Upper bound on the predictability of rating prediction in recommender systems

The task of rating prediction has undergone extensive scrutiny, employing diverse modeling approaches to enhance accuracy. However, it remains uncertain whether a maximum accuracy, synonymous with predictability, exists for a given dataset, guiding the quest for optimal algorithms. While existing theories quantify predictability in one-dimensional symbol sequences, extending this to multidimensional and heterogeneous data poses challenges, rendering it unsuitable for rating prediction tasks. Our approach initially employs conditional entropy to quantify rating entropy, overcoming its inherent complexity by transforming it into two easily calculable entropies. Unlike conventional entropy measures, we utilize sample entropy to account for the numerical impact of rating sequences. Furthermore, novel metrics for quantifying entropy in numerical sequences are integrated to enhance predictability scaling. Demonstrating the effectiveness of our method across datasets of varying sizes and domains, current leading rating prediction algorithms achieve approximately 80% predictability.