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Conditionally Identifiable Latent Representation for Multivariate Time Series with Structural Dynamics

Minkey Chang, Jae-Young Kim

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.

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.
Paper Structure (60 sections, 2 theorems, 9 equations, 1 figure, 4 tables, 1 algorithm)

This paper contains 60 sections, 2 theorems, 9 equations, 1 figure, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Identification Problem
  4. Static representations.
  5. Dynamic representations.
  6. Modeling Temporal Dynamics
  7. Causal Inference
  8. Identifiable Variational Dynamic Factor Model
  9. Innovation
  10. Dynamics
  11. Estimation
  12. Experiments
  13. Factor Recovery
  14. Causal Intervention
  15. Probabilistic Forecasting
  16. ...and 45 more sections

Key Result

Theorem A.2

Under the generative model above, assume: Then the innovations $\{\boldsymbol{\eta}_t\}_{t=1}^T$ are identifiable from $(\boldsymbol{y}_{1:T}, \boldsymbol{u}_{1:T})$ up to $\mathcal{T}$ (Definition def:identifiability, with $\mathcal{T}$ the class of permutation and component-wise affine maps; or monotone invertible under additional regular

Figures (1)

  • Figure :

Theorems & Definitions (4)

  • Definition A.1: Identifiability up to a class
  • Theorem A.2: Identifiability of dynamic factors
  • proof
  • Proposition B.1: Gaussian innovations are not identifiable