Toward Implicit Sample Noise Modeling: Deviation-driven Matrix Factorization

Abstract

The objective function of a matrix factorization model usually aims to minimize the average of a regression error contributed by each element. However, given the existence of stochastic noises, the implicit deviations of sample data from their true values are almost surely diverse, which makes each data point not equally suitable for fitting a model. In this case, simply averaging the cost among data in the objective function is not ideal. Intuitively we would like to emphasize more on the reliable instances (i.e., those contain smaller noise) while training a model. Motivated by such observation, we derive our formula from a theoretical framework for optimal weighting under heteroscedastic noise distribution. Specifically, by modeling and learning the deviation of data, we design a novel matrix factorization model. Our model has two advantages. First, it jointly learns the deviation and conducts dynamic reweighting of instances, allowing the model to converge to a better solution. Second, during learning the deviated instances are assigned lower weights, which leads to faster convergence since the model does not need to overfit the noise. The experiments are conducted in clean recommendation and noisy sensor datasets to test the effectiveness of the model in various scenarios. The results show that our model outperforms the state-of-the-art factorization and deep learning models in both accuracy and efficiency.