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Large-scale online recommender system spreads all over the Internet being incharge of two basic tasks: Click-Through Rate (CTR) and Post-Click ConversionRate (CVR) estimations. However, traditional CVR estimators suffer fromwell-known Sample Selection Bias and Data Sparsity issues. Entire space modelswere proposed to address the two issues via tracing the decision-making path of"exposure_click_purchase". Further, some researchers observed that there arepurchase-related behaviors between click and purchase, which can better drawthe user's decision-making intention and improve the recommendationperformance. Thus, the decision-making path has been extended to"exposure_click_in-shop action_purchase" and can be modeled with conditionalprobability approach. Nevertheless, we observe that the chain rule ofconditional probability does not always hold. We report Probability SpaceConfusion (PSC) issue and give a derivation of difference between ground-truthand estimation mathematically. We propose a novel Entire Space Multi-Task Modelfor Post-Click Conversion Rate via Parameter Constraint (ESMC) and twoalternatives: Entire Space Multi-Task Model with Siamese Network (ESMS) andEntire Space Multi-Task Model in Global Domain (ESMG) to address the PSC issue.Specifically, we handle "exposure_click_in-shop action" and "in-shopaction_purchase" separately in the light of characteristics of in-shop action.The first path is still treated with conditional probability while the secondone is treated with parameter constraint strategy. Experiments on both offlineand online environments in a large-scale recommendation system illustrate thesuperiority of our proposed methods over state-of-the-art models. Thereal-world datasets will be released.

ESMC: Entire Space Multi-Task Model for Post-Click Conversion Rate via Parameter Constraint