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HyperNSDE: Personalized Neural SDEs for Joint Static-Longitudinal Clinical Data Generation

Perrine Chassat, Agathe Guilloux

arXiv:2610.07383v1stat.MLcs.LGstat.APstat.ME

TL;DR

Clinical data generation requires jointly modeling heterogeneous static covariates, irregular trajectories, and informative observation times, a combination existing approaches address only partially. HyperNSDE combines static-conditioned stochastic dynamics with a latent-state-dependent observation process and a training decomposition for irregular paths. Across simulated and real clinical datasets, it improves observation-time fidelity and shows competitive performance, while evaluation metrics are sensitive to grid regularity and trajectory smoothness.

  • Problem

    Clinical records couple heterogeneous baseline covariates, irregular longitudinal trajectories, and informative observation times, while prior approaches address this joint setting only partially.

    Source: §1 · pp. 1–2

  • Method

    HyperNSDE combines a static generative model with a hypernetwork-conditioned latent Neural SDE, models observation times through a latent-state-dependent intensity, and stabilizes irregular-path training with deterministic–stochastic decomposition.

    Source: §1 · p. 2, §4 · p. 5

  • Results

    Across simulated and real clinical datasets, HyperNSDE improves observation-time fidelity and has competitive performance, while forecasting and correlation results are more heterogeneous and sensitive to evaluation-grid regularity and trajectory smoothness.

    Source: §1 · p. 2, §7 · p. 10

  • Takeaways & Limitations

    The results support benchmarking use cases, but the authors say further progress is needed before confident use for cohort augmentation or clinical-trial simulation.

    Source: §7 · p. 10

    HyperNSDE learns the training cohort’s observational distribution, not causal counterfactuals, and cannot by itself correct selection bias or extrapolate to unsupported subgroups.

    Source: §7 · p. 10

Abstract

from arXiv · show

Synthetic patient data generation is a promising solution to the dual challenge of data scarcity and privacy constraints in healthcare machine learning. Realistic synthesis of patient-level clinical data requires jointly modeling heterogeneous static covariates, irregularly sampled longitudinal trajectories, and informative observation times - three tightly coupled components in practice yet rarely addressed together. We propose HyperNSDE, a continuous-time generative model that conditions a latent Neural SDE on static patient representations through a hypernetwork, allowing baseline characteristics to shape trajectory evolution beyond the initial condition without requiring a trajectory encoder, while stochastic latent dynamics capture realistic variability in generated paths. Observation times are modeled jointly through a latent-state-dependent intensity process, and training on irregular stochastic paths is stabilized via a deterministic-stochastic path decomposition with a non-adversarial signature-kernel objective. Experiments on simulated and real clinical datasets show improved observation-time fidelity and competitive performance, while matched-grid analyses reveal that forecasting and correlation metrics are affected by observation-grid regularity and trajectory smoothness.

1 Introduction

Clinical records combine heterogeneous baseline covariates, irregular longitudinal measurements, and informative observation patterns, but existing models address these components only partially. HyperNSDE jointly generates them using static-conditioned stochastic dynamics and models observation times explicitly.

1 Introduction

  • Clinical cohorts are costly to collect and difficult to share, yet patient-level synthetic data could support benchmarking, trial-population simulation, rare-subgroup study, and cohort augmentation.Generated samples need to preserve real records’ multimodal structure, heterogeneity, and variability.Source: §1 · p. 1
  • Clinical data generation must jointly capture heterogeneous baseline features, irregular trajectories, informative observation patterns, cross-subject heterogeneity, and residual temporal variability.Baseline characteristics can influence disease progression, while observation frequency can depend on health state.Source: §1 · p. 1
  • Most time-series generators assume regular discrete-time sampling, while continuous-time models generally do not jointly generate static covariates and longitudinal trajectories.MultiNODEs also uses trajectory-wide information for latent initialization, keeps dynamics deterministic, and does not model informative observation times.Source: §1 · pp. 1–2

Contributions

  • HyperNSDE combines static-data generation with a personalized Neural SDE conditioned on static latent representations, and models informative observation times through a latent-state-dependent intensity process.Its deterministic–stochastic path decomposition and signature-kernel objective are designed to stabilize training.Source: §1 · p. 2, Contributions · p. 2
  • HyperNSDE’s stochastic latent dynamics capture variability beyond baseline covariates, while its hypernetwork lets baseline features modulate the full temporal vector field rather than only initialization.The model does not require trajectory encoding or pre-imputation.Source: Contributions · p. 2

2 Background and related work

Prior generative models cover different subsets of joint static and irregular longitudinal generation, while continuous-time stochastic models offer a way to represent temporal uncertainty. Hypernetworks provide a personalization mechanism beyond input concatenation or feature-wise modulation.

