Non-linear matrix factorization with Gaussian processes

By Neil D. Lawrence, Raquel Urtasun. 2009

251 citations recorded by the source corpus.

Subfields: Information Systems, Management Science and Operations Research, Transportation

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Citations in the corpus

A Neural Autoregressive Approach to Collaborative Filtering (2016, methodology): “Along this line, Lawrence & Urtasun (2009) proposed a non-linear PMF using Gaussian process latent variable models.”
Non-Linear Regression for Bag-of-Words Data via Gaussian Process Latent Variable Set Model (2015, methodology): “The GP-LVSM is related to but different from the Gaussian process latent variable model (GP-LVM), which is used for dimension reduction (Lawrence 2004) and matrix factorization (Lawrence and Urtasun 2009).”
Deep Gaussian Processes (2012, methodology): “Work with Raquel Urtasun (Lawrence and Urtasun, 2009) and ongoing work with Max Zwießele and Nicoló Fusi.”
StarSpace: Embed All The Things! (2017, methodology): “In the domain of recommendation, embedding models have had a large degree of success, starting from SVD (Goldberg et al. 2001) and its improvements such as SVD++ (Koren and Bell 2015), as well as a host of other techniques, e.g. (Rendle 2010; Lawrence and Urtasun 2009; Shi et al. 2012).”
Probabilistic Matrix Factorization for Automated Machine Learning (2017, methodology): “In nonlinear probabilistic matrix factorization (Lawrence & Urtasun, 2009), the elements of Y are given by a nonlinear function of the latent variables, , where (cid:15) is independent Gaussian noise.”
On Nonparametric Guidance for Learning Autoencoder Representations (2011, methodology): “While initially used for visualization of high dimensional data, GPLVMs have achieved stateof-the-art results for a number of tasks, including modeling human motion (Wang et al., 2008), classification (Urtasun and Darrell, 2007) and collaborative filtering (Lawrence and Urtasun, 2009).”
Learning multiple-question decision trees for cold-start recommendation (2013, methodology): “The input to the linear model would be all the previous answers that the user has submitted and the output is the user profile.”
Spike and Slab Variational Inference for Multi-Task and Multiple Kernel Learning (2011, methodology): “8740 RMSE reported in [24] using GP-LVM.”
A hierarchical model for ordinal matrix factorization (2011, methodology): “…and item features (Ansari et al. 2000; Stern et al. 2009), those using user rating proﬁles (Mar-lin 2004), restricted Boltzmann machines (Salakhutdinov et al. 2007), nearest neighbours (Bell and Koren 2007), and non-parametric models (Lawrence and Urtasun 2009; Yu et al. 2009a; Zhu et al. 2009).”
Nonparametric guidance of autoencoder representations using label information (2012, methodology): “…initially introduced for the visualization of high dimensional data, they have been used to obtain state-of-the-art results for a number of tasks, including modeling human motion (Wang et al., 2008), classiﬁcation (Urtasun and Darrell, 2007) and collaborative ﬁltering (Lawrence and Urtasun, 2009).”
Local Low-Rank Matrix Approximation (2013, background): “Salakhutdinov & Mnih (2008a) and Salakhutdinov & Mnih (2008b) extended matrix factorization to probabilistic and Bayesian approach, and Lawrence & Urtasun (2009) proposed non-linear version of PMF. Rennie & Srebro (2005) proposed a maximum-margin method.”
Automatic model construction with Gaussian processes (2014, methodology): “Extensions of the GP-LVM The GP-LVM has been used effectively in a wide variety of applications (Lawrence, 2004; Lawrence and Urtasun, 2009; Salzmann et al., 2008).”
Nonparametric Bayesian Dictionary Learning for Analysis of Noisy and Incomplete Images (2011, background): “This problem is closely related to the problem of matrix completion [6], [23], [33], where the incomplete matrix has columns defined by .”
fLDA: matrix factorization through latent dirichlet allocation (2010, background): “Recently, several papers have explored models to better regularize the latent factors, primarily inspired by the task of improving RMSE for the Netflix data[19].”
Bayesian Optimization and Semiparametric Models with Applications to Assistive Technology (2014, background): “, 2008], classification [Urtasun and Darrell, 2007] and collaborative filtering [Lawrence and Urtasun, 2009].”
Multi-Domain Collaborative Filtering (2010, methodology): “Among all model-based CF methods, matrix factorization methods are perhaps the most popular one in recent years [2, 25, 20, 5, 21, 22, 14, 32, 29].”
Nonparametric bayesian multitask collaborative filtering (2013, methodology): “Among all model-based CF methods, matrix factorization (MF)-based methods are perhaps the most popular ones in recent years [5, 29, 25, 22, 26, 27, 15].”
On the properties of variational approximations of Gibbs posteriors (2015, methodology): “Since then, this prior and variants were used in several papers [e.g. Lawrence and Urtasun, 2009, Zhou et al., 2010].”