Analysis of the Mean Absolute Error (MAE) and the Root Mean Square Error (RMSE) in Assessing Rounding Model

TLDR

Existing collaborative filtering algorithms predict decimal ratings, whereas real‑world datasets record integer ratings. The study aims to show that rounding influences MAE and RMSE differently, prove its necessity in post‑processing, and eliminate prediction bias to improve accuracy. We propose two new rounding methods based on the predicted rating probability distribution that optimally map predictions to integer ratings and outperform the basic rounding approach. Experiments on multiple datasets confirm the analysis and demonstrate that the proposed rounding methods improve prediction accuracy.

Abstract

Most existing Collaborative Filtering (CF) algorithms predict a rating as the preference of an active user toward a given item, which is always a decimal fraction. Meanwhile, the actual ratings in most data sets are integers. In this paper, we discuss and demonstrate why rounding can bring different influences to these two metrics; prove that rounding is necessary in post-processing of the predicted ratings, eliminate of model prediction bias, improving the accuracy of the prediction. In addition, we also propose two new rounding approaches based on the predicted rating probability distribution, which can be used to round the predicted rating to an optimal integer rating, and get better prediction accuracy compared to the Basic Rounding approach. Extensive experiments on different data sets validate the correctness of our analysis and the effectiveness of our proposed rounding approaches.