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End-to-End Identifiable and Consistent Recurrent Switching Dynamical Systems
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Establishes identifiability for recurrent nonlinear switching dynamical systems with invertible emissions and proposes ΩSDS, a flow-based estimator that optimises the exact likelihood via EM-style gradients, outperforming VAE-based SDS on synthetic and bouncing-ball/dance video data.
Problem
Identifiable and consistent latent representations for sequential data with regime-switching dynamics, where prior identifiability results require restrictive stationarity or emission assumptions and VAE estimators introduce approximation gaps.
Approach
Combines identifiability theory for recurrent Markov switching models (latent affine identifiability, regime permutation identifiability, and variance-ratio disentanglement) with an invertible flow emission and exact likelihood optimisation via forward-backward posteriors, replacing the VAE/ELBO estimator.
Key results
- On noiseless synthetic data, ΩSDS maintains consistently high MCC across dimensions while VAE-based methods degrade as latent dimensionality increases.
- On bouncing-ball videos, the recurrent ΩSDS (R) achieves the strongest regime F1 and best long-horizon LPIPS (20 and 500 steps), competitive with VRNN.
- Non-recurrent ΩSDS (A) and iSDS recover regimes on observed sequences but struggle to predict future dynamics.
Surprising findings
- Non-recurrent switching can recover regimes on observed sequences yet predicts future dynamics poorly, highlighting the value of recurrent switches.
Limitations
- Identifiability requires constraining latent dynamics; the likelihood-separation condition does not trivially generalise to arbitrary nonlinear dynamics.
- Consistency result relies on additional MLE regularity assumptions beyond identifiability; a dedicated consistency analysis of nonlinear rSDS is open.
- Identifying K for unknown-K case requires analytic switching function Q.
Experimental setup
Datasets: synthetic piecewise-linear emission data (iSDS setting) 2D bouncing ball videos (synthetic, 10k) AIST dance videos
Benchmarks: synthetic iSDS settings (F1, MCC) 2D bouncing ball videos (regime F1, LPIPS) AIST dance videos (qualitative rollouts)
Metrics: regime F1 MCC LPIPS
Baselines: iSDS NCTRL CtrlNS TDRL iVAE VRNN KVAE SNLDS REDSDS
Builds on: iSDS TarFlow RealNVP Glow iVAE SNLDS
Closest papers by meaning
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- Inference of Neural Dynamics Using Switching Recurrent Neural Networks (NeurIPS 2024 · similarity 0.86)
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