Conditionally Identifiable Latent Representation for Multivariate Time Series with Structural Dynamics

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.