Decomposing feature-level variation with Covariate Gaussian Process Latent Variable Models

Kaspar Märtens, Kieran Campbell, Christopher Yau
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:4372-4381, 2019.

Abstract

The interpretation of complex high-dimensional data typically requires the use of dimensionality reduction techniques to extract explanatory low-dimensional representations. However, in many real-world problems these representations may not be sufficient to aid interpretation on their own, and it would be desirable to interpret the model in terms of the original features themselves. Our goal is to characterise how feature-level variation depends on latent low-dimensional representations, external covariates, and non-linear interactions between the two. In this paper, we propose to achieve this through a structured kernel decomposition in a hybrid Gaussian Process model which we call the Covariate Gaussian Process Latent Variable Model (c-GPLVM). We demonstrate the utility of our model on simulated examples and applications in disease progression modelling from high-dimensional gene expression data in the presence of additional phenotypes. In each setting we show how the c-GPLVM can extract low-dimensional structures from high-dimensional data sets whilst allowing a breakdown of feature-level variability that is not present in other commonly used dimensionality reduction approaches.

Cite this Paper

BibTeX
@InProceedings{pmlr-v97-martens19a, title = {Decomposing feature-level variation with Covariate {G}aussian Process Latent Variable Models}, author = {M{\"a}rtens, Kaspar and Campbell, Kieran and Yau, Christopher}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, pages = {4372--4381}, year = {2019}, editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan}, volume = {97}, series = {Proceedings of Machine Learning Research}, month = {09--15 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v97/martens19a/martens19a.pdf}, url = {https://proceedings.mlr.press/v97/martens19a.html}, abstract = {The interpretation of complex high-dimensional data typically requires the use of dimensionality reduction techniques to extract explanatory low-dimensional representations. However, in many real-world problems these representations may not be sufficient to aid interpretation on their own, and it would be desirable to interpret the model in terms of the original features themselves. Our goal is to characterise how feature-level variation depends on latent low-dimensional representations, external covariates, and non-linear interactions between the two. In this paper, we propose to achieve this through a structured kernel decomposition in a hybrid Gaussian Process model which we call the Covariate Gaussian Process Latent Variable Model (c-GPLVM). We demonstrate the utility of our model on simulated examples and applications in disease progression modelling from high-dimensional gene expression data in the presence of additional phenotypes. In each setting we show how the c-GPLVM can extract low-dimensional structures from high-dimensional data sets whilst allowing a breakdown of feature-level variability that is not present in other commonly used dimensionality reduction approaches.} }
Endnote
%0 Conference Paper %T Decomposing feature-level variation with Covariate Gaussian Process Latent Variable Models %A Kaspar Märtens %A Kieran Campbell %A Christopher Yau %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-martens19a %I PMLR %P 4372--4381 %U https://proceedings.mlr.press/v97/martens19a.html %V 97 %X The interpretation of complex high-dimensional data typically requires the use of dimensionality reduction techniques to extract explanatory low-dimensional representations. However, in many real-world problems these representations may not be sufficient to aid interpretation on their own, and it would be desirable to interpret the model in terms of the original features themselves. Our goal is to characterise how feature-level variation depends on latent low-dimensional representations, external covariates, and non-linear interactions between the two. In this paper, we propose to achieve this through a structured kernel decomposition in a hybrid Gaussian Process model which we call the Covariate Gaussian Process Latent Variable Model (c-GPLVM). We demonstrate the utility of our model on simulated examples and applications in disease progression modelling from high-dimensional gene expression data in the presence of additional phenotypes. In each setting we show how the c-GPLVM can extract low-dimensional structures from high-dimensional data sets whilst allowing a breakdown of feature-level variability that is not present in other commonly used dimensionality reduction approaches.
APA
Märtens, K., Campbell, K. & Yau, C.. (2019). Decomposing feature-level variation with Covariate Gaussian Process Latent Variable Models. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:4372-4381 Available from https://proceedings.mlr.press/v97/martens19a.html.

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