Comparison of generative models

  • Table 1 compares models on static-covariate generation, irregular-time-series support, continuous-time latent dynamics, joint static–longitudinal modeling, and explicit observation-intensity modeling.Its footnotes distinguish externally handled irregular timing, conditioned rather than generated static covariates, and static variables represented as time-series channels.Source: Table 1 · p. 2, §2 · p. 2

Time-series and joint generative models

  • Most time-series generators target regular discrete-time sequences [66, 17, 32, 31, 68], while irregular-time methods [59] [22] typically do not jointly model static covariates and observation intensities.RTSGAN [46] includes static covariates and visit-time modeling; HL-VAE, VAMBN [30], and EHR-Safe use discrete-time longitudinal modeling.Source: §2 · pp. 2–3

Continuous-time latent variable models and Neural SDEs

  • Neural ODEs have deterministic latent dynamics, whereas Neural SDEs add learned drift and diffusion so sampled Brownian motion can represent intrinsic temporal uncertainty and richer trajectory variability.Neural SDE training objectives include variational, adversarial Wasserstein, scoring-rule, and signature-kernel approaches.Source: §2 · p. 3

Hypernetworks

  • Hypernetworks generate a target network’s parameters from conditioning inputs, enabling individualization beyond concatenation or feature-wise modulation.They have been applied to personalized scientific and clinical modeling [15] [7].Source: §2 · p. 3

3 Model

HyperNSDE generates static covariates and irregular longitudinal trajectories in a shared pipeline, conditioning continuous-time latent dynamics on each subject’s static representation and modeling observation times from the latent path.

3 Model

  • Synthetic-subject generation samples static latent representations, decodes covariates, generates patient-specific SDE parameters, simulates a latent path, and decodes trajectories at intensity-sampled observation times.Longitudinal data enter through training losses rather than a trajectory encoder.Source: Figure 1 · p. 3

3.1 Static latent representation with HI-VAE

  • The model represents mixed-type baseline covariates with a HI-VAE, whose static latent representation conditions the longitudinal model.Its decoder uses covariate-type-specific likelihoods to handle heterogeneous variables and missing values.Source: §3.1 · p. 4

3.2 Personalized stochastic latent dynamics

  • A continuous-time latent path is decoded into observed trajectories at arbitrary irregular observation times, with latent evolution modeled by a Neural SDE.The SDE’s drift models subject-specific deterministic dynamics and its diffusion models stochastic variability shared across subjects; the formulation assumes global Lipschitz conditions and is conceptual rather than directly trained.Source: §3.2 · p. 4
  • A hypernetwork maps each patient’s static representation to individualized drift parameters, while diffusion remains population-shared.The initial latent state is fixed at zero; the paper states that baseline measurements are encoded in the static representation and the latent path models deviations from baseline.Source: §3.2 · p. 4

3.3 Event intensity from the latent path

  • The observation process is a latent-state-dependent multivariate point process with an explicit end-of-sequence event.The intensity for each longitudinal variable and the termination hazard are modeled separately.Source: §3.3 · pp. 4–5

4 Training procedures

HyperNSDE jointly trains its interconnected static, longitudinal, and observation-process components using a deterministic–stochastic path decomposition. Separate losses train static reconstruction, deterministic trajectories, stochastic residuals, and observation events.

