Conditionally Identifiable Latent Representation for Multivariate Time Series with Structural Dynamics

Minkey Chang, Jae-Young Kim
Proceedings of The 1st Symposium on Probabilistic Machine Learning, PMLR 327:189-213, 2026.

Abstract

We propose the Identifiable Variational Dynamic Factor Model (iVDFM) for multivariate time series. The model combines variational inference with \emph{partial} identifiability guarantees up to a known ambiguity class. Innovations follow a conditional exponential-family prior over observed auxiliary context and regime embeddings. Linear diagonal dynamics map innovations to factors and preserve that class, so factors are partially identifiable up to permutation and component-wise affine maps. We train by maximizing the ELBO and estimate uncertainty in both latent trajectories and forecasts. Under explicit assumptions, we prove partial identifiability up to the stated class and provide the full proof in the appendix. We evaluate factor recovery on synthetic DGPs, intervention behavior on synthetic SCMs, and forecasting on real benchmarks with CRPS and MSE.

Cite this Paper

BibTeX
@InProceedings{pmlr-v327-chang26a, title = {Conditionally Identifiable Latent Representation for Multivariate Time Series with Structural Dynamics}, author = {Chang, Minkey and Kim, Jae-Young}, booktitle = {Proceedings of The 1st Symposium on Probabilistic Machine Learning}, pages = {189--213}, year = {2026}, editor = {Swaroop, Siddharth and Rügamer, David and Kristiadi, Agustinus}, volume = {327}, series = {Proceedings of Machine Learning Research}, month = {05 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v327/main/assets/chang26a/chang26a.pdf}, url = {https://proceedings.mlr.press/v327/chang26a.html}, abstract = { We propose the Identifiable Variational Dynamic Factor Model (iVDFM) for multivariate time series. The model combines variational inference with \emph{partial} identifiability guarantees up to a known ambiguity class. Innovations follow a conditional exponential-family prior over observed auxiliary context and regime embeddings. Linear diagonal dynamics map innovations to factors and preserve that class, so factors are partially identifiable up to permutation and component-wise affine maps. We train by maximizing the ELBO and estimate uncertainty in both latent trajectories and forecasts. Under explicit assumptions, we prove partial identifiability up to the stated class and provide the full proof in the appendix. We evaluate factor recovery on synthetic DGPs, intervention behavior on synthetic SCMs, and forecasting on real benchmarks with CRPS and MSE. } }
Endnote
%0 Conference Paper %T Conditionally Identifiable Latent Representation for Multivariate Time Series with Structural Dynamics %A Minkey Chang %A Jae-Young Kim %B Proceedings of The 1st Symposium on Probabilistic Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Siddharth Swaroop %E David Rügamer %E Agustinus Kristiadi %F pmlr-v327-chang26a %I PMLR %P 189--213 %U https://proceedings.mlr.press/v327/chang26a.html %V 327 %X We propose the Identifiable Variational Dynamic Factor Model (iVDFM) for multivariate time series. The model combines variational inference with \emph{partial} identifiability guarantees up to a known ambiguity class. Innovations follow a conditional exponential-family prior over observed auxiliary context and regime embeddings. Linear diagonal dynamics map innovations to factors and preserve that class, so factors are partially identifiable up to permutation and component-wise affine maps. We train by maximizing the ELBO and estimate uncertainty in both latent trajectories and forecasts. Under explicit assumptions, we prove partial identifiability up to the stated class and provide the full proof in the appendix. We evaluate factor recovery on synthetic DGPs, intervention behavior on synthetic SCMs, and forecasting on real benchmarks with CRPS and MSE.
APA
Chang, M. & Kim, J.. (2026). Conditionally Identifiable Latent Representation for Multivariate Time Series with Structural Dynamics. Proceedings of The 1st Symposium on Probabilistic Machine Learning, in Proceedings of Machine Learning Research 327:189-213 Available from https://proceedings.mlr.press/v327/chang26a.html.

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