Dimensionality Detection and Integration of Multiple Data Sources via the GP-LVM

摘要

The Gaussian Process Latent Variable Model (GP-LVM) is a non-linearprobabilistic method of embedding a high dimensional dataset in terms lowdimensional `latent' variables. In this paper we illustrate that maximum aposteriori (MAP) estimation of the latent variables and hyperparameters can beused for model selection and hence we can determine the optimal number orlatent variables and the most appropriate model. This is an alternative to thevariational approaches developed recently and may be useful when we want to usea non-Gaussian prior or kernel functions that don't have automatic relevancedetermination (ARD) parameters. Using a second order expansion of the latentvariable posterior we can marginalise the latent variables and obtain anestimate for the hyperparameter posterior. Secondly, we use the GP-LVM tointegrate multiple data sources by simultaneously embedding them in terms ofcommon latent variables. We present results from synthetic data to illustratethe successful detection and retrieval of low dimensional structure from highdimensional data. We demonstrate that the integration of multiple data sourcesleads to more robust performance. Finally, we show that when the data are usedfor binary classification tasks we can attain a significant gain in predictionaccuracy when the low dimensional representation is used.