Joint training

  • Joint optimization is needed because the static representation must align with the hypernetwork; independently pretrained HI-VAE embeddings may not capture features needed for personalized drift functions.The model’s components include the HI-VAE, hypernetwork, latent dynamics, decoder, and intensity model.Source: §4 · p. 5

Stable training via deterministic–stochastic path decomposition

  • The path decomposition separates a smooth, subject-specific trend from residual stochastic variability, with the hypernetwork parameterizing the trend dynamics.The intensity network is conditioned only on the deterministic path, and the decomposition is not generally equivalent to a single latent SDE.Source: §4 · p. 5

Loss terms

  • Training combines a static ELBO, point-process likelihood for observation and end-of-sequence events, deterministic reconstruction loss, and stochastic residual loss.Point-process integral terms are approximated numerically on the latent-dynamics discretization grid.Source: §4 · pp. 5–6
  • The deterministic component is trained to reconstruct observed longitudinal values with mean squared error, while the stochastic component matches reconstructed and empirical residual paths using a signature-kernel score.The paper describes the signature-kernel score as suited to irregularly sampled trajectories.Source: §4 · pp. 5–6

5 Evaluation methodology

The evaluation framework addresses the lack of a universally accepted protocol for irregular longitudinal data by assessing fidelity, utility, and privacy. Simulated and real clinical datasets, alongside selected baselines, provide the evaluation settings.

5 Evaluation methodology

  • Performance is assessed across three complementary axes: fidelity, utility, and privacy.The paper notes that no universally accepted protocol exists for irregular longitudinal data with missingness.Source: §5 · p. 6
  • Fidelity metrics cover statistical structure and diversity in static and longitudinal data, observation-intensity KL divergence, and real-versus-synthetic discrimination.Longitudinal fidelity uses signature-kernel MMD and masked correlation matrices without interpolation.Source: §5 · p. 6
  • Utility is evaluated with TSTR forecasting: a model trained on synthetic data predicts held-out real trajectories, with MSE compared against a TRTR reference.The predictor uses static covariates and the first part of each trajectory to forecast remaining time points.Source: §5 · p. 6
  • Privacy is assessed using NNAA, membership-inference risk, and residual dependence between generated samples and training individuals.Dependence is computed on joint multimodal representations.Source: §5 · p. 6
  • Simulated data test whether models recover static-to-longitudinal dependencies, with irregular visits sampled from a non-homogeneous Poisson process.The reference setting has 1,000 individuals, two static variables, three longitudinal variables, and an average of 50 visits per patient over T = 7.Source: §5 · p. 6
  • Evaluation uses VELOUR and PPMI clinical cohorts and compares HyperNSDE with MultiNODEs, RTSGAN, and DGBFGP+HI-VAE on simulated data.DGBFGP+HI-VAE is restricted to simulated data because DGBFGP requires substantial dataset-specific manual configuration; simulated results average 30 Monte Carlo runs and 50 generated datasets per trained model.Source: §5 · p. 7

6 Results

HyperNSDE performs competitively across evaluation axes in simulation, with mixed results on real clinical datasets; its observation-time fidelity is stronger than MultiNODEs but not RTSGAN. Matched-grid analyses show that correlation and prediction comparisons depend on observation-grid regularity and trajectory smoothness.

6 Results

  • HyperNSDE performs competitively across simulated-data evaluation axes, leading on discriminative, dependence, KL λ, and predictive mean scores and achieving longitudinal MMD 16× lower than RTSGAN.It is the only method reported to simultaneously reproduce static-covariate color stratification, stochastic trajectory variability, and irregular observation patterns.Source: §6 · p. 7, Table 2 · p. 8, Figure 2 · p. 9
  • Matched-grid reevaluations show that correlation and prediction comparisons depend on grid regularity, while drift-only results indicate that the MSE objective favors smoother trajectories.On simulated data's real observation grid, MultiNODEs Corr. RMSE rises from 0.084 to 0.494, while HyperNSDE changes from 0.118 to 0.115.Source: §6 · pp. 7–9, Table 3 · p. 8
  • Paired tests across 30 Monte Carlo runs find significant longitudinal and static MMD improvements over all baselines, but no significant longitudinal Corr. RMSE differences.KL λ improvements are significant over MultiNODEs and DGBFGP+HI-VAE, but are baseline-dependent.Source: §6 · p. 8
  • On VELOUR and PPMI, results are mixed: HyperNSDE leads on NNAA, has the lowest VELOUR longitudinal MMD, and beats MultiNODEs on observation-intensity KL λ, while RTSGAN has the lowest KL λ.VELOUR longitudinal MMD is about 5× and 4000× lower than MultiNODEs and RTSGAN, respectively; HyperNSDE has competitive longitudinal MMD on PPMI.Source: §6 · p. 8, Table 2 · p. 8
  • Ablations show that replacing the Neural SDE with an ODE degrades correlation RMSE and MMD, removing the det–sto decomposition destabilizes trajectories, and removing the observation model raises KL λ from 0.687 to 67.616.Alternative conditioning methods are competitive on individual metrics but do not dominate HyperNSDE; the hypernetwork is supported as effective, not uniquely necessary.Source: §6 · p. 9, Table 4 · p. 10

