Probabilistic Models for Incomplete Multi-dimensional Arrays

By Wei Chu, Zoubin Ghahramani. 2009

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A semantic matching energy function for learning with multi-relational data (2013, methodology): “Other directions have also been proposed derived from probabilistic matrix factorization for multi-dimensional data (Chu and Ghahramani, 2009) or by adapting dimension reduction techniques such as SVD (Speer et al, 2008; Cambria et al, 2009).”
Position-Transitional Particle Swarm Optimization-Incorporated Latent Factor Analysis (2022, unknown): “Representative ones include a probabilistic MF model [16], a multi‐dimensional probabilistic model [17], an SVD++ [18], a non‐parametric Bayesian‐based latent factor model [19], and a weighted trace‐norm regularization‐based model [20].”
Modelling Relational Data using Bayesian Clustered Tensor Factorization (2009, methodology): “Models based on matrix or tensor factorization [18, 19, 3] ha ve the potential of making better predictions than interpretable models of similar complexity, as w e demonstrate in our experimental results section.”
A latent factor model for highly multi-relational data (2012, background): “This approach, which induces inherently some sharing of parameters between both different terms and different relations, has been applied successfully [8] and has inspired some probabilistic formulations [4].”
Personalized recommendation on dynamic content using predictive bilinear models (2009, background): “[11] W. Chu and Z. Ghahramani.”
A case study of behavior-driven conjoint analysis on Yahoo!: front page today module (2009, background): “For example, Tenenbaum and Freeman [18] developed a bilinear model for separating “style” and “content” in images, and recently Chu and Ghahramani [3] derived a probabilistic framework of the Tucker family for modeling structural dependency from partially observed highdimensional array data.”
Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 1 Low-Rank Tensor Decompositions (2016, unknown): “,rN , of an Nth-order core tensor, G P RR1ˆ ̈ ̈ ̈ˆRN , in order to marginalize out G and express the probability density function of tensor X [36, 225, 233] in the form p ( X |B(1), .”
Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination (2014, methodology): “The probabilistic frameworks of tensor factorization were presented in [33], [34], [35].”
Theoretical Analysis of Bayesian Matrix Factorization (2011, methodology): “Among various methods, Bayesian methods of tensor factorization have been shown to be promising (Tao et al., 2008; Yu et al., 2008; Hayashi et al., 2009; Chu and Ghahramani, 2009).”