Conditionally Identifiable Latent Representation for Multivariate Time Series with Structural Dynamics

TL;DR

This paper introduces iVDFM, a novel model for multivariate time series that guarantees identifiable latent factors, improving factor recovery, intervention accuracy, and forecasting performance.

Contribution

The paper presents the iVDFM model with a new conditioning approach that ensures latent factor identifiability under certain dynamics, advancing multivariate time series analysis.

Findings

Improved latent factor recovery on synthetic data

Stable intervention accuracy on synthetic SCMs

Competitive forecasting on real-world benchmarks

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.