Bayesian probabilistic matrix factorization using Markov chain Monte Carlo

By Ruslan Salakhutdinov, Andriy Mnih. 2008

1,553 citations recorded by the source corpus.

Subfields: Computational Mechanics, Probabilistic & Bayesian Methods, Recommender Systems, Signal Processing

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Citations in the corpus

Recurrent Latent Variable Networks for Session-Based Recommendation (2017, methodology): “MF-based methods are perhaps the most popular class of model-based CF approaches [9, 21, 26, 27].”
A Neural Autoregressive Approach to Collaborative Filtering (2016, methodology): “Among all these models, matrix factorization is most popular and successful, c.f. (Ko-ren et al., 2009; Salakhutdinov & Mnih, 2008; Mackey et al., 2011; Gopalan et al., 2013).”
Learning Distributed Representations from Reviews for Collaborative Filtering (2015, background): “In this setting, collaborative filtering is usually cast as a problem of matrix factorization with missing values [10, 16, 18].”
Explainable Recommendation: A Survey and New Perspectives (2018, background): “By now, the related explainable recommendation models cover a wide range of deep learning techniques, including CNN (Seo et al. [2017], Tang and Wang [2018]), RNN/LSTM (Donkers et al.”
Word Representations via Gaussian Embedding (2014, background): “Related work in probabilistic matrix factorization (Mnih & Salakhutdinov, 2007) embeds rows and columns as Gaussians, and some forms of this do provide each row and column with its own variance (Salakhutdinov & Mnih, 2008).”
Stochastic Gradient Hamiltonian Monte Carlo (2014, background): “Due to the sparsity in the ratings matrix (users versus items) in recommender systems, over-ﬁtting is a severe issue with Bayesian approaches providing a natural solution (Salakhutdinov and Mnih, 2008a).”
SoRec: social recommendation using probabilistic matrix factorization (2008, methodology): “Recently, several matrix factorization methods [15, 17, 18, 23] have been proposed for collaborative filtering.”
Deep Exponential Families (2014, positive): “As examples, the DEF can be made part of a multi-level model of grouped data [10], time-series model of sequential data [3], or a factorization model of pairwise data [31].”
Deep and Hierarchical Implicit Models (2017, background): “Formally, for layers 1 , . . . , L , the local variables for data point x n are generated via where g (cid:96) is the transformation for layer (cid:96) , s is random noise, and β = { β 1 , . . . , β L } are parameters of the L transformations (e.g., weights and biases).”
A Hybrid Collaborative Filtering Model with Deep Structure for Recommender Systems (2017, methodology): “By specifying different L(·, ·), many matrix factorization models have been proposed, for example, non-negative matrix factorization (Lee and Seung 2001), probabilistic matrix factorization (Salakhutdinov and Mnih 2011), Bayesian probabilistic matrix factorization (Salakhutdinov and Mnih 2008), max-”
Collaborative filtering and deep learning based recommendation system for cold start items (2017, background): “A N Authors (Salakhutdinov, & Mnih, 2007) introduce the probabilistic matrix factorization (PMF) that scales linearly on large data sets and outperforms standard singular value decomposition (SVD) models.”
Collaborative Web Service QoS Prediction via Neighborhood Integrated Matrix Factorization (2013, methodology): “matrix factorization methods [43], [44], [20], [45] have been proposed for collaborative filtering.”
Nonparametric Bayesian Dictionary Learning for Analysis of Noisy and Incomplete Images (2011, result): “This is closely related to recent research on matrix completion [6], [23], [33], but here, we move beyond simple low-rank assumptions associated with such previous research.”
Testing for Associations between Loci and Environmental Gradients Using Latent Factor Mixed Models (2012, methodology): “To perform parameter estimation, we extend probabilistic principal component analysis (PCA) and recent statistical learning approaches (Tipping and Bishop 1999; Salakhutdinov and Mnih 2008; Engelhardt and Stephens 2010; Frichot et al. 2012).”
Aspect Based Recommendations: Recommending Items with the Most Valuable Aspects Based on User Reviews (2017, methodology): “Comparing our proposed approach with these two models is su cient for our purposes because these are strong baselines that outperformed various other approaches discussed in Section 2, including EFM, PMF, and RTF.”
A hierarchical model for ordinal matrix factorization (2011, methodology): “The hierarchical prior structure on U and V , as speciﬁed here, is the same as that used in the Bayesian probabilistic matrix factorization model of Salakhutdinov and Mnih (2008a).”
Bayesian Matrix Factorization with Side Information and Dirichlet Process Mixtures (2010, methodology): “The work most closely related to our own is the Bayesian probabilistic matrix factorization model (Salakhut- dinov and Mnih 2008), which features a Gaussian bi-linear factor model complete with Gaussian-Wishart priors.”