  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.
