Kay H. Brodersen
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Variance Reduction in Bipartite Experiments through Correlation Clustering
Warren Schudy
Thirty-third Conference on Neural Information Processing Systems (2019) (to appear)
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Causal inference in randomized experiments typically assumes that the units of randomization and the units of analysis are one and the same. In some applications, however, these two roles are played by distinct entities linked by a bipartite graph. The key challenge in such bipartite settings is how to avoid interference bias, which would typically arise if we simply randomized the treatment at the level of analysis units. One effective way of minimizing interference bias in standard experiments is through cluster randomization, but this design has not been studied in the bipartite setting where conventional clustering schemes can lead to poorly powered experiments. This paper introduces a novel clustering objective and a corresponding algorithm that partitions a bipartite graph so as to maximize the statistical power of a bipartite experiment on that graph. Whereas previous work relied on balanced partitioning, our formulation suggests the use of a correlation clustering objective. We use a publicly-available graph of Amazon user-item reviews to validate our solution and illustrate how it substantially increases the statistical power in bipartite experiments.
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Inferring causal impact using Bayesian structural time-series models
Fabian Gallusser
Jim Koehler
Nicolas Remy
Steven L. Scott
Annals of Applied Statistics, 9 (2015), pp. 247-274
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An important problem in econometrics and marketing is to infer the causal impact that a designed market intervention has exerted on an outcome metric over time. In order to allocate a given budget optimally, for example, an advertiser must assess to what extent different campaigns have contributed to an incremental lift in web searches, product installs, or sales. This paper proposes to infer causal impact on the basis of a diffusion-regression state-space model that predicts the counterfactual market response that would have occurred had no intervention taken place. In contrast to classical difference-in-differences schemes, state-space models make it possible to (i) infer the temporal evolution of attributable impact, (ii) incorporate empirical priors on the parameters in a fully Bayesian treatment, and (iii) flexibly accommodate multiple sources of variation, including the time-varying influence of contemporaneous covariates, i.e., synthetic controls. Using a Markov chain Monte Carlo algorithm for model inversion, we illustrate the statistical properties of our approach on synthetic data. We then demonstrate its practical utility by evaluating the effect of an online advertising campaign on search-related site visits. We discuss the strengths and limitations of state-space models in enabling causal attribution in those settings where a randomised experiment is unavailable. The CausalImpact R package provides an implementation of our approach.
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