7 Conclusion

HyperNSDE jointly generates static covariates, irregular trajectories, and informative observation times, with stochastic dynamics capturing variability beyond baseline characteristics. Its results are competitive, but its observational scope, computational cost, and current evaluation metrics constrain use.

7 Conclusion

  • HyperNSDE captures inter-individual variability driven by baseline characteristics and intra-individual stochastic fluctuations, while improving observation-time fidelity and achieving competitive performance across complementary metrics.Matched-grid analyses also show that metrics are sensitive to sampling regularity and trajectory smoothness.Source: §7 · p. 10
  • The model learns the training cohort’s observational distribution, not causal counterfactuals, and cannot by itself correct selection bias or extrapolate to unsupported subgroups.It is also more computationally demanding than the baselines.Source: §7 · p. 10
  • Current metrics can disagree with trajectory realism for sparse, irregular, stochastic data, while discriminative scores remain high for all methods.Further progress is needed before models can be confidently used for cohort augmentation or clinical trial simulation; they may already support benchmarking.Source: §7 · p. 10
  • Future work includes richer diffusion parameterizations, typed longitudinal outputs, differential privacy, analysis of the path decomposition, and improved evaluation metrics.The authors identify evaluation protocols and metrics as the most important open problem for reliable quality assessment and fair comparisons.Source: §7 · p. 10

A.1 Additional details on the HI-VAE

  • The HI-VAE represents each individual’s static covariates with discrete and continuous latent variables, and uses feature-specific decoders with likelihoods adapted to each variable type.Variational inference factorizes as q(s_i, u_i | W_i) = q(s_i | W_i) q(u_i | W_i, s_i); the discrete and continuous latents use Gumbel–Softmax and Gaussian reparameterization, respectively.Source: §A.1 · p. 15

A.2 Additional details on the event intensity model

  • To reduce memory use and computational cost, the event-intensity model solves the latent path first, evaluates intensity at required times, then approximates integrated intensity by numerical quadrature.This decoupled strategy retains a latent-state-dependent point-process model and is intended to scale to high-dimensional latent spaces and large cohorts.Source: §A.2 · p. 15

A.3 Extended details on synthetic data generation

Synthetic subjects are generated hierarchically: static covariates condition personalized dynamics, while a shared stochastic component and latent-state-dependent event process produce variable trajectories and irregular observation times. The appendix explains the decomposition’s modeling role and the signature-kernel path objective used to train stochastic residuals.

A.3 Extended details on synthetic data generation

  • Synthetic subjects are generated by sampling and decoding static latents, mapping them through a hypernetwork to personalize drift, simulating deterministic and stochastic trajectory components, sampling observation times, and decoding longitudinal values.The procedure is described as preserving static–longitudinal dependence, temporal variability, and irregular observation patterns.Source: §A.3 · pp. 15–16

B.1 Deterministic–stochastic decomposition: further discussion

  • The deterministic component solves a personalized Neural ODE with hypernetwork-generated parameters; a population-shared Neural SDE models residual fluctuations using a low-capacity drift and diffusion.The total process matches a single latent SDE only when drift decomposes additively across the two components, exactly in the linear case and approximately otherwise; the residual drift absorbs missed trend.Source: §B.1 · p. 16
  • The deterministic–stochastic decomposition is a modeling choice inspired by Doob–Meyer decomposition and functional data analysis, rather than a directly estimated drift–diffusion split.Classical separate estimation typically requires the number of observed time points per path to tend to infinity, incompatible with sparse irregular data.Source: §B.1 · p. 16

