B1724
Title: Bayesian Tucker decomposition model with time varying factor matrices
Authors: Ryota Yuasa - The Institute of Statistical Mathematics (Japan) [presenting]
Genya Kobayashi - Meiji University (Japan)
Shonosuke Sugasawa - Keio University (Japan)
Yuta Yamauchi - Nagoya University (Japan)
Abstract: Many of the data obtained have a time series tensor structure. For tensor data, the Tucker decomposition can be used to save parameters while flexibly taking into account factor interactions. However, it is known that the Tucker decomposition is generally not unique. Therefore, in order to be able to estimate the structure, it is necessary to impose additional constraints and consider modelling with uniqueness in mind. A Bayesian model is proposed based on a type of Tucker decomposition called higher-order singular value decomposition. The matrix Langevin distribution is used in an autoregressive manner as a prior over the column orthogonal factor matrices of the decomposition. For identification of the core tensor, the order constraint on the subtensor norms and all-orthogonality constraint is introduced through constraint relaxation to facilitate the posterior computation. The model is estimated by using the Markov chain Monte Carlo method. The proposed model is illustrated through numerical examples.
