Most data for evaluating and training recommender systems is subject to selection biases, either through self-selection by the users or through the actions of the recommendation system itself. In this paper, we provide a principled approach to handling selection biases, adapting models and estimation techniques from causal inference. The approach leads to unbiased performance estimators despite biased data, and to a matrix factorization method that provides substantially improved prediction performance on real-world data. We theoretically and empirically characterize the robustness of the approach, finding that it is highly practical and scalable.
Propensity-based approaches have been widely used in causal inference from observational studies @cite_39 , as well as in complete-case analysis for missing data @cite_0 @cite_12 and in survey sampling @cite_7 . However, their use in matrix completion is new to our knowledge. Weighting approaches are also widely used in domain adaptation and covariate shift, where data from one source is used to train for a different problem [e.g.,][] Huang et al 06,Bickel et al 09,Sugiyama Kawanabe 12 . We will draw upon this work, especially the learning theory of weighting approaches in @cite_27 @cite_6 .
@cite_7 @cite_6 @cite_39 @cite_0 @cite_27 @cite_12
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We study optimal covariate balance for causal inferences from observational data when rich covariates and complex relationships necessitate flexible modeling with neural networks. Standard approaches such as propensity weighting and matching balancing fail in such settings due to miscalibrated propensity nets and inappropriate covariate representations, respectively. We propose a new method based on adversarial training of a weighting and a discriminator network that effectively addresses this methodological gap. This is demonstrated through new theoretical characterizations of the method as well as empirical results using both fully connected architectures to learn complex relationships and convolutional architectures to handle image confounders, showing how this new method can enable strong causal analyses in these challenging settings. We propose a novel approach for inferring the individualized causal effects of a treatment (intervention) from observational data. Our approach conceptualizes causal inference as a multitask learning problem; we model a subject's potential outcomes using a deep multitask network with a set of shared layers among the factual and counterfactual outcomes, and a set of outcome-specific layers. The impact of selection bias in the observational data is alleviated via a propensity-dropout regularization scheme, in which the network is thinned for every training example via a dropout probability that depends on the associated propensity score. The network is trained in alternating phases, where in each phase we use the training examples of one of the two potential outcomes (treated and control populations) to update the weights of the shared layers and the respective outcome-specific layers. Experiments conducted on data based on a real-world observational study show that our algorithm outperforms the state-of-the-art. Machine learning techniques such as classification and regression trees (CART) have been suggested as promising alternatives to logistic regression for the estimation of propensity scores. The authors examined the performance of various CART-based propensity score models using simulated data. Hypothetical studies of varying sample sizes (n=500, 1000, 2000) with a binary exposure, continuous outcome, and ten covariates were simulated under seven scenarios differing by degree of non-linear and non-additive associations between covariates and the exposure. Propensity score weights were estimated using logistic regression (all main effects), CART, pruned CART, and the ensemble methods of bagged CART, random forests, and boosted CART. Performance metrics included covariate balance, standard error, percent absolute bias, and 95 confidence interval coverage. All methods displayed generally acceptable performance under conditions of either non-linearity or non-additivity alone. However, under conditions of both moderate non-additivity and moderate non-linearity, logistic regression had subpar performance, while ensemble methods provided substantially better bias reduction and more consistent 95 CI coverage. The results suggest that ensemble methods, especially boosted CART, may be useful for propensity score weighting. In observational studies, propensity scores are commonly estimated by maxi- mum likelihood but may fail to balance high-dimensional pre-treatment covariates even after specification search. We introduce a general framework that unifies and generalizes several recent proposals to improve covariate balance when designing an observational study. In- stead of the likelihood function, we propose to optimize special loss functions---covariate balancing scoring rules (CBSR)---to estimate the propensity score. A CBSR is uniquely determined by the link function in the GLM and the estimand (a weighted average treatment effect). We show CBSR does not lose asymptotic efficiency to the Bernoulli likelihood in estimating the weighted average treatment effect compared, but CBSR is much more robust in finite sample. Borrowing tools developed in statistical learning, we propose practical strategies to balance covariate functions in rich function classes. This is useful to estimate the maximum bias of the inverse probability weighting (IPW) estimators and construct honest confidence interval in finite sample. Lastly, we provide several numerical examples to demonstrate the trade-off of bias and variance in the IPW-type estimators and the trade-off in balancing different function classes of the covariates.