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Real-valued (Medical) Time Series Generation with Recurrent Conditional GANs

Cristóbal Esteban, Stephanie L. Hyland, Gunnar Rätsch

arXiv:1706.02633v2stat.MLcs.LG

TL;DR

Medical research is constrained by limited access to sensitive time-series data and by inadequate evaluation methods for generated multidimensional sequences. The paper develops recurrent and conditional recurrent GANs, together with supervised-data evaluation and privacy analyses. RCGAN-generated datasets supported supervised training with only minor degradation on real test data, including serialised MNIST and an ICU early-warning task.

  • Problem

    Sensitive medical data are difficult to access, while visual evaluation is inadequate for multidimensional time series and limits assessment of generated data.

  • Method

    The paper uses recurrent neural networks in GAN generators and discriminators, conditions both networks on auxiliary information in RCGANs, and evaluates synthetic labelled data through supervised transfer tests.

  • Results

    RCGAN-generated datasets supported supervised training with only minor degradation on real test data across serialised MNIST and an ICU early-warning task.

  • Takeaways & Limitations

    With further refinement, synthetic medical time series could support real tasks and synthetic benchmarking datasets in sensitive domains.

  • Takeaways & Limitations

    The proposed empirical privacy evaluations can check privacy properties quickly but do not provide strong privacy guarantees.

Abstract

from arXiv · show

Generative Adversarial Networks (GANs) have shown remarkable success as a framework for training models to produce realistic-looking data. In this work, we propose a Recurrent GAN (RGAN) and Recurrent Conditional GAN (RCGAN) to produce realistic real-valued multi-dimensional time series, with an emphasis on their application to medical data. RGANs make use of recurrent neural networks in the generator and the discriminator. In the case of RCGANs, both of these RNNs are conditioned on auxiliary information. We demonstrate our models in a set of toy datasets, where we show visually and quantitatively (using sample likelihood and maximum mean discrepancy) that they can successfully generate realistic time-series. We also describe novel evaluation methods for GANs, where we generate a synthetic labelled training dataset, and evaluate on a real test set the performance of a model trained on the synthetic data, and vice-versa. We illustrate with these metrics that RCGANs can generate time-series data useful for supervised training, with only minor degradation in performance on real test data. This is demonstrated on digit classification from 'serialised' MNIST and by training an early warning system on a medical dataset of 17,000 patients from an intensive care unit. We further discuss and analyse the privacy concerns that may arise when using RCGANs to generate realistic synthetic medical time series data.

1 INTRODUCTION

The paper targets limited access to sensitive medical time-series data and inadequate evaluation methods for generated multidimensional sequences. It introduces adversarial approaches for generating real-valued sequences and proposes novel GAN evaluation methods, including synthetic medical time-series generation.

  • Sensitive and inaccessible medical data hinder model comparison, reproducibility, and scientific progress.
  • Visual inspection is impractical and inappropriate for evaluating generated multidimensional medical time series.
  • The work demonstrates adversarial training for generating real-valued sequences.
  • It introduces novel approaches for evaluating GANs.
  • The paper generates synthetic medical time-series data for potential use in medical applications.The proposed application includes realistic ICU situations that could support medical training simulations.
  • The work includes empirical privacy analysis of GANs and differentially private GANs.

2 RELATED WORK

Prior GAN research largely focused on images, discrete language tokens, or discrete electronic health records, leaving continuous-valued sequence generation comparatively underexplored. Related work also motivates conditional generation, supervised-data evaluation, and privacy-preserving GAN training.

  • Earlier medical GAN work generated discrete-valued electronic health records and patient snapshots rather than real-valued time series.
  • Most sequential GAN generation focused on discrete tokens for natural language processing, with only preliminary work on continuous-valued polyphonic music sequences.
  • Conditional GANs use additional information to direct the data-generation process and have mainly been applied to images, translation, and dialogue.
  • The paper’s supervised-model evaluation differs from related semisupervised GAN work because its target tasks may be unknown when the GAN is trained.
  • Differentially private stochastic gradient descent is explored as a way to train RGANs with stronger privacy guarantees for sensitive medical data.

