The cold-start problem is a common challenge for most recommender systems. With extremely limited interactions of cold-start users, conventional recommender models often struggle to generate embeddings with sufficient expressivity. Moreover, the absence of auxiliary content information of users exacerbates the presence of challenges, rendering most cold-start methods difficult to apply. To address this issue, our motivation is based on the observation that if a model can generate expressive embeddings for existing users with relatively more interactions, who were also initially cold-start users, then we can establish a mapping from few initial interactions to expressive embeddings, simulating the process of generating embeddings for cold-start users. Based on this motivation, we propose a Variational Mapping approach for cold-start user Recommendation (VM-Rec). Firstly, we generate a personalized mapping function for cold-start users based on their initial interactions, and parameters of the function are generated from a variational distribution. For the sake of interpretability and computational efficiency, we model the personalized mapping function as a sparse linear model, where each parameter indicates the association to a specific existing user. Consequently, we use this mapping function to map the embeddings of existing users to an embedding of the cold-start user in the same space. The resulting embedding has similar expressivity to that of existing users and can be directly integrated into a pre-trained recommender model to predict click through rates or ranking scores. We evaluate our method based on three widely used recommender models as pre-trained base recommender models, outperforming four popular cold-start methods on two datasets under the same base model.

翻译：冷启动问题是大多数推荐系统面临的常见挑战。由于冷启动用户的交互数据极为有限，传统推荐模型往往难以生成具有足够表现力的嵌入向量。此外，用户辅助内容信息的缺失加剧了这一挑战，导致大多数冷启动方法难以应用。为解决该问题，我们的动机源于以下观察：若模型能为当前交互较多的用户——这些用户最初也是冷启动用户——生成具有表现力的嵌入向量，那么我们可以建立一个从少量初始交互到表现力嵌入的映射，模拟冷启动用户的嵌入生成过程。基于这一动机，我们提出了一种面向冷启动用户推荐的变分映射方法（VM-Rec）。首先，我们根据冷启动用户的初始交互为其生成个性化映射函数，该函数的参数由一个变分分布生成。为兼顾可解释性与计算效率，我们将个性化映射函数建模为稀疏线性模型，其中每个参数表示与特定现有用户的关联性。随后，我们利用该映射函数将现有用户的嵌入向量映射到同一空间中冷启动用户的嵌入向量。所得嵌入向量具有与现有用户相当的表现力，可直接集成到预训练推荐模型中，用于预测点击率或排序分数。我们基于三种广泛使用的推荐模型作为预训练基础模型进行评估，在相同基础模型下，本方法在两个数据集上优于四种主流冷启动方法。