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Infinite Sparse Factor Analysis and Infinite Independent Components Analysis [chapter]

David Knowles, Zoubin Ghahramani
Independent Component Analysis and Signal Separation  
A nonparametric Bayesian extension of Independent Components Analysis (ICA) is proposed where observed data Y is modelled as a linear superposition, G, of a potentially infinite number of hidden sources  ...  Whether a given source is active for a specific data point is specified by an infinite binary matrix, Z. The resulting sparse representation allows increased data reduction compared to standard ICA.  ...  We define two variants based on the prior for x kt : infinite sparse Factor Analysis (isFA) has a unit Gaussian prior; infinite Independent Components Analysis (iICA) has a Laplacian(1) prior.  ... 
doi:10.1007/978-3-540-74494-8_48 dblp:conf/ica/KnowlesG07 fatcat:ibjt4denxndlvbasro77yf7fvq

Nonparametric factor analysis with beta process priors

John Paisley, Lawrence Carin
2009 Proceedings of the 26th Annual International Conference on Machine Learning - ICML '09  
This beta process factor analysis (BP-FA) model allows for a dataset to be decomposed into a linear combination of a sparse set of factors, providing information on the underlying structure of the observations  ...  We propose a nonparametric extension to the factor analysis problem using a beta process prior.  ...  While several nonparametric factor analysis models have been proposed for applications such as independent components analysis (Knowles & Ghahramani, 2007) and gene expression analysis (Rai & Daumé,  ... 
doi:10.1145/1553374.1553474 dblp:conf/icml/PaisleyC09 fatcat:he5etvvro5bn7lyxbfk3sacyma

Nonparametric Bayesian sparse factor models with application to gene expression modeling

David Knowles, Zoubin Ghahramani
2011 Annals of Applied Statistics  
A nonparametric Bayesian extension of Factor Analysis (FA) is proposed where observed data Y is modeled as a linear superposition, G, of a potentially infinite number of hidden factors, X.  ...  Coli, and on three biological data sets of increasing complexity.  ...  Principal Components Analysis (PCA), Factor Analysis (FA) and Independent Components Analysis (ICA) are models which explain observed data, y n ∈ R D , in terms of a linear superposition of independent  ... 
doi:10.1214/10-aoas435 fatcat:t3ivms3fyzailaiqnlwlo5qwya

The Infinite Hierarchical Factor Regression Model [article]

Piyush Rai, Hal Daumé III
2009 arXiv   pre-print
We apply this model to two problems (factor analysis and factor regression) in gene-expression data analysis.  ...  To accomplish this, we propose a sparse variant of the Indian Buffet Process and couple this with a hierarchical model over factors, based on Kingman's coalescent.  ...  Conclusions and Discussion We have presented a fully nonparametric Bayesian approach to sparse factor regression, modeling the gene-factor relationship using a sparse variant of the IBP.  ... 
arXiv:0908.0570v1 fatcat:5vpgpauwkbbrfng72362dx45q4

The interface between neighborhood density and optional infinitives: normal development and Specific Language Impairment

JILL R. HOOVER, HOLLY L. STORKEL, MABEL L. RICE
2011 Journal of Child Language  
Half of the sentences in each task presented a dense verb, and half presented a sparse verb. Children's third person singular accuracy was compared across dense and sparse verbs.  ...  In contrast, the distribution of optional infinitives for the SLI group was independent of verb neighborhood density.  ...  We also acknowledge Stephanie Dickinson, from the Indiana Statistical Consulting Center, for her guidance on the statistical analysis of the data.  ... 
doi:10.1017/s0305000911000365 pmid:22123500 pmcid:PMC3306845 fatcat:liyk23i57jdnnfowkhbt447ipa

Bayesian Information Sharing Between Noise And Regression Models Improves Prediction of Weak Effects [article]

Jussi Gillberg, Pekka Marttinen, Matti Pirinen, Antti J Kangas, Pasi Soininen, Marjo-Riitta Järvelin, Mika Ala-Korpela, Samuel Kaski
2013 arXiv   pre-print
infinite factor model as a flexible low-rank noise model.  ...  Further reduction of the effective number of parameters is achieved by introducing an infinite shrinkage prior and group sparsity in the context of the Bayesian reduced rank regression, and using the Bayesian  ...  Similarly to the Bayesian infinite sparse factor analysis model (Bhattacharya & Dunson, 2011) , we assume the number of columns, S 2 , in the weight matrix for the latent variables, Λ, to be infinite.  ... 
arXiv:1310.4362v1 fatcat:lxxpypvdjbcahobbkn5st677oq

Multi-Label Prediction via Sparse Infinite CCA

Piyush Rai, Hal Daumé III
2009 Neural Information Processing Systems  
Building upon the recently suggested probabilistic interpretation of CCA, we propose a nonparametric, fully Bayesian framework that can automatically select the number of correlation components, and effectively  ...  Canonical Correlation Analysis (CCA) is a useful technique for modeling dependencies between two (or more) sets of variables.  ...  Besides, the sparse factor analysis model is limited to factor analysis whereas the proposed model can be seen as an infinite generalization of both an unsupervised problem (sparse CCA), and (semi)supervised  ... 
dblp:conf/nips/RaiD09 fatcat:5chiv6sgbrdqdph3rmwws3yfri

Page 447 of Mathematical Reviews Vol. , Issue 96a [page]

1996 Mathematical Reviews  
Summary: “Sparse matrix vector multiplication (SpMxV) is of- ten one of the core components of many scientific applications.  ...  We-also exploit the idea of multi-coloring and independent set orderings to introduce a multi- elimination incomplete LU factorization named ILUM, which is related to multifrontal elimination.  ... 

