Bayesian Semi-Supervised Tensor Decomposition using Natural Gradients for Anomaly Detection

Anomaly Detection has several important applications. In this paper, our focus is on detecting anomalies in seller-reviewer data using tensor decomposition. While tensor-decomposition is mostly unsupervised, we formulate Bayesian semi-supervised tensor decomposition to take advantage of sparse labeled data. In addition, we use Polya-Gamma data augmentation for the semi-supervised Bayesian tensor decomposition. Finally, we show that the Polya-Gamma formulation simplifies calculation of the Fisher information matrix for partial natural gradient learning. Our experimental results show that our semi-supervised approach outperforms state of the art unsupervised baselines. And that the partial natural gradient learning outperforms stochastic gradient learning and Online-EM with sufficient statistics.