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Amortized Control of Continuous State Space Feynman-Kac Model for Irregular Time Series
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Proposes ACSSM, a variational inference method for irregular time series that uses a multi-marginal Doob's h-transform, stochastic optimal control, and amortized, simulation-free linear latent dynamics with transformer-based data assimilation.
Problem
Modeling irregularly sampled, discrete-observation time series with continuous-time state space models, where Bayesian filtering/smoothing and numerical SDE/ODE simulation are costly and unstable.
Approach
Extends Doob's h-transform to multiple observation marginals, reformulates posterior simulation as a stochastic optimal control problem yielding a tight ELBO, and parameterizes locally linear drifts with a transformer and auxiliary encoded variables so that marginal Gaussian moments can be computed in parallel via a scan without numerical simulation.
Key results
- Human Activity per-time classification accuracy 91.4 ± 0.4%, above mTAND (91.1) and Latent-SDE_H (90.6).
- USHCN interpolation MSE 0.006 ± 0.001 (x10^-2) and extrapolation MSE 0.941 (x10^-2), best among compared baselines on USHCN.
- Runtime 2.3 s/epoch on USHCN and 3.8 s/epoch on Physionet, reported as more than 16-25x faster than CRU.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ACSSM instead of mTAND | Per-time-point classification · Human Activity | test accuracy (%): 91.1 \pm 0.2 -> 91.4 \pm 0.4 | Helped |
| Use ACSSM instead of mTAND | Pendulum regression · Pendulum | test MSE (× 10^-3): 3.20 \pm 0.60 -> 2.98 \pm 0.30 | Helped |
| Use ACSSM instead of RKN-Δt | Sequence interpolation · USHCN | test MSE (× 10^-2): 0.009 ± 0.002 -> 0.006 ± 0.001 | Helped |
| Use ACSSM instead of CRU | Sequence interpolation · Physionet | test MSE (× 10^-2): 0.182 ± 0.091 -> 0.116 ± 0.011 | Helped |
| Use ACSSM instead of CRU | Sequence extrapolation · USHCN | test MSE (× 10^-2): 1.273 ± 0.066 -> 0.941± 0.014 | Helped |
| Use ACSSM instead of mTAND | Sequence extrapolation · Physionet | test MSE (× 10^-2): 0.340 ± 0.020 -> 0.627 ± 0.019 | Hurt |
| Use ACSSM instead of CRU | Training · USHCN | runtime (sec./epoch): 122 (57.8)$^{*}$ -> 2.3 | Helped |
| Use ACSSM instead of CRU | Training · Physionet | runtime (sec./epoch): 114 (63.5)$^{*}$ -> 3.8 | Helped |
Surprising findings
- On Physionet extrapolation, ACSSM (0.627) is comparable to rather than better than the best baselines such as mTAND (0.340).
Limitations
- Variational gap from linear drift approximation may accumulate errors over long time series.
- Relies on high-capacity neural networks to approximate the optimal control, unlike particle-based SMC methods.
- Long sequences such as LLM-scale settings remain untested.
Experimental setup
Datasets: Human Activity USHCN Physionet Pendulum
Benchmarks: Human Activity Pendulum USHCN Physionet
Metrics: accuracy MSE runtime per epoch
Baselines: Latent-ODE Latent-SDE_H mTAND RKN-Δt GRU-Δt GRU-D ODE-RNN GRU-ODE-B CRU S5
Builds on: Latent SDE CD-SSM Doob's h-transform Feynman-Kac model S5 mTAND
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