  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.
