Conditionally Identifiable Latent Representation for Multivariate Time Series with Structural Dynamics

• URL: http://arxiv.org/abs/2603.22886v1
• Date: Tue, 24 Mar 2026 07:35:27 GMT
• Title: Conditionally Identifiable Latent Representation for Multivariate Time Series with Structural Dynamics
• Abstract summary: We show that factors are identifiable up to permutation and component-wise affine (or monotone invertible) transformations.<n>We demonstrate improved factor recovery on synthetic data, stable intervention accuracy on synthetic SCMs, and competitive probabilistic forecasting on real-world benchmarks.
• Score: 9.736137697615003
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose the Identifiable Variational Dynamic Factor Model (iVDFM), which learns latent factors from multivariate time series with identifiability guarantees. By applying iVAE-style conditioning to the innovation process driving the dynamics rather than to the latent states, we show that factors are identifiable up to permutation and component-wise affine (or monotone invertible) transformations. Linear diagonal dynamics preserve this identifiability and admit scalable computation via companion-matrix and Krylov methods. We demonstrate improved factor recovery on synthetic data, stable intervention accuracy on synthetic SCMs, and competitive probabilistic forecasting on real-world benchmarks.

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