PSLR Co-Evolves Imputation and Generation for Irregular Time Series
Summary:The paper identifies a structural limitation in conventional irregular time-series generation: the pipeline imputes missing values once, freezes the completed dataset, and then trains a generator. Deterministic imputers collapse uncertainty into conditional means, while stochastic imputers become stale as the generator evolves. The proposed co-evolving Monte Carlo EM framework closes this loop. Its E-step samples missing values from the current generator posterior, while its M-step retrains the
The core problem: one-shot imputation is not the endpoint
Conventional pipelines for generating regular time series from irregular observations usually fill in missing values once, freeze the completed dataset, and train a generator on it. The paper argues that this open-loop design is structurally flawed. Point imputers collapse ambiguous missing regions into conditional means, while stochastic imputers become stale as the generator evolves. The binding issue is therefore the lack of feedback between imputation and generation.
PSLR organizes the two components as a co-evolving Monte Carlo EM process. In the E-step, missing values are sampled from the posterior induced by the current generator. In the M-step, the generator is retrained on the refreshed completions. As the generator learns a better approximation of the data manifold, the imputation distribution can follow it rather than remaining tied to a one-shot surrogate dataset.
Sampling posterior distributions in a lifted representation
The diffusion prior operates in a lifted two-dimensional representation, whereas observations live in time-series space. Naively transferring samples between these spaces can violate the operators that define temporal structure and can produce completions that are numerically plausible but semantically inconsistent with the original process.
PSLR, or Posterior Sampling for Lifted Representations, addresses three requirements: operator-consistent conditioning, preservation of posterior uncertainty in ambiguous missing regions, and consistency with the original data manifold. In probabilistic terms, the E-step samples from p(missing | observed, G_t) rather than from a fixed imputation distribution q(missing). The M-step then trains the generator on the resulting completed sequences.
This feedback can reduce distribution mismatch between the generator and its training data. It does not, however, guarantee global convergence. A biased early generator can influence the posterior samples used in the next round, potentially reinforcing its own errors. Initialization, update frequency, posterior diagnostics, and convergence controls are therefore important rather than optional implementation details.
Results and evaluation caveats
Across ten datasets and four corruption regimes, the paper reports a 59% improvement in discriminative score, a 15% improvement in predictive score, a 73% reduction in Context-FID, and a 71% reduction in feature-correlation error over the strongest baselines. Its ablations report a 73% reduction in average discriminative score relative to single-step baselines, closing most of the remaining gap to the clean-data oracle.
These gains are substantial, but the metric definitions still matter. Context-FID, feature-correlation error, and discriminative scores depend on feature extractors and statistical estimators, while predictive scores can be influenced by evaluation protocols and conditioning information. The abstract does not provide confidence intervals, run-to-run variance, statistical significance tests, or detailed convergence schedules.
Real-world missingness in healthcare and industrial systems is often not random. It may be caused by equipment state, treatment decisions, or sensor faults. Whether the four corruption regimes adequately represent such MNAR behavior will determine how reliably the method transfers outside synthetic experiments.
Engineering trade-offs
The quality gains come with additional computation. If each EM round uses K posterior samples and M generator-training epochs, its cost is approximately:
C_round ≈ K · C_sample + M · C_train
The total cost is then multiplied by the number of EM rounds T. If sampling count, training epochs, and rounds all scale linearly, the closed-loop method can cost far more than one-shot imputation followed by a single training run. Diffusion sampling also incurs sequential denoising overhead, particularly for long sequences.
The lifted representation may add memory and compute overhead, while rapidly changing imputation distributions can create instability. Production implementations should track posterior entropy, distributional quality, and the gap to a clean-data oracle rather than relying only on the training loss.
Practical guidance
The implementation is available at https://github.com/azencot-group/PSLR. When reproducing the results, hold the generator architecture and total training budget fixed, record sampling, training, memory, and EM-round costs separately, and evaluate temporal splits rather than random splits to avoid leakage.
Tests should distinguish MCAR, MAR, and MNAR mechanisms and report additional metrics such as coverage, calibration, worst-quantile error, and downstream predictive utility. The key contribution of PSLR is that it reframes irregular time-series generation as a closed-loop learning problem rather than a static data-cleaning problem. Whether it becomes the default approach depends on sampling cost, convergence stability, and independent validation under realistic missingness processes.
— END —Source: ArXiv Machine Learning (cs.LG) (2026-11-13)
Tags: #Irregular Time Series #Diffusion Generation #Monte Carlo EM #Posterior Sampling #PSLR
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