instance to be jointly equipped with two types of labels: the taken action and its outcome. However, obtaining two labels for each instance at the same time is difficult or expensive in many real-world problems. In this paper, we propose a novel method of uplift modeling that is applicable to a more practical setting where only one type of labels is available for each instance. We show a mean squared error bound for the proposed estimator and demonstrate its effectiveness through experiments.
This paper proposes an approach to heterogeneous treatment effect estimation (what it calls “uplift modeling”) from separate populations. A simple version of the setup of this paper is as follows. We have two populations, k = 1, 2, with different probabilities of treatment conditional on observed features, Pk[T|X] (the paper also allows for the case where these need to be estimated). We have access to covariate-outcome pairs (X, Y) drawn from both populations, so we can estimate Ek[Y|X]. We assume potential outcomes Y(-1), Y(1), and assume that E[Y(T) | X] doesn’t depend on setup k.  What we would really want is to estimate a conditional average treatment effect tau(x) = E[Y(1) - Y(-1) | X = x]. However, we don’t observe assigned treatments for each sample, i.e., we don’t see (X, T, Y); rather we only know marginal treatment probabilities Pk[T|X] along with data (X, Y). The main result of the paper is that we can still identify tau(x) in terms of observable moments,  (A) tau(x) = 2 (E2[Y|X=x] - E1[Y|X=x]) / (E2[T|X=x] - E1[T|X=x]),  and it then derives estimators for tau(x).  Overall, I found this to be a fascinating paper, in that it states a simple, seemingly difficult problem, and pushes quite far in its results. However, it appears that the setup discussed in this paper is closely related to instrumental variables regression, and that the authors have essentially re-derived (fairly sophisticated forms of) two-stage least-squares.  As background, in instrumental variables regression, we usually observe an instrument Z that “nudges” individuals towards treatment; we then observe a tuple (X, Y, T, Z). There is a concern, however, that the treatment T itself may not be unconfounded. The solution, then, is to use the effect of Z on Y to identify the causal effect of T (because we assume that Z nudges on T in a random way), resulting in an identification result:  (B) tau(x) = 2 (E[Y|X=x, Z=2] - E[Y|X=x, Z=1]) / (E[T|X=x, Z=2] - E[T|X=x, Z=1]).  Notice that (A) and (B) are exactly the same, provided we use “setup” in case (A) as our instrument Z in case (B). Several methods for heterogeneous treatment effect estimation via instrumental variables have recently been considered, including  Athey, Susan, Julie Tibshirani, and Stefan Wager. "Generalized random forests." arXiv preprint arXiv:1610.01271 (2016). Lewis, Greg, and Vasilis Syrgkanis. "Adversarial Generalized Method of Moments." arXiv preprint arXiv:1803.07164 (2018). Hartford, Jason, Greg Lewis, Kevin Leyton-Brown, and Matt Taddy. "Deep iv: A flexible approach for counterfactual prediction." In International Conference on Machine Learning, pp. 1414-1423. 2017.  For a review of fundamental results, see  Imbens, Guido W. "Instrumental Variables: An Econometrician’s Perspective." Statistical Science 29.3 (2014): 323-358.  The approach presented here (based on solving a min-max optimization problem) appears to be novel, and potentially interesting, in the context of the existing literature. However, because the paper seems unaware of its nearest neighbors in the literature, it is very difficult to accurately assess its merit.  Thus, although I enjoyed reading this paper, I am now voting for rejection. However, this should really be taken as an encouragement for the authors to re-visit their research question in light of the IV literature, and then resubmit to ICML or JMLR.  Furthermore, I think this paper has potential for considerable impact; but as it’s currently written, it seems to mostly just target a niche problem in marketing, and so would probably not get the readership it deserves even if published at NIPS. Relatedly, for broader scientific impact, I’d recommend the authors use nomenclature around heterogeneous treatment effect estimation rather than uplift (which is, as far as I can tell, a term only used in marketing). Some recent references include:  Hill, Jennifer L. "Bayesian nonparametric modeling for causal inference." Journal of Computational and Graphical Statistics 20.1 (2011): 217-240. Imai, Kosuke, and Marc Ratkovic. "Estimating treatment effect heterogeneity in randomized program evaluation." The Annals of Applied Statistics 7.1 (2013): 443-470. Künzel, Sören R., et al. "Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning." arXiv preprint arXiv:1706.03461 (2017). Wager, Stefan, and Susan Athey. "Estimation and Inference of Heterogeneous Treatment Effects using Random Forests." arXiv preprint arXiv:1510.04342 (2015).