A unified probabilistic model for learning latent factors and their connectivities from high-dimensional data

Ricardo Pio Monti, Aapo Hyvarinen
Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence, PMLR R16:299-308, 2018.

Abstract

Connectivity estimation is challenging in the context of high-dimensional data. A useful preprocessing step is to group variables into clusters, however, it is not always clear how to do so from the perspective of connectivity estimation. Another practical challenge is that we may have data from multiple related classes (e.g., multiple subjects or conditions) and wish to incorporate constraints on the similarities across classes. We propose a probabilistic model which simultaneously performs both a grouping of variables (i.e., detecting community structure) and estimation of connectivities between the groups which correspond to latent variables. The model is essentially a factor analysis model where the factors are allowed to have arbitrary correlations, while the factor loading matrix is constrained to express a community structure. The model can be applied on multiple classes so that the connectivities can be different between the classes, while the community structure is the same for all classes. We propose an efficient estimation algorithm based on score matching, and prove the identifiability of the model. Finally, we present an extension to directed (causal) connectivities over latent variables. Simulations and experiments on fMRI data validate the practical utility of the method.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR16-monti18a, title = {A unified probabilistic model for learning latent factors and their connectivities from high-dimensional data}, author = {Monti, Ricardo Pio and Hyvarinen, Aapo}, booktitle = {Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence}, pages = {299--308}, year = {2018}, editor = {Globerson, Amir and Silva, Ricardo}, volume = {R16}, series = {Proceedings of Machine Learning Research}, month = {06--10 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r16/main/assets/monti18a/monti18a.pdf}, url = {https://proceedings.mlr.press/r16/monti18a.html}, abstract = {Connectivity estimation is challenging in the context of high-dimensional data. A useful preprocessing step is to group variables into clusters, however, it is not always clear how to do so from the perspective of connectivity estimation. Another practical challenge is that we may have data from multiple related classes (e.g., multiple subjects or conditions) and wish to incorporate constraints on the similarities across classes. We propose a probabilistic model which simultaneously performs both a grouping of variables (i.e., detecting community structure) and estimation of connectivities between the groups which correspond to latent variables. The model is essentially a factor analysis model where the factors are allowed to have arbitrary correlations, while the factor loading matrix is constrained to express a community structure. The model can be applied on multiple classes so that the connectivities can be different between the classes, while the community structure is the same for all classes. We propose an efficient estimation algorithm based on score matching, and prove the identifiability of the model. Finally, we present an extension to directed (causal) connectivities over latent variables. Simulations and experiments on fMRI data validate the practical utility of the method.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T A unified probabilistic model for learning latent factors and their connectivities from high-dimensional data %A Ricardo Pio Monti %A Aapo Hyvarinen %B Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2018 %E Amir Globerson %E Ricardo Silva %F pmlr-vR16-monti18a %I PMLR %P 299--308 %U https://proceedings.mlr.press/r16/monti18a.html %V R16 %X Connectivity estimation is challenging in the context of high-dimensional data. A useful preprocessing step is to group variables into clusters, however, it is not always clear how to do so from the perspective of connectivity estimation. Another practical challenge is that we may have data from multiple related classes (e.g., multiple subjects or conditions) and wish to incorporate constraints on the similarities across classes. We propose a probabilistic model which simultaneously performs both a grouping of variables (i.e., detecting community structure) and estimation of connectivities between the groups which correspond to latent variables. The model is essentially a factor analysis model where the factors are allowed to have arbitrary correlations, while the factor loading matrix is constrained to express a community structure. The model can be applied on multiple classes so that the connectivities can be different between the classes, while the community structure is the same for all classes. We propose an efficient estimation algorithm based on score matching, and prove the identifiability of the model. Finally, we present an extension to directed (causal) connectivities over latent variables. Simulations and experiments on fMRI data validate the practical utility of the method. %Z Reissued by PMLR on 04 October 2026.
APA
Monti, R.P. & Hyvarinen, A.. (2018). A unified probabilistic model for learning latent factors and their connectivities from high-dimensional data. Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R16:299-308 Available from https://proceedings.mlr.press/r16/monti18a.html. Reissued by PMLR on 04 October 2026.

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