VARIATIONAL BAYESIAN PARTIALLY OBSERVED NON-NEGATIVE TENSOR FACTORIZATION

• Published in: 2018 IEEE 28th International Workshop on Machine Learning for Signal Processing (MLSP) pp. 1 - 6
• Main Authors: Hinrich, Jesper L., Nielsen, Soren F. V., Madsen, Kristoffer H., Morup, Morten
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01-09-2018
• Subjects: Bayes methods; Brain modeling; Data models; Gene expression; human brain microarray data; Matrix decomposition; missing data; non-negative tensor factorization; Probabilistic logic; probabilistic modeling; Tensile stress
• DOI: 10.1109/MLSP.2018.8516924

Non-negative matrix and tensor factorization (NMF/NTF) have become important tools for extracting part based representations in data. It is however unclear when an NMF or NTF approach is most suited for data and how reliably the models predict when trained on partially observed data. We presently extend a recently proposed variational Bayesian NMF (VB-NMF) to non-negative tensor factorization (VB-NTF) for partially observed data. This admits bi- and multi-linear structure quantification considering both model prediction and evidence. We evaluate the developed VB-NTF on synthetic and a real dataset of gene expression in the human brain and contrast the performance to VB-NMF and conventional NMF/NTF. We find that the gene expressions are better accounted for by VB-NMF than VB-NTF and that VB-NMF/VB-NTF more robustly handle partially observed data than conventional NMF/NTF. In particular, probabilistic modeling is beneficial when large amounts of data is missing and/or the model order over-specified.