Deep Gaussian Processes

Andreas DamianouNeil D. Lawrence
,  31:207-215, 2013.

Abstract

In this paper we introduce deep Gaussian process (GP) models. Deep GPs are a deep belief network based on Gaussian process mappings. The data is modeled as the output of a multivariate GP. The inputs to that Gaussian process are then governed by another GP. A single layer model is equivalent to a standard GP or the GP latent variable model (GP-LVM). We perform inference in the model by approximate variational marginalization. This results in a strict lower bound on the marginal likelihood of the model which we use for model selection (number of layers and nodes per layer). Deep belief networks are typically applied to relatively large data sets using stochastic gradient descent for optimization. Our fully Bayesian treatment allows for the application of deep models even when data is scarce. Model selection by our variational bound shows that a five layer hierarchy is justified even when modelling a digit data set containing only 150 examples.

Cite this Paper


BibTeX
@InProceedings{pmlr-v-damianou-deepgp13, title = {Deep Gaussian Processes}, author = {Andreas Damianou and Neil D. Lawrence}, pages = {207--215}, year = {}, editor = {}, volume = {31}, address = {AZ, USA}, url = {http://inverseprobability.com/publications/damianou-deepgp13.html}, abstract = {In this paper we introduce deep Gaussian process (GP) models. Deep GPs are a deep belief network based on Gaussian process mappings. The data is modeled as the output of a multivariate GP. The inputs to that Gaussian process are then governed by another GP. A single layer model is equivalent to a standard GP or the GP latent variable model (GP-LVM). We perform inference in the model by approximate variational marginalization. This results in a strict lower bound on the marginal likelihood of the model which we use for model selection (number of layers and nodes per layer). Deep belief networks are typically applied to relatively large data sets using stochastic gradient descent for optimization. Our fully Bayesian treatment allows for the application of deep models even when data is scarce. Model selection by our variational bound shows that a five layer hierarchy is justified even when modelling a digit data set containing only 150 examples.} }
Endnote
%0 Conference Paper %T Deep Gaussian Processes %A Andreas Damianou %A Neil D. Lawrence %B %C Proceedings of Machine Learning Research %D %E %F pmlr-v-damianou-deepgp13 %I PMLR %J Proceedings of Machine Learning Research %P 207--215 %U http://inverseprobability.com %V %W PMLR %X In this paper we introduce deep Gaussian process (GP) models. Deep GPs are a deep belief network based on Gaussian process mappings. The data is modeled as the output of a multivariate GP. The inputs to that Gaussian process are then governed by another GP. A single layer model is equivalent to a standard GP or the GP latent variable model (GP-LVM). We perform inference in the model by approximate variational marginalization. This results in a strict lower bound on the marginal likelihood of the model which we use for model selection (number of layers and nodes per layer). Deep belief networks are typically applied to relatively large data sets using stochastic gradient descent for optimization. Our fully Bayesian treatment allows for the application of deep models even when data is scarce. Model selection by our variational bound shows that a five layer hierarchy is justified even when modelling a digit data set containing only 150 examples.
RIS
TY - CPAPER TI - Deep Gaussian Processes AU - Andreas Damianou AU - Neil D. Lawrence BT - PY - DA - ED - ID - pmlr-v-damianou-deepgp13 PB - PMLR SP - 207 DP - PMLR EP - 215 L1 - UR - http://inverseprobability.com/publications/damianou-deepgp13.html AB - In this paper we introduce deep Gaussian process (GP) models. Deep GPs are a deep belief network based on Gaussian process mappings. The data is modeled as the output of a multivariate GP. The inputs to that Gaussian process are then governed by another GP. A single layer model is equivalent to a standard GP or the GP latent variable model (GP-LVM). We perform inference in the model by approximate variational marginalization. This results in a strict lower bound on the marginal likelihood of the model which we use for model selection (number of layers and nodes per layer). Deep belief networks are typically applied to relatively large data sets using stochastic gradient descent for optimization. Our fully Bayesian treatment allows for the application of deep models even when data is scarce. Model selection by our variational bound shows that a five layer hierarchy is justified even when modelling a digit data set containing only 150 examples. ER -
APA
Damianou, A. & Lawrence, N.D.. (). Deep Gaussian Processes. , in PMLR :207-215

Related Material