# Multi-view Learning as a Nonparametric Nonlinear Inter-Battery Factor Analysis

Andreas Damianou, University of Sheffield
Neil D. Lawrence, University of Sheffield
Carl Henrik Ek, University of Bristol

#### Abstract

Factor analysis aims to determine latent factors, or traits, which summarize a given data set. Inter-battery factor analysis extends this notion to multiple views of the data. In this paper we show how a nonlinear, nonparametric version of these models can be recovered through the Gaussian process latent variable model. This gives us a flexible formalism for multi-view learning where the latent variables can be used both for exploratory purposes and for learning representations that enable efficient inference for ambiguous estimation tasks. Learning is performed in a Bayesian manner through the formulation of a variational compression scheme which gives a rigorous lower bound on the log likelihood. Our Bayesian framework provides strong regularization during training, allowing the structure of the latent space to be determined efficiently and automatically. We demonstrate this by producing the first (to our knowledge) published results of learning from dozens of views, even when data is scarce. We further show experimental results on several different types of multi-view data sets and for different kinds of tasks, including exploratory data analysis, generation, ambiguity modelling through latent priors and classification.

  @TechReport{damianou-ibfa16, title = {Multi-view Learning as a Nonparametric Nonlinear Inter-Battery Factor Analysis}, author = {Andreas Damianou and Neil D. Lawrence and Carl Henrik Ek}, year = {2016}, institution = {arXiv}, month = {00}, edit = {https://github.com/lawrennd//publications/edit/gh-pages/_posts/2016-04-17-damianou-ibfa16.md}, url = {http://inverseprobability.com/publications/damianou-ibfa16.html}, abstract = {Factor analysis aims to determine latent factors, or traits, which summarize a given data set. Inter-battery factor analysis extends this notion to multiple views of the data. In this paper we show how a nonlinear, nonparametric version of these models can be recovered through the Gaussian process latent variable model. This gives us a flexible formalism for multi-view learning where the latent variables can be used both for exploratory purposes and for learning representations that enable efficient inference for ambiguous estimation tasks. Learning is performed in a Bayesian manner through the formulation of a variational compression scheme which gives a rigorous lower bound on the log likelihood. Our Bayesian framework provides strong regularization during training, allowing the structure of the latent space to be determined efficiently and automatically. We demonstrate this by producing the first (to our knowledge) published results of learning from dozens of views, even when data is scarce. We further show experimental results on several different types of multi-view data sets and for different kinds of tasks, including exploratory data analysis, generation, ambiguity modelling through latent priors and classification.}, key = {Damianou:ibfa16}, linkpdf = {http://arxiv.org/pdf/1604.04939v1.pdf}, OPTgroup = {} }
 %T Multi-view Learning as a Nonparametric Nonlinear Inter-Battery Factor Analysis %A Andreas Damianou and Neil D. Lawrence and Carl Henrik Ek %B %D %F damianou-ibfa16 %P -- %R %U http://inverseprobability.com/publications/damianou-ibfa16.html %X Factor analysis aims to determine latent factors, or traits, which summarize a given data set. Inter-battery factor analysis extends this notion to multiple views of the data. In this paper we show how a nonlinear, nonparametric version of these models can be recovered through the Gaussian process latent variable model. This gives us a flexible formalism for multi-view learning where the latent variables can be used both for exploratory purposes and for learning representations that enable efficient inference for ambiguous estimation tasks. Learning is performed in a Bayesian manner through the formulation of a variational compression scheme which gives a rigorous lower bound on the log likelihood. Our Bayesian framework provides strong regularization during training, allowing the structure of the latent space to be determined efficiently and automatically. We demonstrate this by producing the first (to our knowledge) published results of learning from dozens of views, even when data is scarce. We further show experimental results on several different types of multi-view data sets and for different kinds of tasks, including exploratory data analysis, generation, ambiguity modelling through latent priors and classification. 
 TY - CPAPER TI - Multi-view Learning as a Nonparametric Nonlinear Inter-Battery Factor Analysis AU - Andreas Damianou AU - Neil D. Lawrence AU - Carl Henrik Ek PY - 2016/04/17 DA - 2016/04/17 ID - damianou-ibfa16 SP - EP - L1 - http://arxiv.org/pdf/1604.04939v1.pdf UR - http://inverseprobability.com/publications/damianou-ibfa16.html AB - Factor analysis aims to determine latent factors, or traits, which summarize a given data set. Inter-battery factor analysis extends this notion to multiple views of the data. In this paper we show how a nonlinear, nonparametric version of these models can be recovered through the Gaussian process latent variable model. This gives us a flexible formalism for multi-view learning where the latent variables can be used both for exploratory purposes and for learning representations that enable efficient inference for ambiguous estimation tasks. Learning is performed in a Bayesian manner through the formulation of a variational compression scheme which gives a rigorous lower bound on the log likelihood. Our Bayesian framework provides strong regularization during training, allowing the structure of the latent space to be determined efficiently and automatically. We demonstrate this by producing the first (to our knowledge) published results of learning from dozens of views, even when data is scarce. We further show experimental results on several different types of multi-view data sets and for different kinds of tasks, including exploratory data analysis, generation, ambiguity modelling through latent priors and classification. ER - 
 Damianou, A., Lawrence, N.D. & Ek, C.H.. (2016). Multi-view Learning as a Nonparametric Nonlinear Inter-Battery Factor Analysis.:-