A Mutually-Dependent Hadamard Kernel for Modelling Latent Variable Couplings

Sami Remes, Markus Heinonen, Samuel Kaski
Proceedings of the Ninth Asian Conference on Machine Learning, PMLR 77:455-470, 2017.

Abstract

We introduce a novel kernel that models input-dependent couplings across multiple latent processes. The pairwise joint kernel measures covariance along inputs and across different latent signals in a mutually-dependent fashion. A latent correlation Gaussian process (LCGP) model combines these non-stationary latent components into multiple outputs by an input-dependent mixing matrix. Probit classification and support for multiple observation sets are derived by Variational Bayesian inference. Results on several datasets indicate that the LCGP model can recover the correlations between latent signals while simultaneously achieving state-of-the-art performance. We highlight the latent covariances with an EEG classification dataset where latent brain processes and their couplings simultaneously emerge from the model.

Cite this Paper

BibTeX
@InProceedings{pmlr-v77-remes17a, title = {A Mutually-Dependent Hadamard Kernel for Modelling Latent Variable Couplings}, author = {Remes, Sami and Heinonen, Markus and Kaski, Samuel}, booktitle = {Proceedings of the Ninth Asian Conference on Machine Learning}, pages = {455--470}, year = {2017}, editor = {Zhang, Min-Ling and Noh, Yung-Kyun}, volume = {77}, series = {Proceedings of Machine Learning Research}, address = {Yonsei University, Seoul, Republic of Korea}, month = {15--17 Nov}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v77/remes17a/remes17a.pdf}, url = {https://proceedings.mlr.press/v77/remes17a.html}, abstract = {We introduce a novel kernel that models input-dependent couplings across multiple latent processes. The pairwise joint kernel measures covariance along inputs and across different latent signals in a mutually-dependent fashion. A latent correlation Gaussian process (LCGP) model combines these non-stationary latent components into multiple outputs by an input-dependent mixing matrix. Probit classification and support for multiple observation sets are derived by Variational Bayesian inference. Results on several datasets indicate that the LCGP model can recover the correlations between latent signals while simultaneously achieving state-of-the-art performance. We highlight the latent covariances with an EEG classification dataset where latent brain processes and their couplings simultaneously emerge from the model.} }
Endnote
%0 Conference Paper %T A Mutually-Dependent Hadamard Kernel for Modelling Latent Variable Couplings %A Sami Remes %A Markus Heinonen %A Samuel Kaski %B Proceedings of the Ninth Asian Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2017 %E Min-Ling Zhang %E Yung-Kyun Noh %F pmlr-v77-remes17a %I PMLR %P 455--470 %U https://proceedings.mlr.press/v77/remes17a.html %V 77 %X We introduce a novel kernel that models input-dependent couplings across multiple latent processes. The pairwise joint kernel measures covariance along inputs and across different latent signals in a mutually-dependent fashion. A latent correlation Gaussian process (LCGP) model combines these non-stationary latent components into multiple outputs by an input-dependent mixing matrix. Probit classification and support for multiple observation sets are derived by Variational Bayesian inference. Results on several datasets indicate that the LCGP model can recover the correlations between latent signals while simultaneously achieving state-of-the-art performance. We highlight the latent covariances with an EEG classification dataset where latent brain processes and their couplings simultaneously emerge from the model.
APA
Remes, S., Heinonen, M. & Kaski, S.. (2017). A Mutually-Dependent Hadamard Kernel for Modelling Latent Variable Couplings. Proceedings of the Ninth Asian Conference on Machine Learning, in Proceedings of Machine Learning Research 77:455-470 Available from https://proceedings.mlr.press/v77/remes17a.html.

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