Fast Bayesian Factor Analysis via Automatic Rotations to Sparsity

Veronika Ročková, Edward I. George
2016 Journal of the American Statistical Association  
For accurate recovery and estimation of factor loadings, we propose a spike-and-slab LASSO prior, a two-component refinement of the Laplace prior.  ...  By iterating between soft-thresholding of small factor loadings and transformations of the factor basis, we obtain dramatic accelerations yielding convergence towards better oriented sparse solutions.  ...  The EM Approach to Bayesian Factor Analysis We will leverage the resemblance between factor analysis and multivariate regression, and implement a sparse variant of the EM algorithm for probabilistic principal  ... 
doi:10.1080/01621459.2015.1100620 fatcat:prd24z7brvddlje4rodoif4oxi

Infinite Mixtures of Infinite Factor Analysers

Keefe Murphy, Cinzia Viroli, Isobel Claire Gormley
2019 Bayesian Analysis  
For computational reasons, having the number of factors differ across clusters is rarely considered. Here the infinite mixture of infinite factor analysers (IMIFA) model is introduced.  ...  Automatic inference of the cluster-specific numbers of factors is achieved using multiplicative gamma process shrinkage priors and an adaptive Gibbs sampler.  ...  The authors thank the members of the UCD Working Group in Statistical Learning and Prof. Adrian Raftery's Working Group in Model-based Clustering and Prof. David Dunson for helpful discussions.  ... 
doi:10.1214/19-ba1179 fatcat:irkezrharjhnrcyxbx6hlvpiuq

Spectral Methods for Indian Buffet Process Inference

Hsiao-Yu Fish Tung, Alexander J. Smola
2014 Neural Information Processing Systems  
We provide an efficient spectral algorithm as an alternative to costly Variational Bayes and sampling-based algorithms.  ...  We derive a novel tensorial characterization of the moments of the Indian Buffet Process proper and for two of its applications.  ...  as Infinite Sparse Factor Analysis (isFA) or Infinite Independent Component Analysis (iICA) depending on the choice of p(y) respectively.  ... 
dblp:conf/nips/TungS14 fatcat:tjvlgxktc5bmhpzct3wdw4zjsy

A tutorial on Bayesian nonparametric models

Samuel J. Gershman, David M. Blei
2012 Journal of Mathematical Psychology  
This problem appears in many settings, most prominently in choosing the number of clusters in mixture models or the number of factors in factor analysis.  ...  This tutorial is a high-level introduction to Bayesian nonparametric methods and contains several examples of their application.  ...  Different assumptions about the distribution of factors lead to variants such as factor analysis, principal component analysis, independent component analysis, and others.  ... 
doi:10.1016/j.jmp.2011.08.004 fatcat:allxc5i5qbcnvazdss67z7qw3y

A Tutorial on Bayesian Nonparametric Models [article]

Samuel J. Gershman, David M. Blei
2011 arXiv   pre-print
This problem appears in many settings, most prominently in choosing the number ofclusters in mixture models or the number of factors in factor analysis.  ...  This tutorial is a high-level introduction to Bayesian nonparametric methods and contains several examples of their application.  ...  Sloan foundation, and a grant from Google.  ... 
arXiv:1106.2697v2 fatcat:2s3yprihfzc4rnnhgo3yfpfxxq

Nonlinear mixture-wise expansion approach to underdetermined blind separation of nonnegative dependent sources

Ivica Kopriva, Ivanka Jerić, Lidija Brkljačić
2013 Journal of Chemometrics  
The method performs nonlinear mixturewise mapping of observed data in high-dimensional reproducible kernel Hilbert space (RKHS) of functions and sparseness constrained nonnegative matrix factorization  ...  Herein the library of pure components is such an "expert". The same concept is also in use in hyperspectral image analysis.  ...  sparseness measure approach to NBSS [13] , and sparse component analysis (SCA) that combines data clustering and 1 ℓ -minimization [14, 15] .  ... 
doi:10.1002/cem.2512 fatcat:xg326qf345anhgwsufe6kdjej4

Robust Stability Analysis of Sparsely Interconnected Uncertain Systems

Martin S. Andersen, Sina Khoshfetrat Pakazad, Anders Hansson, Anders Rantzer
2014 IEEE Transactions on Automatic Control  
The sparse formulation of the analysis problem allows us to apply methods that rely on efficient sparse factorization techniques, and our numerical results illustrate the effectiveness of this approach  ...  We also show that a sparse formulation of the analysis problem is equivalent to the classical formulation of the robustness analysis problem and hence does not introduce any additional conservativeness  ...  This frequency dependent semi-infinite LMI can be reformulated using the Kalman-Yakubovich-Popov (KYP) lemma as a finite-dimensional frequency independent LMI which is generally dense [3] , [4] .  ... 
doi:10.1109/tac.2014.2305934 fatcat:7cvnv257l5dwfkc6hpana5rkra
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