Variational Extensions to EM and Multinomial PCA

By Wray L. Buntine. 2002

204 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Computer Vision and Pattern Recognition, Probabilistic & Bayesian Methods

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Citations in the corpus

Rethinking LDA: Moment Matching for Discrete ICA (2015, positive): “The LDA model (2) can be seen as a discretization of principal component analysis (PCA) via replacement of the normal likelihood with the multinomial one and adjusting the prior [9] in the following probabilistic PCA model [10, 11]: θ ∼ Normal(0, IK) and x|θ ∼ Normal(Dθ, σ(2)IM ), where D ∈ RM×K is ”
Probabilistic topic models (2012, unknown): “It relates to PCA and matrix factorization (Jakulin and Buntine, 2002) Was independently invented for genetics (Pritchard et al., 2000) LDA summary by emerging groups.”
Variational learning for latent Gaussian model of discrete data (2012, methodology): “This model is closely related to the class of multinomial PCA (mPCA) model where the latent vector z is a probability vector [Buntine, 2002].”
Modeling User Rating Profiles For Collaborative Filtering (2003, unknown): “As with LDA, URP could be generalized to use any continuous distribution on the simplex, but in this case the Dirichlet leads to efficient prediction equations.”
Relation between PLSA and NMF and implications (2005, methodology): “Despite their different inspirations, both methods are instances of multinomial PCA [1].”
Applying Discrete PCA in Data Analysis (2004, methodology): “Using the mean field formulation of Ghahramani and Beal (Ghahramani & Beal, 2000) presented for discrete PCA in (Buntine, 2002), the development is tedious but straightforward, and has the same form as its non-hierarchical version.”
Proximal Methods for Sparse Hierarchical Dictionary Learning (2010, methodology): “When one marginalizes over the topic random variable, one gets multinomial PCA (Buntine, 2002).”
The rate adapting poisson model for information retrieval and object recognition (2006, background): “As pointed out by Buntine and Jakulin (2004), the basic architecture of LDA is known under various names such as add-mixtures, grade of memberships model, multiple aspect model and multinomial PCA.”
Constrained Nonnegative Matrix Factorization for Image Representation (2012, methodology): “Earlier studies [18] showed that NMF and Probabilistic Latent Semantic Analysis (PLSA) are both instances of multinomial PCA.”
Bayesian Inference for Nonnegative Matrix Factorisation Models (2009, result): “The prior structure here is qualitatively similar to an entropic prior [20, 27], and we find qualitatively similar representations to the ones found by NMF reported earlier by [1, 18].”
Unsupervised Object Discovery: A Comparison (2010, methodology): “The Dirichlet-multinomial form was introduced as MPCA (Multinomial PCA) in Buntine (2002), but is also equivalent to LDA (Blei et al. 2003).”
Proximal Methods for Hierarchical Sparse Coding (2010, unknown): “• Our method establishes a bridge between hierarchical dictionary learning and hierarchical topic models (Blei et al., 2010), which builds upon the interpretation of topic models as multinomial PCA (Buntine, 2002), and can learn similar hierarchies of topics.”
Linear dimensionality reduction: survey, insights, and generalizations (2014, background): “Nonnegative matrix factorization (NMF; Lee and Seung, 1999; sometimes called multinomial PCA; Buntine, 2002), solves the objective fX(H,Y ) = ||X−HY || for a nonnegative linear basis H ∈ IRd×r + and a nonnegative low-dimensional mapping Y ∈ IRr×n + .”
Collaborative Filtering: A Machine Learning Perspective (2004, unknown): “70 7 .5 URP: Vector aspect model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 7 .6 LDA model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 7 .7 URP model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .”