Conditionally Identifiable Latent Representation for Multivariate Time Series with Structural Dynamics

Minkey Chang and Jae-Young Kim

Papers from arXiv.org

Abstract: We propose the Identifiable Variational Dynamic Factor Model (iVDFM) for multivariate time series. The model combines variational inference with 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.

Date: 2026-03, Revised 2026-10
New Economics Papers: this item is included in nep-ecm and nep-ets
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Published in Proceedings of Machine Learning Research 327:189-213, 2026

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