A Survey on Causal Inference <s> Recommendation <s> 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 handle selection biases by 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, and find that it is highly practical and scalable. <s> BIB001 </s> A Survey on Causal Inference <s> Recommendation <s> This paper studies the evaluation of policies that recommend an ordered set of items (e.g., a ranking) based on some context---a common scenario in web search, ads, and recommendation. We build on techniques from combinatorial bandits to introduce a new practical estimator that uses logged data to estimate a policy's performance. A thorough empirical evaluation on real-world data reveals that our estimator is accurate in a variety of settings, including as a subroutine in a learning-to-rank task, where it achieves competitive performance. We derive conditions under which our estimator is unbiased---these conditions are weaker than prior heuristics for slate evaluation---and experimentally demonstrate a smaller bias than parametric approaches, even when these conditions are violated. Finally, our theory and experiments also show exponential savings in the amount of required data compared with general unbiased estimators. <s> BIB002 </s> A Survey on Causal Inference <s> Recommendation <s> Causal inference in observational settings typically rests on a pair of identifying assumptions: (1) unconfoundedness and (2) covariate overlap, also known as positivity or common support. Investigators often argue that unconfoundedness is more plausible when many covariates are included in the analysis. Less discussed is the fact that covariate overlap is more difficult to satisfy in this setting. In this paper, we explore the implications of overlap in high-dimensional observational studies, arguing that this assumption is stronger than investigators likely realize. Our main innovation is to frame (strict) overlap in terms of bounds on a likelihood ratio, which allows us to leverage and expand on existing results from information theory. In particular, we show that strict overlap bounds discriminating information (e.g., Kullback-Leibler divergence) between the covariate distributions in the treated and control populations. We use these results to derive explicit bounds on the average imbalance in covariate means under strict overlap and a range of assumptions on the covariate distributions. Importantly, these bounds grow tighter as the dimension grows large, and converge to zero in some cases. We examine how restrictions on the treatment assignment and outcome processes can weaken the implications of certain overlap assumptions, but at the cost of stronger requirements for unconfoundedness. Taken together, our results suggest that adjusting for high-dimensional covariates does not necessarily make causal identification more plausible. <s> BIB003 </s> A Survey on Causal Inference <s> Recommendation <s> Many current applications use recommendations in order to modify the natural user behavior, such as to increase the number of sales or the time spent on a website. This results in a gap between the final recommendation objective and the classical setup where recommendation candidates are evaluated by their coherence with past user behavior, by predicting either the missing entries in the user-item matrix, or the most likely next event. To bridge this gap, we optimize a recommendation policy for the task of increasing the desired outcome versus the organic user behavior. We show this is equivalent to learning to predict recommendation outcomes under a fully random recommendation policy. To this end, we propose a new domain adaptation algorithm that learns from logged data containing outcomes from a biased recommendation policy and predicts recommendation outcomes according to random exposure. We compare our method against state-of-the-art factorization methods, in addition to new approaches of causal recommendation and show significant improvements. <s> BIB004 </s> A Survey on Causal Inference <s> Recommendation <s> Decision makers in health, public policy, technology, and social science are increasingly interested in going beyond 'one-size-fits-all' policies to personalized ones. Thus, they are faced with the problem of estimating heterogeneous causal effects. Unfortunately, estimating heterogeneous effects from randomized data requires large amounts of statistical power and while observational data is often available in much larger quantities the presence of unobserved confounders can make using estimates derived from it highly suspect. We show that under some assumptions estimated heterogeneous treatment effects from observational data can preserve the rank ordering of the true heterogeneous causal effects. Such an approach is useful when observational data is large, the set of features is high-dimensional, and our priors about feature importance are weak. We probe the effectiveness of our approach in simulations and show a real-world example in a large-scale recommendations problem. <s> BIB005 </s> A Survey on Causal Inference <s> Recommendation <s> Addressing the non-uniform missing mechanism of rating feedback is critical to build a well-performing recommeder in the real-world systems. To tackle the challenging issue, we first define an ideal loss function that should be optimized to achieve the goal of recommendation. Then, we derive the generalization error bound of the ideal loss that alleviates the variance and the misspecification problems of the previous propensity-based methods. We further propose a meta-learning method minimizing the bound. Empirical evaluation using real-world datasets validates the theoretical findings and demonstrates the practical advantages of the proposed upper bound minimization approach. <s> BIB006
The recommendation is highly correlated with the treatment effect estimation, as exposing the user to an item in the recommendation system can be viewed as applying one specific treatment to a unit BIB005 BIB001 . Similar to the dataset used in the treatment effect estimation, the dataset used in the recommendation are usually biased due to the self-selection of the users. For example, in the movie rate dataset, users tend to rate the movies that they like: the horrible movie ratings are mostly made by horror movie fans and less by romantics movie fans. Another example is the advertisement recommendation datasets. The recommendation system would only recommend the advertisements to the users whom the system believes are interested in those advertisements. In the above examples, the records in the datasets are not representative of the whole population, which is the selection bias. The selection bias brings challenges to both recommendation model training and evaluation. Re-weighting samples based on the propensity score is a powerful method to solve the problems that stem from selection bias. The improved performance estimation after propensity score weighting can be calculated as follows: whereŶ is the value upon which to measure the quality of a recommendation system, U is the number of users, and I is the number of items. O u,i is a binary variable to indicates the interaction of the u-th user with the i-th item in the observational data. δ u,i (·, ·) can be any classical quality measure of a recommendation, such as cumulative gain(CG), discounted cumulative gain (DCG), and precision at k. P is the marginal probability matrix, whose entry is defined as P u,i = P(O u,i = 1). The improved quality measure is an unbiased estimation to the real measurement R(Ŷ ) over the whole population, which is defined as R(Ŷ ) = 1 U ·I U u=1 I i=1 δ u,i (Y ,Ŷ ). Based on the unbiased quality measurement, in BIB001 , the propensity-score empirical risk minimization (ERM) for recommendation is proposed:Ŷ ∈ H is selected to optimize the following problem:Ŷ ERM = argminŶ ∈H {R IPS (Ŷ |P)}, whereR IPS (Ŷ |P) is defined in Eqn. BIB003 . Later, various works are developed to drawbacks of propensity score weighting, including estimation variance reduction BIB006 BIB002 , handle data sparsity BIB006 BIB002 , doubly robust estimation  . In addition to using IPS or doubly robust estimation based method to overcome the selection bias, similar to the advertisement domain, some works also adopt a small unbiased dataset to correct selection bias. In this case, the dataset contains a large set of logged feedback records under control policy and a small set of records under the randomized recommendation. CausalEmbed(CausE) BIB004 is a representative method in this direction, which proposed a new matrix factorization algorithm. In detail, CausalEmbed jointly factorizes the matrix of those two datasets and links these two models by regularizing the difference between treated and control representation.