Recommender systems are important and valuable tools for many personalized services. Collaborative Filtering (CF) algorithms -- among others -- are fundamental algorithms driving the underlying mechanism of personalized recommendation. Many of the traditional CF algorithms are designed based on the fundamental idea of mining or learning correlative patterns from data for matching, including memory-based methods such as user/item-based CF as well as learning-based methods such as matrix factorization and deep learning models. However, advancing from correlative learning to causal learning is an important problem, because causal/counterfactual modeling can help us to think outside of the observational data for user modeling and personalization. In this paper, we propose Causal Collaborative Filtering (CCF) -- a general framework for modeling causality in collaborative filtering and recommendation. We first provide a unified causal view of CF and mathematically show that many of the traditional CF algorithms are actually special cases of CCF under simplified causal graphs. We then propose a conditional intervention approach for $do$-calculus so that we can estimate the causal relations based on observational data. Finally, we further propose a general counterfactual constrained learning framework for estimating the user-item preferences. Experiments are conducted on two types of real-world datasets -- traditional and randomized trial data -- and results show that our framework can improve the recommendation performance of many CF algorithms.
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