Non-negative tensor factorization models for Bayesian audio processing

We provide an overview of matrix and tensor factorization methods from a Bayesian perspective, giving emphasis on both the inference methods and modeling techniques. Factorization based models and their many extensions such as tensor factorizations have proved useful in a broad range of applications, supporting a practical and computationally tractable framework for modeling. Especially in audio processing, tensor models help in a unified manner the use of prior knowledge about signals, the data generation processes as well as available data from different modalities. After a general review of tensor models, we describe the general statistical framework, give examples of several audio applications and describe modeling strategies for key problems such as deconvolution, source separation, and transcription.