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Compositional simulation-based inference for time series
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Proposes factorized neural score estimation (FNSE) that learns local posterior scores from single-state transitions of Markovian simulators and composes them into a global posterior for arbitrary-length time series, extended also to FNLE/FNRE.
Problem
Amortized simulation-based inference for time series simulators is simulation-expensive and hard to scale because full-trajectory simulations are costly and high-dimensional, especially for Markovian simulators.
Approach
Exploit the Markov factorization of the simulator: train a local score (or likelihood) estimator on single-state transitions sampled from a proposal, then compose local scores into a global posterior score for time series of any length, using a Gaussian-approximation composition rule (GAUSS/JAC) adapted from i.i.d. work to handle noisy parameters at diffusion times a>0.
Key results
- FNSE is more simulation-efficient than NPE with RNN embedding on several synthetic benchmarks, outperforming NPE and FNRE in most tasks; e.g., on Mixture RW at T=11 FNSE reaches C2ST 0.69 vs. better-than-baseline results reported in its table.
- On the SIR task, FNSE significantly outperforms all other approaches, with C2ST around 0.67 to 0.78 across T=1 to T=101.
- Scales to Kolmogorov flow with about one million data dimensions using only 200k transition evaluations, with posteriors concentrated around true Reynolds number and density parameters.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a prior predictive proposal instead of the default proposal (ablation) | FNSE · Periodic SDE | C2ST: T=1: 0.53 -> 0.53; T=11: 0.60 -> 0.60; T=101: 0.76 -> 0.71 | Mixed |
| Use a prior predictive proposal instead of the default proposal (ablation) | FNSE · Linear SDE | C2ST: T=1: 0.53 -> 0.53; T=11: 0.70 -> 0.70; T=101: 0.90 -> 0.90 | No clear effect |
| Use a prior predictive proposal instead of the default proposal (ablation) | FNSE · Mixture RW | C2ST: T=1: 0.52 -> 0.52; T=11: 0.69 -> 0.69; T=101: 0.69 -> 0.75 | Mixed |
| Use a prior predictive proposal instead of the default proposal (ablation) | FNSE · Double Well | C2ST: T=1: 0.50 -> 0.50; T=11: 0.59 -> 0.57; T=101: 0.81 -> 0.80 | Mixed |
| Use a prior predictive proposal instead of the default proposal (ablation) | FNSE · Lotka-Volterra | C2ST: T=1: 0.57 -> 0.52; T=11: 0.78 -> 0.65; T=101: 0.94 -> 0.88 | Helped |
| Use a prior predictive proposal instead of the default proposal (ablation) | FNSE · SIR | C2ST: T=1: 0.67 -> 0.67; T=11: 0.78 -> 0.79; T=101: 0.74 -> 0.74 | Mixed |
Surprising findings
- For Markovian time series, posterior uncertainty does not necessarily decrease with more time points (e.g., SIR posterior barely changes between T=10 and T=100).
- NPE fails to generalize to longer time series on the SIR task while FNSE does.
Limitations
- Approximate score composition (GAUSS/JAC) assumes Gaussian posteriors, which is violated for multimodal tasks and can make the composed precision non-positive definite, requiring ad hoc adjustments.
- Restricted to Markovian simulators; hidden Markov models are out of scope.
- Posterior calibration deteriorates for longer time series (T=100) on Kolmogorov flow given the simulation budget.
Experimental setup
Datasets: Gaussian random walk mixture random walk periodic SDE linear SDE double well SDE Lotka-Volterra SIR Kolmogorov flow
Benchmarks: Gaussian RW Mixture RW Periodic SDE Linear SDE Double Well Lotka-Volterra SIR Kolmogorov flow
Metrics: C2ST sliced Wasserstein distance simulation-based calibration mean absolute error of predictives
Baselines: NPE with RNN embedding FNLE FNRE FNPE
Builds on: neural posterior score estimation factorized neural posterior estimation (i.i.d. composition) neural likelihood estimation neural ratio estimation
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