3 MODELS: RECURRENT GAN AND RECURRENT CONDITIONAL GAN

The paper defines recurrent GAN architectures for generating real-valued sequences, including a conditional variant, and evaluates them with distributional and supervised-task metrics. The evaluation includes MMD and TSTR-style testing of whether synthetic labelled data supports models tested on real data.

  • Models: RGAN replaces the generator and discriminator in a regular GAN with recurrent neural networks for generating real-valued sequences.RCGAN additionally conditions both recurrent networks on auxiliary inputs.
  • Models: The generator receives a different random seed at each time step, while the discriminator classifies each input time step as synthetic or real.In RCGANs, both recurrent networks also receive conditional information.
  • Training objective: The discriminator minimizes average per-time-step negative cross-entropy against sequence labels, using ones for real sequences and zeros for synthetic sequences.The generator minimizes the same loss against the all-ones label to make generated sequences appear real.
  • Maximum mean discrepancy: MMD compares statistics from generated and real samples through a kernel to assess whether they could come from the same distribution.The implementation treats aligned time series as vectors or matrices and uses an RBF kernel based on squared ℓ2 or Frobenius distance.
  • Maximum mean discrepancy: The authors find MMD^2 more informative than generator or discriminator loss and report that it correlates well with quality assessed by visualization.They optimize the kernel bandwidth using a validation split and also use a mixed kernel formed from two RBF bandwidths.
  • Supervised evaluation: TSTR trains a supervised model on GAN-generated labelled data and evaluates it on held-out real examples.The reverse TRTS procedure trains on real data and evaluates on a synthetic test set.

4 LEARNING TO GENERATE REALISTIC SEQUENCES

The RGAN generates realistic-looking sequences across synthetic and serialized-MNIST settings, while training improves likelihood and captures smooth variation. The experiments also introduce comparisons with recurrent variational autoencoders and supervised evaluation setups.

  • Synthetic sequences: RGAN experiments generate realistic-looking sine waves, smooth signals, and serialized MNIST sequences.The paper evaluates sequences visually and through likelihood and MMD-based measures.
  • Synthetic sequences: The model captures smoothness with local correlations in arbitrary smooth signals.The authors report that this structure is rapidly captured by the RGAN.
  • Evaluation: Likelihood of generated samples increases during training, although MMD2 is preferred because likelihood does not measure sample diversity.The paper notes that likelihood can miss mode collapse.
  • MNIST as a time series: Serialized MNIST represents each 28 × 28 digit as a 784-dimensional sequence, while a second experiment uses 28 sequential 28-dimensional outputs.The latter representation produces generated digits that appear realistic.
  • Memorization analysis: Latent interpolation between back-projected training examples produces clear incremental variation rather than abrupt switching between memorized examples.The interpolation experiment uses the smooth-function dataset.

5 LEARNING TO GENERATE REALISTIC ICU DATA

The ICU experiments generate conditioned, multivariate time series from selected eICU measurements and evaluate them through supervised early-warning tasks. Synthetic data is assessed by training classifiers on it and testing on real data.

  • Data preparation: The study uses eICU data containing around 200,000 patients from 208 care units, focusing on four bedside-monitor variables.The variables are SpO2, heart rate, respiratory rate, and mean arterial pressure.
  • Data preparation: Measurements are downsampled from five-minute intervals to fifteen-minute medians, and the first four ICU hours provide 16 measurements per variable.Patients with missing data after downsampling are discarded, yielding a cohort of 17,693 patients.
  • Evaluation: TSTR evaluates ICU synthetic data by training a classifier on generated sequences and testing it on a held-out real set.This evaluation is used because synthetic ICU plots are insufficient for judging similarity.
  • TSTR tasks: The supervised task predicts whether each physiological variable will exceed a critical threshold during the next hour.Labels concern the interval between hours 4 and 5 after the first four hours are treated as observed.
  • TSTR tasks: Conditioning labels are sampled from real data so the synthetic and real datasets share the same label distribution and label dependencies.The labels are supplied as conditioning inputs to the RCGAN.

