Variational AutoEncoder (VAE) has been extended as a representative nonlinear method for collaborative filtering. However, the bottleneck of VAE lies in the softmax computation over all items, such that it takes linear costs in the number of items to compute the loss and gradient for optimization. This hinders the practical use due to millions of items in real-world scenarios. Importance sampling is an effective approximation method, based on which the sampled softmax has been derived. However, existing methods usually exploit the uniform or popularity sampler as proposal distributions, leading to a large bias of gradient estimation. To this end, we propose to decompose the inner-product-based softmax probability based on the inverted multi-index, leading to sublinear-time and highly accurate sampling. Based on the proposed proposals, we develop a fast Variational AutoEncoder (FastVAE) for collaborative filtering. FastVAE can outperform the state-of-the-art baselines in terms of both sampling quality and efficiency according to the experiments on three real-world datasets.

翻译：挥发性自动编码器(VAE)作为具有代表性的非线性合作过滤法(VAE)已经扩展,但VAE的瓶颈在于对所有物品的软式计算,因此计算损失和坡度以优化所需的项目数量需要线性成本。这妨碍了实际使用实实在在的几百万个物品。重要取样是一种有效的近似方法,根据这种方法,抽样软体压轴(FastVAE)已经得出。但是,现有方法通常利用统一或流行采样器作为建议分布,导致梯度估计的偏差。为此,我们提议根据反向多指数将内基于产品的软性负负值概率进行分解,导致次直线时间和高度精确的采样。根据提议,我们为协作过滤开发了快速挥发式自动 Encoder(FastVAE) 。FastVAE 根据三个真实世界数据集的实验,在采样质量和效率两方面都超越了最先进的基线。