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

*
Independent Component Analysis and Signal Separation
*

A nonparametric Bayesian extension of

doi:10.1007/978-3-540-74494-8_48
dblp:conf/ica/KnowlesG07
fatcat:ibjt4denxndlvbasro77yf7fvq
*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. ...##
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Nonparametric factor analysis with beta process priors

2009
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Proceedings of the 26th Annual International Conference on Machine Learning - ICML '09
*

This beta process

doi:10.1145/1553374.1553474
dblp:conf/icml/PaisleyC09
fatcat:he5etvvro5bn7lyxbfk3sacyma
*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, ...##
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Nonparametric Bayesian sparse factor models with application to gene expression modeling

2011
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Annals of Applied Statistics
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A nonparametric Bayesian extension of

doi:10.1214/10-aoas435
fatcat:t3ivms3fyzailaiqnlwlo5qwya
*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*...##
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The Infinite Hierarchical Factor Regression Model
[article]

2009
*
arXiv
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pre-print

We apply this model to two problems (

arXiv:0908.0570v1
fatcat:5vpgpauwkbbrfng72362dx45q4
*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. ...##
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The interface between neighborhood density and optional infinitives: normal development and Specific Language Impairment

2011
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Journal of Child Language
*

Half of the sentences in each task presented a dense verb,

doi:10.1017/s0305000911000365
pmid:22123500
pmcid:PMC3306845
fatcat:liyk23i57jdnnfowkhbt447ipa
*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. ...##
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Bayesian Information Sharing Between Noise And Regression Models Improves Prediction of Weak Effects
[article]

2013
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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*. ...

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Multi-Label Prediction via Sparse Infinite CCA

2009
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Neural Information Processing Systems
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Building upon the recently suggested probabilistic interpretation of CCA, we propose a nonparametric, fully Bayesian framework that can automatically select the number of correlation

dblp:conf/nips/RaiD09
fatcat:5chiv6sgbrdqdph3rmwws3yfri
*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 ...##
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Page 447 of Mathematical Reviews Vol. , Issue 96a
[page]

1996
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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. ...##
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Fast Bayesian Factor Analysis via Automatic Rotations to Sparsity

2016
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Journal of the American Statistical Association
*

For accurate recovery

doi:10.1080/01621459.2015.1100620
fatcat:prd24z7brvddlje4rodoif4oxi
*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 ...##
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Infinite Mixtures of Infinite Factor Analysers

2019
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Bayesian Analysis
*

For computational reasons, having the number of

doi:10.1214/19-ba1179
fatcat:irkezrharjhnrcyxbx6hlvpiuq
*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. ...##
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Spectral Methods for Indian Buffet Process Inference

2014
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Neural Information Processing Systems
*

We provide an efficient spectral algorithm as an alternative to costly Variational Bayes

dblp:conf/nips/TungS14
fatcat:tjvlgxktc5bmhpzct3wdw4zjsy
*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. ...##
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A tutorial on Bayesian nonparametric models

2012
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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

doi:10.1016/j.jmp.2011.08.004
fatcat:allxc5i5qbcnvazdss67z7qw3y
*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. ...##
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A Tutorial on Bayesian Nonparametric Models
[article]

2011
*
arXiv
*
pre-print

This problem appears in many settings, most prominently in choosing the number ofclusters in mixture models or the number of

arXiv:1106.2697v2
fatcat:2s3yprihfzc4rnnhgo3yfpfxxq
*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. ...##
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Nonlinear mixture-wise expansion approach to underdetermined blind separation of nonnegative dependent sources

2013
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Journal of Chemometrics
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The method performs nonlinear mixturewise mapping of observed data in high-dimensional reproducible kernel Hilbert space (RKHS) of functions

doi:10.1002/cem.2512
fatcat:xg326qf345anhgwsufe6kdjej4
*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] . ...##
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Robust Stability Analysis of Sparsely Interconnected Uncertain Systems

2014
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IEEE Transactions on Automatic Control
*

The

doi:10.1109/tac.2014.2305934
fatcat:7cvnv257l5dwfkc6hpana5rkra
*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] . ...
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