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Life sciences · Preprint
arXiv · August 18, 2026
Raises a question worth testing. It does not answer one.
This preprint proposes Continuous-time Squared Error (CSE), an importance-weighted metric intended to correct bias in mean squared error (MSE) evaluation of irregular time-series forecasts. The authors provide theoretical proof that CSE's asymptotic estimation error does not exceed that of MSE, and computational experiments on synthetic, semi-synthetic, and real-world datasets show CSE recovers continuous-time risk more accurately than MSE. However, as an unrefereed methodological proposal without independent peer validation or demonstration of downstream impact on model selection or clinical decision-making, the evidence remains preliminary to hypothesis.
Methodological proposal with theoretical analysis and computational benchmarking. Intervention: Continuous-time Squared Error (CSE) metric with importance weighting. Compared with: Mean Squared Error (MSE).
MSE in irregular forecasting is biased because it is determined not only by model prediction but also by sample-specific timestamp sampling distributions CSE asymptotic estimation error with respect to continuous-time risk is theoretically no greater than that of MSE Experiments show CSE recovers continuous-time risk more accurately than MSE across synthetic, semi-synthetic, and eight real-world datasets
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This is a methodological proposal for an improved evaluation metric in time-series forecasting, supported by theoretical argument and computational validation but lacking clinical or real-world outcome data demonstrating practice impact.
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Existing research on irregular time-series forecasting has primarily focused on model design, while evaluation metrics remain insufficiently studied. Existing benchmarks typically use mean squared error (MSE) as the evaluation metric. We show that, in irregular forecasting, MSE is determined not only by the model prediction but also by the sample-specific timestamp sampling distributions, leading to a biased assessment of the models' continuous-time predictive performance. To address this issue, we propose the Continuous-time Squared Error (CSE), which employs importance weighting to eliminate the influence of the timestamp sampling distributions. We further theoretically prove that CSE's asymptotic estimation error with respect to continuous-time risk is no greater than that of MSE. Finally, we construct a systematic benchmark covering synthetic, semi-synthetic, and eight real-world datasets to validate the effectiveness of CSE and systematically evaluate models' continuous-time predictive performance. Experiments show that CSE can recover continuous-time risk more accurately than MSE, while relying solely on MSE may not fully reflect models' continuous-time predictive performance in real-world scenarios. Our code can be obtained at https://github.com/hnu-vis/ITS-Bench.
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