Explore probabilistic tensor decomposition methods based on Bayesian inference in this 54-minute conference talk that contrasts traditional least squares approaches with advanced probabilistic techniques. Learn how probabilistic methods offer superior robustness to noise and model misspecification compared to conventional Gaussian maximum likelihood estimation used in most tensor decomposition approaches. Discover innovative strategies for determining optimal component numbers and gain access to built-in tools for characterizing model uncertainty. Master the theoretical foundations that distinguish non-probabilistic from probabilistic tensor decomposition while understanding their similarities and key differences. Access practical implementation through the freely available probabilistic tensor toolbox demonstrated throughout the presentation, providing hands-on experience with these advanced mathematical techniques for multiway data analysis.