Debiased collaborative filtering aims to learn an unbiased prediction model by removing different biases in observational datasets. To solve this problem, one of the simple and effective methods is based on the propensity score, which adjusts the observational sample distribution to the target one by reweighting observed instances. Ideally, propensity scores should be learned with causal balancing constraints. However, existing methods usually ignore such constraints or implement them with unreasonable approximations, which may affect the accuracy of the learned propensity scores. To bridge this gap, in this paper, we first analyze the gaps between the causal balancing requirements and existing methods such as learning the propensity with cross-entropy loss or manually selecting functions to balance. Inspired by these gaps, we propose to approximate the balancing functions in reproducing kernel Hilbert space and demonstrate that, based on the universal property and representer theorem of kernel functions, the causal balancing constraints can be better satisfied. Meanwhile, we propose an algorithm that adaptively balances the kernel function and theoretically analyze the generalization error bound of our methods. We conduct extensive experiments to demonstrate the effectiveness of our methods, and to promote this research direction, we have released our project at https://github.com/haoxuanli-pku/ICLR24-Kernel-Balancing.

翻译：去偏协同过滤旨在通过消除观测数据集中的不同偏差来学习无偏预测模型。解决该问题的一种简单有效的方法基于倾向得分，通过对观测实例进行重加权，将观测样本分布调整为目标分布。理想情况下，倾向得分应在因果平衡约束下进行学习。然而，现有方法通常忽略此类约束，或通过不合理近似实现这些约束，这可能影响所学倾向得分的准确性。为弥补这一差距，本文首先分析了因果平衡要求与现有方法（如使用交叉熵损失学习倾向得分或手动选择平衡函数）之间的差距。受此启发，我们提出在再生核希尔伯特空间中逼近平衡函数，并基于核函数的普适性与表示定理证明，因果平衡约束可得到更充分的满足。同时，我们提出一种自适应平衡核函数的算法，并从理论上分析该方法的泛化误差界。我们通过大量实验验证了方法的有效性，为促进该研究方向，我们已在https://github.com/haoxuanli-pku/ICLR24-Kernel-Balancing 开源项目代码。