Reinforce Matrix Factorization for Time Series Modeling: Probabilistic Sequential Matrix Factorization

How to integrate state-space model into matrix factorization in a probabilistic framework?

Matrix factorization is a classical machine learning approach for modeling real-world data. It shows great potential for solving various data reconstruction and imputation problems such as recommender system and image inpainting. Recently, matrix factorization has also become an efficient tool for modeling real-world time series data. Since time series data involve strong temporal dependencies, matrix factorization variants are required to achieve temporal/sequential modeling. Today, we will introduce a probabilistic sequential matrix factorization (PSMF) model to high-dimensional time series modeling. The model takes into account nonlinear Gaussian state-space models for achieving temporal nonlinearities. Notably, PSMF model was proposed in the following paper:

Akyildiz, O. D., van den Burg, G., Damoulas, T., & Steel, M. (2021). Probabilistic sequential matrix factorization. In International Conference on Artificial Intelligence and Statistics (AISTATS 2021) (pp. 3484–3492). PMLR.

• Slides: https://probnum2022.github.io/pdf/akyildiz.pdf
• Python implementation: https://github.com/alan-turing-institute/rPSMF