# Bayesian Gaussian Process Latent Variable Model

Michalis K. Titsias, University of Athens
Neil D. Lawrence, University of Sheffield

in Proceedings of the Thirteenth International Workshop on Artificial Intelligence and Statistics 9, pp 844-851

#### Abstract

We introduce a variational inference framework for training the Gaussian process latent variable model and thus performing Bayesian nonlinear dimensionality reduction. This method allows us to variationally integrate out the input variables of the Gaussian process and compute a lower bound on the exact marginal likelihood of the nonlinear latent variable model. The maximization of the variational lower bound provides a Bayesian training procedure that is robust to overfitting and can automatically select the dimensionality of the nonlinear latent space. We demonstrate our method on real world datasets. The focus in this paper is on dimensionality reduction problems, but the methodology is more general. For example, our algorithm is immediately applicable for training Gaussian process models in the presence of missing or uncertain inputs.

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 %T Bayesian Gaussian Process Latent Variable Model %A Michalis K. Titsias and Neil D. Lawrence %B %C Proceedings of the Thirteenth International Workshop on Artificial Intelligence and Statistics %D %E Yee Whye Teh and D. Michael Titterington %F titsias-bayesgplvm10 %I JMLR W\&CP 9 %P 844--851 %R %U http://inverseprobability.com/publications/titsias-bayesgplvm10.html %V 9 %X We introduce a variational inference framework for training the Gaussian process latent variable model and thus performing Bayesian nonlinear dimensionality reduction. This method allows us to variationally integrate out the input variables of the Gaussian process and compute a lower bound on the exact marginal likelihood of the nonlinear latent variable model. The maximization of the variational lower bound provides a Bayesian training procedure that is robust to overfitting and can automatically select the dimensionality of the nonlinear latent space. We demonstrate our method on real world datasets. The focus in this paper is on dimensionality reduction problems, but the methodology is more general. For example, our algorithm is immediately applicable for training Gaussian process models in the presence of missing or uncertain inputs. 
 TY - CPAPER TI - Bayesian Gaussian Process Latent Variable Model AU - Michalis K. Titsias AU - Neil D. Lawrence BT - Proceedings of the Thirteenth International Workshop on Artificial Intelligence and Statistics PY - 2010/01/01 DA - 2010/01/01 ED - Yee Whye Teh ED - D. Michael Titterington ID - titsias-bayesgplvm10 PB - JMLR W\&CP 9 SP - 844 EP - 851 L1 - http://jmlr.csail.mit.edu/proceedings/papers/v9/titsias10a/titsias10a.pdf UR - http://inverseprobability.com/publications/titsias-bayesgplvm10.html AB - We introduce a variational inference framework for training the Gaussian process latent variable model and thus performing Bayesian nonlinear dimensionality reduction. This method allows us to variationally integrate out the input variables of the Gaussian process and compute a lower bound on the exact marginal likelihood of the nonlinear latent variable model. The maximization of the variational lower bound provides a Bayesian training procedure that is robust to overfitting and can automatically select the dimensionality of the nonlinear latent space. We demonstrate our method on real world datasets. The focus in this paper is on dimensionality reduction problems, but the methodology is more general. For example, our algorithm is immediately applicable for training Gaussian process models in the presence of missing or uncertain inputs. ER - 
 Titsias, M.K. & Lawrence, N.D.. (2010). Bayesian Gaussian Process Latent Variable Model. Proceedings of the Thirteenth International Workshop on Artificial Intelligence and Statistics 9:844-851