协同过滤的信道编码视角
A Channel Coding Perspective of Collaborative Filtering
摘要：
我们认为协同过滤的问题，从信道编码的角度来看。我们将潜在的评级矩阵建模为具有块常数结构的有限字母矩阵。通过离散无记忆信道从该底层矩阵获得观测，该离散无记忆信道具有表示噪声用户行为的噪声部分和表示丢失数据的擦除部分。此外，基础矩阵为常数的聚类是{ \it未知}。我们建立了一个尖锐的阈值结果，这个模型：如果最大的集群大小小于$C_1 \log(mn)$（其中的评级矩阵的大小为$m \times n$），那么底层矩阵不能恢复与任何估计，但如果最小的集群大小大于$C_2 \log(mn)$，那么我们显示一个多项式时间估计与减少的错误概率。在均匀簇大小的情况下，不仅阈值的顺序，而且常数被识别。
英文摘要：
We consider the problem of collaborative filtering from a channel coding perspective. We model the underlying rating matrix as a finite alphabet matrix with block constant structure. The observations are obtained from this underlying matrix through a discrete memoryless channel with a noisy part representing noisy user behavior and an erasure part representing missing data. Moreover, the clusters over which the underlying matrix is constant are {\it unknown}. We establish a sharp threshold result for this model: if the largest cluster size is smaller than $C_1 \log(mn)$ (where the rating matrix is of size $m \times n$), then the underlying matrix cannot be recovered with any estimator, but if the smallest cluster size is larger than $C_2 \log(mn)$, then we show a polynomial time estimator with diminishing probability of error. In the case of uniform cluster size, not only the order of the threshold, but also the constant is identified.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
