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On the Identifiability of Switching Dynamical Systems
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Proves identifiability of first-order Markov switching models with non-linear Gaussian transitions and of switching dynamical systems (up to affine transformations) built on them, and gives estimation algorithms validated on synthetic data, climate causal discovery, and video segmentation.
Problem
Identifiability of sequential latent variable models, specifically switching dynamical systems with Markov switching latent priors, where latent variables are temporally dependent (not independent as in non-linear ICA).
Approach
Reduce Markov switching models to finite mixtures of trajectories and use linear independence of products of consecutive transition functions to show identifiability under analytic non-linear Gaussian transitions, independent of the discrete state prior; then extend to SDSs via identifiable deep LVM techniques (weakly injective or injective piecewise-linear emissions), without requiring auxiliary
Key results
- iSDS achieves MCC-weak 0.992 ± 0.008 versus 0.979 for Δ-SNICA and 0.770 for iVAE* on 50-dimensional observations generated from 2D latent MSMs.
- On synthetic salsa videos the identifiable SDS reconstructs with pixel MSE 2.26e-4 per frame; on AIST Hip-Hop videos pixel MSE is 7.85e-3 per frame.
- On climate data, the linear MSM finds an ENSO-to-AIR effect only during summer months (May-September).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use iSDS instead of Δ-SNICA | Synthetic SDS · Synthetic SDS (5 datasets) | MCC-weak: 0.979 ± 0.043 -> 0.992 ± 0.008 | Helped |
| Use iSDS instead of Δ-SNICA | Synthetic SDS · Synthetic SDS (5 datasets) | MCC-strong: 0.940 ± 0.041 -> 0.936 ± 0.041 | Hurt |
Surprising findings
- Overparametrised linear SDS (Δ-SNICA) still achieves high MCC despite linear prior dynamics differing from the ground-truth cosine-network MSM, because transition identifiability is lost while latent recovery holds.
Limitations
- Emission model must be (weakly) injective, a restriction shared by prior work.
- Estimation relies on ELBO or GEM maximisation with no consistency guarantees; identifiability covers only first-order Markov dynamics in experiments.
- Current estimation requires heavy hyperparameter tuning and is prone to state collapse in high-dimensional settings.
Experimental setup
Datasets: synthetic MSM data ENSO and All India Rainfall climate data (1871-2016) CMU mocap salsa dancing AIST Dance DB Hip-Hop videos
Benchmarks: synthetic MSM data CMU mocap salsa AIST Hip-Hop videos
Metrics: L2 distance F1 score MCC-strong MCC-weak pixel MSE
Baselines: iVAE Δ-SNICA KVAE
Builds on: identifiable VAE finite mixture identifiability switching dynamical systems KVAE SNICA
Closest papers by meaning
- End-to-End Identifiable and Consistent Recurrent Switching Dynamical Systems (NeurIPS 2026 · similarity 0.90)
- Disentangling Continuous-Time Latent Dynamics: Identifiability of Latent SDEs via Diffusion Shifts (NeurIPS 2026 · similarity 0.89)
- Identifying latent state transitions in non-linear dynamical systems (ICLR 2025 · similarity 0.89)
- Identifiability Analysis of Linear ODE Systems with Hidden Confounders (NeurIPS 2024 · similarity 0.89)
- Identifiable Latent Polynomial Causal Models through the Lens of Change (ICLR 2024 · similarity 0.88)
- Time series analysis with Gumbel dynamics (NeurIPS 2026 · similarity 0.87)
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