The Sample Complexity of Online One-Class Collaborative Filtering

TL;DR

This paper analyzes the sample complexity of online one-class collaborative filtering, showing how the probability of user response affects the number of ratings needed for effective recommendations, and demonstrating that negative ratings can significantly reduce initial exploration costs.

Contribution

The paper introduces a probabilistic user model and proves that negative ratings improve sample complexity, especially during the cold start phase, compared to positive-only feedback.

Findings

Number of ratings for cold start is proportional to 1/p_f

Negative ratings reduce initial exploration ratings by a factor of 1/p_f

Algorithm achieves near-perfect recommendations after cold start

Abstract

We consider the online one-class collaborative filtering (CF) problem that consists of recommending items to users over time in an online fashion based on positive ratings only. This problem arises when users respond only occasionally to a recommendation with a positive rating, and never with a negative one. We study the impact of the probability of a user responding to a recommendation, p_f, on the sample complexity, i.e., the number of ratings required to make `good' recommendations, and ask whether receiving positive and negative ratings, instead of positive ratings only, improves the sample complexity. Both questions arise in the design of recommender systems. We introduce a simple probabilistic user model, and analyze the performance of an online user-based CF algorithm. We prove that after an initial cold start phase, where recommendations are invested in exploring the user's preferences, this algorithm makes---up to a fraction of the recommendations required for updating the user's preferences---perfect recommendations. The number of ratings required for the cold start phase is nearly proportional to 1/p_f, and that for updating the user's preferences is essentially independent of p_f. As a consequence we find that, receiving positive and negative ratings instead of only positive ones improves the number of ratings required for initial exploration by a factor of 1/p_f, which can be significant.