Bayesian Adaptive Tucker Decompositions for Tensor Factorization
提出一种贝叶斯自适应塔克分解模型，自动推断张量的多秩，适用于连续和二元数据，并能处理缺失值，在化学计量学和生态学数据上优于现有方法。
Tucker tensor decomposition offers a more effective representation for multiway data compared to the widely used PARAFAC model. However, its flexibility brings the challenge of selecting the appropriate latent multi-rank. To overcome the issue of pre-selecting the latent multi-rank, we introduce a Bayesian adaptive Tucker decomposition model that infers the multi-rank automatically via an infinite increasing shrinkage prior. The model introduces local sparsity in the core tensor, inducing rich and at the same time parsimonious dependency structures. Posterior inference proceeds via an efficient adaptive Gibbs sampler, supporting both continuous and binary data and allowing for straightforward missing data imputation when dealing with incomplete multiway data. We discuss fundamental properties of the proposed modeling framework, providing theoretical justification. Simulation studies and applications to chemometrics and complex ecological data offer compelling evidence of its advantages over existing tensor factorization methods.