B.2.1 Signature-kernel score

  • The signature-kernel score compares path distributions through a positive-definite kernel on path signatures and differs from full kernel MMD only by a data-only term, making it equivalent for model optimization.Signatures provide a path representation that can be computed from discretely observed trajectories on irregular grids.Source: §B.2.1 · p. 17

B.3 Hyperparameters optimization method

Hyperparameter selection combines the model’s loss terms and chooses a Pareto-front configuration that balances longitudinal and static reconstruction. The evaluation discussion identifies gaps in existing tools and describes an approach designed for multimodal, irregular data.

B.3 Hyperparameters optimization method

  • Linear weighted loss combination provided the most stable training and best validation trade-off among the tested aggregation strategies.The losses differ in scale and sign; alternatives included uncertainty weighting, GradNorm, and initial-loss scaling.Source: §B.3 · p. 17
  • Optuna selects a configuration from a Pareto front of unweighted validation losses after approximately 100 trials, preventing one component from dominating.On the reference simulated-data setting, the front shows a trade-off between longitudinal deterministic and static reconstruction losses; the selected point is a compromise.Source: §B.3 · p. 18, Figure 3 · p. 18

C.1 Challenges and limitations of existing approaches

  • Existing toolkits often target regular time series or tabular data, and preprocessing irregular records by interpolation or imputation can distort temporal structure.Evaluation protocols and metric selection also remain unsettled, with reported results sensitive to implementation choices.Source: §C.1 · p. 19
  • Joint evaluation of static covariates, irregular trajectories, cross-modal dependencies, observation processes, and missingness falls outside most existing toolkits; adapted metrics are beyond this paper’s scope.The authors identify this evaluation gap as one method papers in this space should explicitly address.Source: §C.1 · p. 19

C.2 Our evaluation strategy

  • The evaluation strategy assesses fidelity, utility, and privacy with metrics adapted to multimodal irregular data, operating directly on observations without interpolation or imputation when standard metrics permit.Source: §C.2 · p. 19

C.2.1 Fidelity metrics

The evaluation uses modality-aware measures for fidelity, forecasting utility, and privacy, including metrics that operate on irregular observations. Signature-kernel MMD requires particular caution when paths are sparse or irregular.

C.2.1 Fidelity metrics

  • Fidelity measures include static RBF-kernel MMD, longitudinal signature-kernel MMD, observation-intensity KL divergence, and classifier two-sample AUROC.Lower MMD and intensity KL indicate better agreement; C2ST AUROC closer to 0.5 indicates greater difficulty distinguishing real from synthetic samples.Source: §C.2.1 · pp. 19–20
  • Signature-kernel MMD compares irregular trajectories directly using time augmentation and observation-mask path compression, but its results warrant caution for sparse, irregular paths.Bandwidth mismatch can saturate kernel values or destabilize estimates; interpolated paths may remain rough proxies for the underlying continuous trajectories.Source: §C.2.1 · p. 20
  • Correlation RMSE compares real and synthetic dependency matrices using overlapping observed pairs and includes a cross-modal measure augmented with static covariates.Source: §C.2.1 · p. 20

C.2.2 Utility metrics

  • Forecasting utility is measured by TSTR MSE on real test data and compared with the TRTR reference; privacy measures include NNAA and membership-inference risk.NNAA uses training-versus-held-out nearest-neighbor distances, while MIR evaluates attack-score AUROC; lower values indicate lower privacy risk for both.Source: §C.2.2 · p. 21, §C.2.3 · p. 21

D.1 Formatting and preprocessing of the data

  • Preprocessing places irregular observations on a common union-of-times grid, tracks missingness with a binary mask, and represents longitudinal variables as standardized deviations from baseline.Baseline longitudinal values are appended to static covariates.Source: §D.1 · p. 22

D.2 Simulated datasets

The simulated data couple static covariates to longitudinal dynamics and vary the observation process between time-dependent and state-dependent sampling. Real datasets undergo shared filtering and time-preserving preprocessing, with dataset-specific adaptations.

