提出新损失函数，让线性自编码推荐模型在更广参数范围下表现更好。
Generalizing Linear Autoencoder Recommenders with Decoupled Expected Quadratic Loss
- 设计解耦期望二次损失，简化模型求解过程。
- 在b>0条件下获得新解，实测性能超越原版模型。
- 算法高效可计算，适合大规模推荐系统应用。
线性自编码器（LAE）因其简洁性和良好表现，在推荐系统中日益流行。现有模型如强调去噪线性自编码器（EDLAE）多采用二次损失训练，但原始EDLAE仅对超参数b=0提供闭式解，限制了模型能力。本文将EDLAE目标泛化为解耦期望二次损失（DEQL），揭示了b>0范围内的新解，扩展了解空间。基于Miller矩阵逆定理提出高效算法，确保b>0情况下的计算可行性。基准数据集上的实验证明，DEQL提供的b>0解优于b=0的基线模型，验证了其在提升测试性能方面的有效性。
原文摘要 · Abstract (English)
Linear autoencoders (LAEs) have gained increasing popularity in recommender systems due to their simplicity and strong empirical performance. Most LAE models, including the Emphasized Denoising Linear Autoencoder (EDLAE) introduced by (Steck, 2020), use quadratic loss during training. However, the original EDLAE only provides closed-form solutions for the hyperparameter choice $b = 0$, which limits its capacity. In this work, we generalize EDLAE objective into a Decoupled Expected Quadratic Loss (DEQL). We show that DEQL simplifies the process of deriving EDLAE solutions and reveals solutions in a broader hyperparameter range $b > 0$, which were not derived in Steck's original paper. Additionally, we propose an efficient algorithm based on Miller's matrix inverse theorem to ensure the computational tractability for the $b > 0$ case. Empirical results on benchmark datasets show that the $b > 0$ solutions provided by DEQL outperform the $b = 0$ EDLAE baseline, demonstrating that DEQL expands the solution space and enables the discovery of models with better testing performance.
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