Recommender systems widely use implicit feedback such as click data because
of its general availability. Although the presence of clicks signals the users'
preference to some extent, the lack of such clicks does not necessarily
indicate a negative response from the users, as it is possible that the users
were not exposed to the items (positive-unlabeled problem). This leads to a
difficulty in predicting the users' preferences from implicit feedback.
Previous studies addressed the positive-unlabeled problem by uniformly
upweighting the loss for the positive feedback data or estimating the
confidence of each data having relevance information via the EM-algorithm.
However, these methods failed to address the missing-not-at-random problem in
which popular or frequently recommended items are more likely to be clicked
than other items even if a user does not have a considerable interest in them.
To overcome these limitations, we first define an ideal loss function to be
optimized to realize recommendations that maximize the relevance and propose an
unbiased estimator for the ideal loss. Subsequently, we analyze the variance of
the proposed unbiased estimator and further propose a clipped estimator that
includes the unbiased estimator as a special case. We demonstrate that the
clipped estimator is expected to improve the performance of the recommender
system, by considering the bias-variance trade-off. We conduct semi-synthetic
and real-world experiments and demonstrate that the proposed method largely
outperforms the baselines. In particular, the proposed method works better for
rare items that are less frequently observed in the training data. The findings
indicate that the proposed method can better achieve the objective of
recommending items with the highest relevance.

针对推荐系统中存在的正 - 未标记问题，本研究提出一种理想损失函数和无偏估计器，并进一步提出一个剪切估计器来通过平衡偏差和方差来改进推荐系统的性能。半合成和真实实验表明，该方法在最大化推荐物品相关性方面具有更好的性能，特别是对于在训练数据中很少出现的物品。