D.2 Simulated datasets

  • Simulated longitudinal processes depend on static covariates, and observation times are generated under time-dependent and state-dependent schemes.Visit times use discrete thinning on a regular grid; latent trajectories are simulated on a fine grid and observed only at sampled visits.Source: §D.2 · pp. 22–23

D.3.1 Preprocessing pipeline

  • Real-data preprocessing preserves original observation times, filters sparse variables and patients, and represents retained trajectories on a shared grid with an observation mask.Patients with fewer than five longitudinal observation times after filtering are removed; variables with low presence are discarded using dataset-specific thresholds.Source: §D.3.1 · p. 23

D.3.2 Dataset-specific notes

  • VELOUR contributes metastatic colorectal cancer trial data, while PPMI contributes Parkinson’s disease cohort data, each with static characteristics and longitudinal clinical measurements.VELOUR observations before treatment initiation are excluded; PPMI includes vital signs and clinical rating scales.Source: §D.3.2 · pp. 23–24

E.1 Experiments setting and compute resources

  • Experiments use AdamW and early stopping, with a maximum of 1,000 epochs and single-V100 GPU jobs subject to a 20-hour wall-clock limit.On the reference simulation, an epoch takes approximately 1 minute 20 seconds and training ends around epoch 500.Source: §E.1 · p. 24

E.2 Baseline implementations and tuning

  • Baselines use public implementations with additional Optuna tuning where needed, while DGBFGP is paired with a separately trained HI-VAE for static data.Because this baseline does not jointly learn static and longitudinal generation and requires substantial manual configuration, it is restricted to simulated experiments.Source: §E.2 · p. 24

E.3 Details on the sensitivity analysis

The sensitivity analysis varies training size, visit frequency, observation-process dependence, and static-latent sampling. Ablations test stochastic dynamics, path decomposition, personalization strategies, and explicit observation-process modeling.

E.3 Details on the sensitivity analysis

  • Sensitivity scenarios reduce training data to 200 patients, reduce visits to 15 per patient, introduce state-dependent sampling, and compare posterior with prior static-latent sampling.The state-dependent intensity scenario changes the visit process while keeping other simulation parameters identical; the latent-sampling comparison tests dependence on sampling choice.Source: §E.3 · pp. 24–25

E.4 Details on the ablation studies

  • The deterministic-latent ablation replaces the Neural SDE with a Neural ODE to test stochastic dynamics against deterministic trajectories.It is conducted on the reference simulated-data setting, with other architectural choices and protocols unchanged unless noted.Source: §E.4 · p. 25
  • The direct-stochastic-training ablation removes deterministic–stochastic path decomposition and trains the full latent path directly from signature-kernel discrepancy.It tests whether decomposition improves optimization stability and separates deterministic dynamics from stochastic fluctuations.Source: §E.4 · p. 25
  • Personalization ablations compare hypernetwork conditioning with direct state concatenation and FiLM-based layer-wise scale-and-shift modulation.The hypernetwork generates full drift parameters, whereas FiLM provides lower-dimensional feature-wise affine modulation; direct concatenation can inject static information at the initial time or throughout the trajectory.Source: §E.4 · pp. 25–26
  • The no-observation-process ablation removes latent-state-dependent intensity modeling, including the explicit end-of-sequence component.Source: §E.4 · p. 26

F.1 Statistical variability and robustness

This appendix supplements mean-based comparisons with median summaries, variability estimates, and paired significance tests to assess stability across Monte Carlo runs and generated datasets.

