A Probabilistic Reformulation of Memory-Based Collaborative Filtering: Implications on Popularity Biases

Rocío Cañamares, Pablo Castells

Abstract: We develop a probabilistic formulation giving rise to a formal version of heuristic k nearest-neighbor (kNN) collaborative filtering. Different independence assumptions in our scheme lead to user-based, item-based, normalized and non-normalized variants that match in structure the traditional formulations, while showing equivalent empirical effectiveness. The probabilistic formulation provides a principled explanation why kNN is an effective recommendation strategy, and identifies a key condition for this to be the case. Moreover, a natural explanation arises for the bias of kNN towards recommending popular items. Thereupon the kNN variants are shown to fall into two groups with similar trends in behavior, corresponding to two different notions of item popularity. We show experiments where the comparative performance of the two groups of algorithms changes substantially, which suggests that the performance measurements and comparison may heavily depend on statistical properties of the input data sample.