6 IS THE GAN JUST MEMORISING THE TRAINING DATA?

The paper tests whether strong supervised performance could reflect memorization of training examples. Its empirical checks compare reconstruction errors, latent interpolations, and distributional distances between generated, training, and test data, but do not provide strong privacy guarantees.

  • Privacy concern: The memorization concern is that reproducing training examples could leak private medical data and make the training data recoverable.The authors distinguish memorization from learning an implicit distribution concentrated near, but not limited to, training examples.
  • Evaluation strategy: The privacy analysis combines one qualitative test with two statistical tests.The authors characterize these evaluations as empirical rather than formal privacy guarantees.
  • Reconstruction test: Nearest neighbours are obtained by minimizing reconstruction error 1 − K(G(Z), y) using an RBF kernel and gradient-based latent optimization.The optimization continues until approximate convergence, defined by a sufficiently small gradient norm.
  • Reconstruction test: The Kolmogorov-Smirnov test compares reconstruction-error distributions for training and test examples, since memorization would produce identifiably lower training errors.Reported p-values are 0.2 ± 0.1 for sine waves and 0.09 ± 0.04 for smooth signals.
  • Interpolation test: Latent interpolation between distinct training examples shows incremental sample variation, contrary to the abrupt switching expected from memorization.The experiment is illustrated for the smooth-function dataset.
  • Distributional test: The MMD three-sample test compares generated-to-test and generated-to-training distances to detect whether generated data is unusually close to the training distribution.The test uses generated samples together with separate training and test sets.

7 TRAINING RGANS WITH DIFFERENTIAL PRIVACY

The paper examines differential privacy for recurrent GANs generating sensitive medical time series, using gradient clipping, noise addition, and privacy accounting. Privacy can substantially reduce utility on MNIST, while eICU downstream performance remains high under stricter privacy settings.

  • Differential privacy limits how much the trained GAN distribution changes when individual records are added or removed, bounded by ϵ and δ.The mechanism is defined over the randomness of the training procedure and its possible GAN outputs.
  • DP-SGD clips per-example gradients, adds batch noise, and uses a moments accountant to track privacy spending during discriminator updates.The procedure limits the signal from any individual example while accumulating a privacy budget across training.
  • On MNIST, accuracy was 0.75±0.03 at ϵ = 1 and δ ≤1.8×10−3, rising to 0.77±0.03 at ϵ = 2 and δ ≤2.5 × 10−4.These results were below the non-private GAN, reflecting the difficulty of generating realistic time-series while preserving privacy.
  • On eICU, performance remained high with differentially private training even at ϵ = 0.5 and δ ≤9.8 × 10−3.Generated sequences were less realistic and more extreme-valued, but those changes appeared unimportant for tasks predicting extreme values.
  • The eICU findings suggest that privacy-preserving noise can retain information useful for downstream models despite reducing sequence realism.The authors identify this as a direction for research at the intersection of privacy and GANs.

8 CONCLUSION

The paper presents recurrent GANs for real-valued sequential data and evaluates conditional versions through supervised learning on synthetic datasets. Across serialized MNIST and ICU data, synthetic-trained models sometimes matched real-data performance, while differential privacy provided stronger guarantees with some performance loss.

  • 8 CONCLUSION: RGAN generates real-valued sequential data with recurrent generator and discriminator architectures, while RCGAN additionally conditions both networks on labels.The models target synthetic datasets containing real-valued time series and associated labels.
  • 8 CONCLUSION: The TSTR technique trains models on labelled synthetic data and evaluates them on a real held-out test set.The paper applies this evaluation to serialized multivariate MNIST and real ICU patients.
  • 8 CONCLUSION: Models trained on the synthetic dataset achieved performance at times comparable to models trained on real data for serialized MNIST and ICU patients.
  • 8 CONCLUSION: Synthetic medical data could support valuable real-task model development and benchmarking where privacy concerns hinder sharing of sensitive data.The authors frame this possibility as requiring refinement of the techniques.
  • 8 CONCLUSION: Differential privacy can strengthen RCGAN privacy guarantees, but with some loss to performance.
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