F.1 Statistical variability and robustness

  • Robustness analyses complement the main-text means with variability measures, paired significance tests, and median-based aggregation.These analyses assess stability across Monte Carlo runs and generated datasets.Source: §F.1 · p. 26
  • Table 7 reports standard deviations for evaluation metrics across 30 Monte Carlo runs and 50 generated datasets from one trained model; corresponding means appear in Table 2.Source: Table 7 · p. 26
  • Table 8 reports standard deviations for simulated-data ablations across 30 Monte Carlo runs and 50 generated datasets from one trained model; corresponding means appear in Table 4.Source: Table 8 · p. 26
  • Table 9 uses two-sided paired Wilcoxon signed-rank tests over 30 seeds, with Holm correction across 30 tests, to compare HyperNSDE with each baseline.Cells give median differences, with signs oriented per metric; symbols mark significant wins or losses after correction.Source: Table 9 · p. 27
  • Table 10 reports median evaluation metrics on simulated and real-world data; lower values are better, except NNAA, where values closer to zero are better.Source: Table 10 · p. 27

F.2 Additional analyses of evaluation metrics

The supplementary material includes analyses of metric discriminability, robustness, subgroup and source-cohort fidelity, and qualitative trajectory comparisons, alongside scope, limitations, and reproducibility information. The supplied passages also cover checklist items on asset credit and licensing, code documentation, and the absence of author-conducted human-subject research or core LLM use.

F.2 Additional analyses of evaluation metrics

  • On simulated data, static covariates were difficult to distinguish across methods, baseline discriminability arose strongly from observation patterns, and HyperNSDE’s remaining discriminability mainly came from trajectory values.The analysis repeats real-versus-synthetic classification separately on static covariates, observation patterns, and trajectory values.Source: §F.2 · p. 27, Table 11 · p. 28

F.3 Sensitivity analysis

  • Robustness was assessed on simulated data under limited training samples, sparse observations, state-dependent sampling, prior versus posterior latent sampling, and state-dependent versus independent observation intensity.The corresponding sensitivity analyses are presented in Tables 12–16; the supplied passages do not report their comparative values.Source: §F.3 · p. 28, Table 12 · p. 28, Table 13 · p. 28

F.4 Subgroup and cohort analyses

  • Median SMD was 0.092 across 26 VELOUR covariates, with 65% below 0.1 and p-value quartiles [0.40, 0.87], measuring fidelity to the source cohort.This does not establish correction of selection bias or representativeness for a broader target population.Source: §F.4 · pp. 30–31, Table 19 · p. 31

F.5 Qualitative results

  • Qualitative figures compare HyperNSDE and baselines, generation modes, and ablation variants on simulated trajectories for x0, x1, and x2.The comparisons distinguish W1 = 0 and W1 = 1 subjects using separate color gradients for W0.Source: §F.5 · p. 31, Figure 4 · p. 31, Figure 5 · p. 32

NeurIPS Paper Checklist

  • The paper reports limitations involving computational cost, real-world evaluation scope, and evaluation metrics for irregular multimodal clinical data, and notes that it claims no formal theoretical results or proofs.The deterministic–stochastic decomposition is presented as a modeling choice with theoretical motivation, not as a theorem.Source: NeurIPS Paper Checklist · pp. 34–35
  • Code and simulated-experiment scripts are released, while access to VELOUR and PPMI requires individual data agreements; the paper reports experimental settings and variability across runs.Results use 30 Monte Carlo runs and 50 generated datasets per trained model for simulated data, and 50 generations for real-world data; standard deviations are reported.Source: NeurIPS Paper Checklist · pp. 35–37
  • The paper identifies potential benefits in privacy-aware data sharing and warns against premature high-stakes use, citing realism limits and the need for stronger safeguards such as differential privacy.The checklist also states that no patient-level data is released and that datasets are accessed through official channels under their terms of use.Source: NeurIPS Paper Checklist · p. 38
  • Existing datasets, baseline implementations, and pySigLib are cited and used under their respective access conditions or open-source licenses.The checklist answers yes to proper credit and licensing of existing assets.Source: NeurIPS Paper Checklist · p. 39
  • The new HyperNSDE research code is documented through manuscript and appendix descriptions of its modeling components, training setup, and implementation details.The checklist says these details are provided to support understanding and reproducibility.Source: NeurIPS Paper Checklist · p. 39
  • The authors report no crowdsourcing or human-subject research, so no IRB approval or equivalent review was required.The checklist marks both crowdsourcing/human-subject research and IRB approval as not applicable.Source: NeurIPS Paper Checklist · p. 40
  • LLMs were not used as an important, original, or non-standard component of the method, experiments, or scientific claims.Source: NeurIPS Paper Checklist · p. 40

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