Negative Binomial Matrix Completion
This addresses the problem of handling overdispersed count data in matrix completion for applications like image processing and network analysis, but it is incremental as it extends existing Poisson methods.
The paper tackled matrix completion for overdispersed count data by proposing a negative binomial model, which outperformed Poisson matrix completion in experiments on real data under various noise and missing data settings.
Matrix completion focuses on recovering missing or incomplete information in matrices. This problem arises in various applications, including image processing and network analysis. Previous research proposed Poisson matrix completion for count data with noise that follows a Poisson distribution, which assumes that the mean and variance are equal. Since overdispersed count data, whose variance is greater than the mean, is more likely to occur in realistic settings, we assume that the noise follows the negative binomial (NB) distribution, which can be more general than the Poisson distribution. In this paper, we introduce NB matrix completion by proposing a nuclear-norm regularized model that can be solved by proximal gradient descent. In our experiments, we demonstrate that the NB model outperforms Poisson matrix completion in various noise and missing data settings on real data.