Bayesian Topic Regression for Causal Inference

Bayesian Topic Regression for Causal Inference Maximilian Ahrens1, Julian Ashwin1, Jan-Peter Calliess1, Vu Nguyen1,2 1University of Oxford, 2Amazon {mahrens,jan}@robots.ox.ac.uk, julian.ashwin@economics.ox.ac.uk, vutngn@amazon.com Abstract Causal inference using observational text data is becoming increasingly popular in many re- search areas. This paper presents the Bayesian Topic Regression (BTR) model that uses both text and numerical information to model an outcome variable. It allows estimation of both discrete and continuous treatment effects. Fur- thermore, it allows for the inclusion of addi- tional numerical confounding factors next to text data. To this end, we combine a super- vised Bayesian topic model with a Bayesian regression framework and perform supervised representation learning for the text features jointly with the regression parameter train- ing, respecting the Frisch-Waugh-Lovell the- orem. Our paper makes two main contribu- tions. First, we provide a regression frame- work that allows causal inference in settings when both text and numerical confounders are of relevance. We show with synthetic and semi-synthetic datasets that our joint approach recovers ground truth with lower bias than any benchmark model, when text and numerical features are correlated. Second, experiments on two real-world datasets demonstrate that a joint and supervised learning strategy also yields superior prediction results compared to strategies that estimate regression weights for text and non-text features separately, being even competitive with more complex deep neu- ral networks. 1 Introduction Causal inference using observational text data is increasingly popular across many research areas (Keith et al., 2020). It expands the range of re- search questions that can be explored when using text data across various fields, such as in the social and data sciences; adding to an extensive literature of text analysis methods and applications Grimmer and Stewart (2013); Gentzkow et al. (2019). Where randomized controlled trials are not possible, ob- servational data might often be the only source of information and statistical methods need to be deployed to adjust for confounding biases. Text data can either serve as a proxy for otherwise un- observed confounding variables, be a confounding factor in itself, or even represent the treatment or outcome variable of interest. The framework: We consider the causal infer- ence settings where we allow for the treatment vari- able to be binary, categorical or continuous. In our setting, text might be either a confounding factor or a proxy for a latent confounding variable. We also allow for additional non-text confounders (covari- ates). To the best of our knowledge, we are the first to provide such statistical inference framework. Considering both text and numerical data jointly can not only improve prediction performance, but can be crucial for conducting unbiased statistical in- ference. When treatment and confounders are cor- related with each other and with the outcome, the Frisch-Waugh-Lovell theorem (Frisch and Waugh, 1933; Lovell, 1963), described in Section 2.2, im- plies that all regression weights must be estimated jointly, otherwise estimates will be biased. Text features themselves are ‘estimated data’. If they stem from supervised learning, which estimated the text features with respect to the outcome variable …

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